Method, device and equipment for determining molecular system energy and storage medium

Abstract

The embodiment of the invention relates to a method and device for determining molecular system energy, equipment and a storage medium. The method comprises: for each fragment in a molecular system, determining a plurality of orbits associated with the fragment, the plurality of orbits including a fragment orbit of the fragment, a first environmental orbit strongly coupled to the fragment, and a second environmental orbit weakly coupled to the fragment; based on the corresponding occupation states of the plurality of tracks, the plurality of tracks are respectively corresponding to the first track space or the second track space, and for the tracks corresponding to the same track space, the occupation state of the second environment track is different from the occupation state of the segment track and the occupation state of the first environment track; selecting a set of target orbits from the plurality of orbits to construct a fragment orbital space of the fragment using reference information related to electron excitation determined based on the first orbital space and the second orbital space; and determining an estimate of system energy of the molecular system based on the fragment orbital spaces of the plurality of fragments.

Description

Technical Field

[0001] The exemplary embodiments disclosed herein generally relate to the field of computer technology, and more specifically, to a method, apparatus, device, and storage medium for determining the energy of a molecular system. Background Technology

[0002] Quantum chemistry is a computational science based on quantum mechanics that studies the microscopic structure and reaction mechanisms of matter. It can predict and explain the properties of molecules or materials at the atomic and electronic levels. In recent years, artificial intelligence (AI) technology has been introduced into the field of quantum chemistry to assist in the analysis of the structural characteristics, energy changes, and reaction behavior of target systems (such as molecular or material systems), thereby improving computational efficiency and predictive capabilities.

[0003] However, there are complex systems involving strong correlations, such as complexes containing transition metals, reaction processes involving chemical bond rearrangements, or surface interactions in catalytic reactions. Traditional quantum chemical methods struggle to accurately describe these complex systems with strong correlations, leading to significant discrepancies between the estimated results and actual conditions. Summary of the Invention

[0004] In a first aspect of this disclosure, a method for determining the energy of a molecular system is provided. The method includes: for a segment among a plurality of segments of the molecular system, determining a plurality of orbitals associated with the segment, the plurality of orbitals including at least one segment orbital of the segment, at least one first environment orbital strongly coupled to the segment, and at least one second environment orbital weakly coupled to the segment; mapping the plurality of orbitals to a first orbital space or a second orbital space based on their respective occupancy states, wherein for the segment orbital, the first environment orbital, and the second environment orbital mapped to the same orbital space, the occupancy state of the second environment orbital differs from the occupancy states of the segment orbital and the first environment orbital; selecting a set of target orbitals from the plurality of orbitals to construct a segment orbital space of the segment using reference information related to electronic excitation determined based on the first orbital space and the second orbital space; and determining an estimate of the system energy of the molecular system based on the segment orbital spaces of each segment among the plurality of segments.

[0005] In a second aspect of this disclosure, an apparatus for determining the energy of a molecular system is provided. The apparatus includes: an orbital determination module configured to determine, for a segment among a plurality of segments of the molecular system, a plurality of orbits associated with the segment, the plurality of orbits including at least one segment orbital of the segment, at least one first environment orbital strongly coupled to the segment, and at least one second environment orbital weakly coupled to the segment; a spatial mapping module configured to map the plurality of orbits to a first orbital space or a second orbital space based on the corresponding occupancy states of the plurality of orbits, wherein for a segment orbital, a first environment orbital, and a second environment orbital mapped to the same orbital space, the occupancy state of the second environment orbital differs from the occupancy states of the segment orbital and the first environment orbital; a segment orbital space construction module configured to construct a segment orbital space of the segment by selecting a set of target orbitals from the plurality of orbitals using reference information related to electronic excitation determined based on the first orbital space and the second orbital space; and a system energy estimation module configured to determine an estimate of the system energy of the molecular system based on the segment orbital spaces of each segment among the plurality of segments.

[0006] In a third aspect of this disclosure, an electronic device is provided. The device includes at least one processor; and at least one memory coupled to the at least one processor and storing instructions for execution by the at least one processor. When executed by the at least one processor, the instructions cause the device to perform the method of the first aspect.

[0007] In a fourth aspect of this disclosure, a computer-readable storage medium is provided. The computer-readable storage medium stores computer-executable instructions that can be executed by a processor to implement the method of the first aspect.

[0008] In a fifth aspect of this disclosure, a computer program product is provided. The computer program product includes computer-executable instructions that, when executed by a processor, implement the method according to a first aspect of this disclosure.

[0009] It should be understood that the content described in this content section is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0010] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0011] Figure 1 A schematic diagram of an example environment in which embodiments of the present disclosure can be implemented is shown;

[0012] Figure 2 A flowchart illustrating an example process for determining the energy of a molecular system according to some embodiments of this disclosure is shown;

[0013] Figure 3A A schematic diagram of an example architecture for determining the energy of a molecular system according to some embodiments of the present disclosure is shown;

[0014] Figure 3B A schematic diagram of a matrix relating to occupancy difference is shown according to some embodiments of the present disclosure;

[0015] Figure 4 A schematic structural block diagram of an apparatus for determining the energy of a molecular system according to some embodiments of the present disclosure is shown; and

[0016] Figure 5 A block diagram of an electronic device in which one or more embodiments of the present disclosure may be implemented is shown. Detailed Implementation

[0017] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0018] It should be noted that the headings of any section / subsection provided herein are not limiting. Various embodiments are described throughout this document, and embodiments of any type may be included under any section / subsection. Furthermore, embodiments described in any section / subsection may be combined in any way with any other embodiments described in the same section / subsection and / or different sections / subsections.

[0019] In the description of embodiments of this disclosure, the term "comprising" and similar terms should be understood as open-ended inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The term "some embodiments" should be understood as "at least some embodiments". Other explicit and implicit definitions may also be included below. The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.

[0020] The embodiments of this disclosure may involve user data, data acquisition, and / or use. All of these aspects comply with applicable laws, regulations, and relevant provisions. In the embodiments of this disclosure, all data collection, acquisition, processing, manipulation, forwarding, and use are conducted with the user's knowledge and confirmation. Accordingly, in implementing the embodiments of this disclosure, the type, scope of use, and usage scenarios of any data or information that may be involved should be communicated to the user and their authorization obtained in accordance with relevant laws and regulations through appropriate means. The specific methods of notification and / or authorization may vary depending on the actual situation and application scenario, and the scope of this disclosure is not limited in this respect.

[0021] In this specification and the embodiments, any processing of personal information will be carried out only under the premise of legality (such as obtaining the consent of the personal information subject, or being necessary for the performance of a contract), and will only be carried out within the scope stipulated or agreed upon. A user's refusal to process personal information other than that necessary for basic functions will not affect the user's use of basic functions.

[0022] As briefly described above, traditional quantum chemical methods often fall short of the required accuracy for complex systems involving strong correlations. To address this challenge, fragment-based quantum embedding algorithms have emerged as a promising solution. Taking molecular systems as an example, quantum embedding algorithms divide the entire system into several smaller, more manageable fragments. Each fragment can be solved in detail using high-precision quantum chemical methods. Subsequently, embedding theory is used to consider the quantum coupling relationships between each fragment and its surrounding environment, thereby constructing a global description of the entire system. Within this framework, the final system properties (such as total energy) can be obtained by integrating the calculation results of each fragment. In this way, computational feasibility is maintained while effectively capturing strong correlation effects. Current quantum embedding algorithms can be implemented based on Density Matrix Embedding Theory (DMET), Dynamical Mean Field Theory (DMFT), Self-Energy Embedding Theory (SEET), and / or Frozen Density Embedding (FDE), among others.

[0023] However, traditional quantum embedding algorithms face significant challenges when dealing with metallic systems. For example, metallic systems lack a distinct band gap and possess highly delocalized electronic states and a clear Fermi surface structure. These characteristics contradict the fundamental assumptions upon which traditional quantum embedding algorithms rely (such as the existence of a band gap), leading to a decrease in accuracy when dealing with metallic systems. Currently, no quantum embedding algorithm can accurately describe both metallic and insulator systems within a unified framework. This limitation restricts the further application of quantum embedding algorithms in complex systems (such as those containing both metallic and insulator systems).

[0024] Embodiments of this disclosure provide a scheme for determining the energy of a molecular system. According to this scheme, firstly, for a segment among multiple segments of the molecular system, multiple orbitals associated with the segment are determined. These multiple orbitals include at least one segment orbital of the segment, at least one first environment orbital strongly coupled to the segment, and at least one second environment orbital weakly coupled to the segment. Then, based on the corresponding occupancy states of the multiple orbitals, they are respectively mapped to a first orbital space or a second orbital space. For the segment orbital, first environment orbital, and second environment orbital mapped to the same orbital space, the occupancy state of the second environment orbital differs from the occupancy states of the segment orbital and the first environment orbital. Next, using reference information related to electronic excitation determined based on the first and second orbital spaces, a set of target orbitals is selected from the multiple orbitals to construct the segment orbital space of the segment. Subsequently, based on the segment orbital spaces of each segment among the multiple segments, an estimate of the system energy of the molecular system is determined.

[0025] As will be more clearly understood from the following description, embodiments of this disclosure improve upon quantum embedding algorithms to enable unified handling of metallic and insulator systems. Specifically, in embodiments of this disclosure, multiple orbitals of a target fragment (e.g., fragment orbitals, a first environment orbital strongly coupled to the target fragment, and a second environment orbital weakly coupled to the target fragment) are divided into two distinct orbital spaces (e.g., a first orbital space and a second orbital space) based on the occupancy state of the orbitals. Furthermore, within the same orbital space, the occupancy state of the second environment orbital differs from that of the fragment orbital and the first environment orbital. This allows for the calculation of reference information (e.g., excitation amplitude) related to electronic excitation based on the interactions between occupied and unoccupied orbitals (also referred to herein as virtual orbitals) within the same orbital space. Based on this, embodiments of this disclosure construct the fragment orbital space of the target fragment using the reference information and, by integrating the fragment orbital spaces of each fragment, calculate the system energy of the molecular system.

[0026] The above process effectively avoids the spurious bandgap problem that may occur in traditional quantum embedding algorithms when dealing with bandgapless systems such as metals, thus achieving a unified description of various systems, including metals and insulators. In this way, the improved quantum embedding algorithm proposed in this disclosure is not only applicable to bandgap systems (such as insulators), but can also accurately describe bandgapless metallic systems, thereby significantly improving the applicability and computational accuracy of the quantum embedding algorithm.

[0027] The following will further describe in detail various example implementations of this scheme with reference to the accompanying drawings. Figure 1 A schematic diagram of an example environment 100 in which embodiments of the present disclosure can be implemented is shown. (Refer to...) Figure 1 Example environment 100 may include terminal device 110 and electronic device 120.

[0028] In example environment 100, user 130 can interact with electronic device 120 via terminal device 110 and / or its attached devices. In response to user 130's operation, electronic device 120 determines the system energy of the target system based on a quantum embedding algorithm. Taking a molecular system as an example, in a specific implementation, electronic device 120 divides the molecular system into multiple segments and constructs a segment orbital space for each segment. For each segment, the segment orbital space can include the segment orbital of the segment itself, the environmental orbital strongly coupled to the segment, and the environmental orbital weakly coupled to the segment. After constructing the segment orbital spaces of all segments, electronic device 120 calculates the system energy of the entire molecular system based on these segment orbital spaces using an appropriate method.

[0029] In example environment 100, terminal device 110 can be any type of mobile terminal, fixed terminal, or portable terminal, including mobile phones, desktop computers, laptop computers, notebook computers, netbook computers, tablet computers, media computers, multimedia tablets, personal communication system (PCS) devices, personal navigation devices, personal digital assistants (PDAs), audio / video players, digital cameras / camcorders, positioning devices, television receivers, radio receivers, e-book devices, gaming devices, or any combination thereof, including accessories and peripherals of these devices or any combination thereof. In some embodiments, terminal device 110 may also support any type of user-facing interface (such as "wearable" circuitry).

[0030] Electronic device 120 can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks, and big data and artificial intelligence platforms. Electronic device 120 may include, for example, computing systems / servers, such as mainframes, edge computing nodes, computing devices in cloud environments, etc.

[0031] A communication connection can be established between electronic device 120 and terminal device 110. This communication connection can be established via wired or wireless means. The communication connection may include, but is not limited to, Bluetooth connections, mobile network connections, Universal Serial Bus connections, and Wi-Fi connections; the embodiments of this disclosure are not limited in this respect. In the embodiments of this disclosure, electronic device 120 and terminal device 110 can achieve signaling interaction through their communication connection.

[0032] It should be understood that the above description of the structure and function of the various elements in environment 100 is for illustrative purposes only and does not imply any limitation on the scope of this disclosure. For example, in addition to a physical server, electronic device 120 can also be any type of mobile terminal, fixed terminal, or portable terminal, etc. In this case, user 130 can directly interact with electronic device 120 to perform analysis of the molecular system.

[0033] Figure 2 A flowchart of an example process 200 for determining the energy of a molecular system according to some embodiments of the present disclosure is shown. Figure 3A A schematic diagram of an example architecture 300A for determining the energy of a molecular system according to some embodiments of this disclosure is shown. The following is in conjunction with... Figure 1 and Figure 3A Process 200 will be described. Process 200 can be implemented at electronic device 120.

[0034] Reference Figure 2 In block 210, for each of the multiple segments of the molecular system, electronic device 120 determines multiple orbitals associated with that segment. The multiple orbitals include at least one segment orbital of the segment, at least one environmental orbital strongly coupled to the segment (e.g., a first environmental orbital), and at least one environmental orbital weakly coupled to the segment (e.g., a second environmental orbital).

[0035] A molecular system comprises at least a plurality of identical or different molecules. In some embodiments, the molecular system may be a complex system that simultaneously contains both metallic and insulating systems. Such a molecular system may consist of molecules with insulating properties and atoms or clusters with metallic properties. In quantum embedding algorithms, a fragment of a molecular system may refer to a local subsystem obtained by dividing the entire molecular system into finer-grained parts. For example, a fragment may consist of a group of molecules. Another example is that a fragment may consist of a functional region, a specific atomic cluster, or a local structure with significant electronic correlation effects within a target molecule. The method of fragment division can be determined according to actual needs, and the embodiments of this disclosure do not limit this. (Refer to...) Figure 3A In example architecture 300A, the molecular system is shown as comprising multiple segments 301-1, 301-2, and 301-M, where M is a positive integer. For ease of discussion, segments 301-1, 301-2, and 301-N will also be referred to individually or collectively as segment 301 below.

[0036] For each fragment 301, the fragment orbital of fragment 301 can refer to the orbital belonging to fragment 301 itself. The fragment orbital can include atomic orbitals and / or molecular orbitals within fragment 301, etc. The environmental orbital of fragment 301 can refer to the orbital belonging to other fragments 301 besides fragment 301. The first environmental orbital can refer to the orbital within the environmental orbital of fragment 301 that directly interacts with fragment 301. The first environmental orbital can also be called the bath orbital of fragment 301. The second environmental orbital can refer to the orbital within the environmental orbital of fragment 301 that interacts less or not at all with fragment 301.

[0037] In some embodiments, the second environmental orbitals may be selected based on preprocessing, which is beneficial for improving the accuracy of subsequent energy calculations. In some embodiments, the electronic device 120 may acquire multiple candidate environmental orbitals that are weakly coupled to fragment 301 in the molecular system. Subsequently, the electronic device 120 may select from the multiple candidate environmental orbitals a candidate environmental orbital that meets a predetermined degree of overlap with the reference region of the molecular system as one of at least one second environmental orbital.

[0038] Candidate environmental orbitals can refer to other environmental orbitals besides the first environmental orbital. In some embodiments, the electronic device 120 can decompose the orbital space of the entire molecular system based on DMET using a reduced density matrix (RDM) to obtain the corresponding fragment orbitals, the first environmental orbital, and candidate environmental orbitals.

[0039] In some embodiments, the electronic device 120 can decompose the orbital space of the entire molecular system based on a first-order reduced density matrix (1-RDM) or other methods. The decomposed orbital space can be represented by formula (1):

[0040]

[0041] Where C frag C represents the orbital coefficient of a segment orbit. bath This represents the orbital coefficient of the first environmental orbit (also known as the orbital coefficient of the Bath orbit). Represents the orbital coefficients of multiple candidate environmental orbits, where The orbit coefficient represents the orbital coefficient of the orbit occupied among multiple candidate environmental orbits. These are the orbital coefficients for unoccupied orbitals among multiple candidate environment orbitals. Occupied orbitals can be those filled with electrons, while unoccupied orbitals can be those not filled with electrons. Unoccupied orbitals can also be called virtual orbitals. The orbital space described above can also be referred to as a DMET cluster.

[0042] The reference region of a molecular system can refer to a local area of ​​interest within the entire space in which the molecular system exists. In some embodiments, the electronic device 120 can define the extent of a corresponding reference region for each of a plurality of segments 301. For example, the electronic device 120 can base its reference region on a domain completeness threshold T. BP Define the range of a corresponding reference region for each fragment 301. Such a reference region can also be called a BP domain (Boughton-Pulay domain). A BP domain can consist of a set of atoms (or N... BP Composed of atomic basis functions, the density of fragment 301 in this BP domain can reach 100×T. BP The range of the reference region can be determined by the domain completeness threshold T. BP Defined by the domain completeness threshold T. BP When the threshold value is →1, the reference region will approximate the entire molecular system (also known as the supercell). In some embodiments, the domain completeness threshold T... BP It can be 0.95 or other appropriate values. Domain completeness threshold T BP It can also be used as a parameter to adjust the size of the embedded Hamiltonian.

[0043] The degree of overlap can indicate the degree of coincidence or correlation between a candidate environmental orbit and a reference region. A higher degree of overlap with the reference region indicates a greater impact of the candidate environmental orbit on the energy calculation of the corresponding segment 301. A predetermined degree requirement can be determined based on actual needs. In some embodiments, if the degree of overlap between a candidate environmental orbit and the reference region exceeds a certain threshold, the electronic device 120 can determine that the candidate environmental orbit meets the predetermined degree requirement. In some embodiments, the degree of overlap between a candidate environmental orbit and the reference region can be determined by projecting the candidate environmental orbit onto the reference region. Specifically, the electronic device 120 can use a projection operator (e.g., a second projection operator) to project multiple candidate environmental orbits onto the reference region, thereby determining a first overlap feature representation (e.g., an overlap matrix). The first overlap feature representation can indicate the degree of overlap between the candidate environmental orbit and the reference region. In this way, the degree of coincidence or correlation between each candidate environmental orbit and the reference region can be measured quickly and accurately, thus helping to better screen for second environmental orbits.

[0044] In some embodiments, the second projection operator may employ any suitable projection operator capable of “projecting” orbital information onto a specific region (e.g., the BP domain). In some embodiments, the second projection operator may be determined based on local orbitals in the molecular system and a second overlap feature representation. The second overlap feature representation may indicate the degree of overlap between at least one orbital in the molecular system belonging to the reference region and other orbitals in the molecular system.

[0045] Local orbitals can refer to orbitals obtained by performing orbital transformations on orbitals (also known as original orbitals) in a molecular system using a predetermined orbital transformation algorithm. Compared to the original orbitals, the transformed orbitals can satisfy a specific distribution (e.g., concentrated in certain regions), thus making it easier to describe local electronic behavior. The second overlap feature representation can be represented by an overlap matrix or other suitable methods. For ease of discussion, the following description uses the representation of the second overlap feature by an overlap matrix as an example. In some embodiments, the electronic device 120 can determine the second projection operator based on the transformation coefficient matrix from orbital (i.e., original orbital, such as atomic orbital) to local orbital, the overlap matrix between orbitals in the reference region (e.g., the BP domain) and other orbitals in the molecular system, and the overlap matrix between orbitals in the reference region and each other. In some embodiments, the second projection operator P BP This can be expressed by formula (2):

[0046]

[0047] Where C ao,lo S represents the transformation coefficient matrix from atomic orbitals (ao) to local orbitals (lo). BP,aoThe S represents the overlap matrix between atomic orbitals belonging to the BP domain and all other atomic orbitals. BP This represents the overlap matrix between atomic orbitals within the BP domain. "-1" is the symbol for the conjugate transpose, and "-1" is the symbol for the inverse matrix.

[0048] In some embodiments, multiple candidate environmental orbits can be represented by orbital coefficients. For example, the orbital coefficients of multiple candidate environmental orbits can be represented as follows: The first overlap feature can be represented by an overlap matrix. In this case, the electronic device 120 can determine the candidate environmental orbit that meets the predetermined degree requirement in terms of overlap with the reference region based on the product of the orbit coefficients of multiple candidate environmental orbits and the diagonalized overlap matrix.

[0049] In some embodiments, the electronic device 120 can perform the above operations on the occupied and unoccupied tracks in the candidate environmental tracks respectively, to obtain the second environmental track in the occupied state and the second environmental track in the unoccupied state. Specifically, the electronic device 120 can divide the occupied tracks in the candidate environmental tracks based on whether the degree of overlap with the reference area meets a predetermined requirement. The division result can be expressed by formula (3):

[0050]

[0051] in express The orbit coefficient of the candidate environmental orbit that overlaps with the reference area to a predetermined degree, which is also the orbit coefficient of the second environmental orbit in the occupied state. express The orbit coefficient of candidate environmental orbits whose overlap with the reference area does not meet the predetermined requirements.

[0052] The specific partitioning process can be as follows. First, electronic device 120 can use the second projection operator P. BP ,Will The image is projected onto a reference region to obtain an overlap matrix. The electronic device 120 can then diagonalize this overlap matrix. In some embodiments, this process can be represented by equations (4) and (5):

[0053]

[0054] in Indicates will The overlap matrix obtained after projection onto the reference region. The diagonalized overlapping matrix σ represents a diagonal matrix, where the diagonal elements represent the degree of overlap between the orbitals in the reference region.occ express The corresponding eigenvector matrix.

[0055] Next, electronic device 120 can be based on Overlapping matrix after diagonalization The product of will Divided into and This process can be represented by formulas (6) and (7):

[0056]

[0057] Where thr is the overlap threshold, which is used to determine whether the overlap between a certain orbit and the reference area meets the predetermined requirements.

[0058] Similarly, the electronic device 120 can perform similar processing on unoccupied orbitals in the candidate environment orbitals. This process can be expressed by formulas (8) to (11):

[0059]

[0060] in Indicates will The overlap matrix obtained after projection onto the reference region. The diagonalized overlapping matrix U vir express The corresponding eigenvector matrix, express The orbit coefficient of the candidate environmental orbit that overlaps with the reference area to a predetermined degree, which is also the orbit coefficient of the second environmental orbit in the non-occupied state. express The orbit coefficient of candidate environmental orbits whose overlap with the reference area does not meet the predetermined requirements.

[0061] After the above processing, the embedding space of each segment 301 can be obtained. This embedding space can be represented by formula (12):

[0062]

[0063] The maximum size of this embedding space can be represented as: 2*N frag +2*N BP N frag This indicates the number of fragment tracks. The embedding space of each fragment 301 can also be referred to as an extended DMET cluster.

[0064] In some embodiments, a series of pre-operations may be performed before the above-described processing begins. These pre-operations include, but are not limited to, standard mean-field calculations (such as Hartree-Fock or DFT) and Random Phase Approximation (RPA) calculations, etc. Standard mean-field calculations provide the gauge orbits, Fock matrix, density matrix, and density fitting integrals required for each step of this disclosure. The gauge RPA calculations can be used for subsequent evaluation of the globally relevant energy and for applying local corrections from the fragment solver. Alternatively or additionally, in some embodiments, selective thermal fuzzing techniques may be applied during wavefunction optimization (particularly in metallic systems) to improve Self-Consistent Field (SCF) convergence, etc. This can be specifically determined according to actual needs, and embodiments of this disclosure are not listed here.

[0065] After obtaining multiple orbitals for each segment 301 in the molecular system, in block 220, for each segment 301, the electronic device 120 maps the multiple orbitals to a first orbital space or a second orbital space based on the corresponding occupancy states of the multiple orbitals of that segment 301 (e.g., the occupancy states of each orbital individually). For orbitals mapped to the same orbital space (e.g., segment orbitals, first environment orbitals, and second environment orbitals), the occupancy state of the second environment orbital differs from the occupancy states of the segment orbitals and the first environment orbitals.

[0066] Occupancy states can include states where the orbital is completely occupied by electrons (e.g., an orbital occupied by two electrons with opposite spins), states where the orbital is not occupied by electrons, and states where the orbital is partially occupied by electrons (e.g., an orbital occupied by an electron with spin up or spin down). In some embodiments, the electronic device 120 can use the above-mentioned occupancy states as a basis to map multiple orbitals to a first orbital space or a second orbital space. Specifically, the electronic device 120 can extract orbitals in a non-occupied state from at least one fragment orbital and at least one first environment orbital to obtain at least one first virtual orbital. The electronic device 120 can extract orbitals in an occupied state (e.g., a state where the orbital is completely occupied by electrons) from at least one fragment orbital and at least one first environment orbital to obtain at least one first occupied orbital. Next, the electronic device 120 can map at least one second occupied orbital in an occupied state from at least one first virtual orbital and at least one second environment orbital to the first orbital space. Furthermore, the electronic device 120 can map at least one first occupied orbital and at least one second virtual orbital in a non-occupied state from at least one second environment orbital to the second orbital space.

[0067] Unoccupied orbitals can refer to orbitals that are not occupied by electrons, while occupied orbitals can refer to orbitals that are fully occupied by electrons. In this way, the multiple orbitals of segment 301 can be clearly divided into fully occupied and unoccupied portions. This allows for a more efficient construction of the reference space for excited states in subsequent steps, especially in calculating reference information related to electronic excitation. Consequently, the excitation process can be restricted to physically meaningful orbitals, thus avoiding numerical difficulties caused by the band gap approaching zero (e.g., metallic systems lack a significant band gap).

[0068] In some embodiments, at least one first virtual orbit and at least one first occupied orbit can both be represented by embedded orbital features, and at least one second occupied orbit and at least one second virtual orbit can both be represented by orbital coefficient features. This allows for effective modeling of the orbital space, thereby improving the accuracy and efficiency of electronic structure calculations. In some embodiments, the first virtual orbit and the first occupied orbit can be represented by formula (13):

[0069]

[0070] in The first occupied orbit is based on the embedded orbital features of DMET. The first virtual orbit is based on the embedded orbit features of DMET. In this case, the embedding space of each segment 301 can be represented by formula (14):

[0071]

[0072] In some embodiments, the electronic device 120 can project the RDM associated with the molecular system into the DMET space and diagonalize it to obtain the corresponding natural orbitals (the basis set with the most natural electron distribution) and their occupancy numbers (the number of electrons in each orbital). The natural orbitals and occupancy numbers can be used to partition first occupied orbitals (e.g., occupancy number 2) and first dummy orbitals (e.g., occupancy number 0). In some embodiments, for metallic systems, due to electron smearing, the occupancy numbers of orbitals may not be integers (e.g., 1.99 or 0.01). In this case, the principle of minimum energy (e.g., Aufbau) can be used to partition the corresponding occupancy numbers to 0 or 2.

[0073] In some embodiments, the first orbital space and the second orbital space can be represented by formula (15):

[0074]

[0075] in Represents the first orbital space. This represents the second orbital space.

[0076] For each segment 301 of the molecular system, after mapping multiple orbitals of segment 301 to a first orbital space and a second orbital space, in block 230, electronic device 120 uses reference information related to electronic excitation determined based on the first and second orbital spaces of segment 301 to select a set of target orbitals from the multiple orbitals of segment 301 to construct the segment orbital space of segment 301. (Refer to...) Figure 3A Electronic device 120 constructs segment orbit space 302-1 for segment 301, segment orbit space 302-2 for segment 302, ..., and segment orbit space 302-M for segment 301. For ease of discussion, segment orbit spaces 302-1, 302-2 and 302-M will be referred to individually or collectively as segment orbit space 302 below.

[0077] Reference information related to electronic excitation can be indicated in a specific orbital space (e.g., a first orbital space or a second orbital space) through calculations of electronic excitation (e.g., calculations using second-order perturbation theory). The Perturbation Theory of Second Order (MP2) is a physical quantity that reflects the excitation probability between orbits. For example, a set of target orbits can refer to orbits with significant excitation intensity during electronic excitation calculations. In some embodiments, for each segment 301, the electronic device 120 can use the individual segment orbits of segment 301 and the first environment orbits as part of a set of target orbits. Then, the electronic device 120 can filter at least one second environment orbit based on the aforementioned reference information and use the filtering result as another part of the set of target orbits. Subsequently, the electronic device 120 constructs the segment orbit space 302 of segment 301 from the set of target orbits. Specifically, the segment orbit space 302 of segment 301 can be constructed from at least one segment orbit, at least one first environment orbit, at least one first reference orbit, and at least one second reference orbit. The at least one first reference orbit can be selected from at least one second occupied orbit based on the reference information. The at least one second reference orbit can be selected from at least one second virtual orbit based on the reference information. In this way, the electronic device 120 can filter out more effective second environment orbits (i.e., the first reference orbit and the second reference orbit) to participate in subsequent calculations.

[0078] In some embodiments, the reference information may include a first electron excitation amplitude determined based on a first orbital space and a second electron excitation amplitude determined based on a second orbital space. At least one first reference orbit and at least one second reference orbit may be selected based on these two electron excitation amplitudes. Specifically, the electronic device 120 may determine an estimate of a first occupancy number for each of the at least one second occupied orbits based on the first electron excitation amplitude. Then, the electronic device 120 may select from the at least one second occupied orbits a second occupied orbit whose estimated first occupancy number is greater than a first predetermined occupancy number as one of the at least one first reference orbits. Furthermore, the electronic device 120 may determine an estimate of a second occupancy number for each of the at least one second virtual orbits based on the second electron excitation amplitude. Then, the electronic device 120 may select from the at least one second virtual orbits a second virtual orbit whose estimated second occupancy number is less than a second predetermined occupancy number as one of the at least one second reference orbits.

[0079] In some embodiments, the electronic device 120 can determine the first electron excitation amplitude by performing an electron excitation calculation (e.g., an MP2 calculation) on the first orbital space. Similarly, the electronic device 120 can determine the second electron excitation amplitude by performing an electron excitation calculation (e.g., an MP2 calculation) on the second orbital space. For ease of discussion, the following description uses an MP2 calculation as an example for electron excitation calculation.

[0080] Before performing MP2 calculations, multiple tracks of fragment 301 (especially...) had already been... and The orbitals are divided into different orbital spaces (e.g., the first orbital space and the second orbital space). Therefore, MP2 calculations are not affected by the "lack of bandgap problem" in metallic systems (where the energies of occupied and unoccupied orbitals are very close, almost degenerate). In this case, the electronic device 120 can target the first orbital space (e.g., the first orbital space). Perform MP2 calculations to obtain an approximate MP2 amplitude. This process can be represented by formula (16):

[0081]

[0082] Where ∈ i and ∈ j express The energy of the middle orbit, ∈ a and ∈ b express The energies of the orbits are denoted by i and j, which represent the indices of the occupied orbits, and a and b, which represent the indices of the virtual orbits. These orbital energies can be obtained by diagonalizing (e.g., quasi-canonicalization) the Fock matrix within the first orbital subspace.

[0083] In some embodiments, the electronic device 120 may be based on amplitude. Using algorithms such as the Brueckner Natural Orbital (BNO), specific sub-blocks (e.g., [occ|occ] blocks) of the RDM (e.g., 1-RDM) are calculated. In this way, estimates of the corresponding natural orbits and their occupancy numbers (e.g., the first occupancy number) in the first orbital subspace can be obtained. Based on this, the electronic device 120 can, based on the first predetermined occupancy number (also referred to as the occupancy bath expansion threshold), […]. Divide into two groups. The division result can be expressed by formula (17):

[0084]

[0085] in yes The orbital coefficient of the orbit whose estimated first occupied number is greater than the first predetermined occupied number. yes The orbit coefficient of the orbit in which the estimated first occupancy number is less than the first predetermined occupancy number.

[0086] Similarly, for the second orbital space (e.g.) For specific sub-blocks of the RDM (e.g., [vir|vir]), the electronic device 120 can also be partitioned using the same process. The partitioning result can be expressed by formula (18):

[0087]

[0088] in yes The orbital coefficient of the orbit with the estimated second occupancy number being less than the second predetermined occupancy number. yes The orbit coefficient of the orbit in which the estimated second occupancy number is greater than the second predetermined occupancy number.

[0089] After the above processing, the final embedding space of fragment 301 (i.e., fragment orbital space 302) can be represented by formula (19):

[0090]

[0091] The domain completeness threshold T mentioned in the previous text BPAt →1, the above process approaches the BNO limit at a certain bath threshold. The BNO limit refers to the ideal state of the orbital space, in which the orbital space contains only the natural orbitals most relevant to the excitation process or electronic correlation. For orbital screening, besides T... BP Other thresholds can be uniformly set to small values ​​(e.g., 1×10). -9 (or other values). In this way, the user only needs to adjust T. BP This allows for the expansion or contraction of the embedded space, thereby enabling good control over available computing resources.

[0092] After constructing the segment orbital space 302 for each segment 301, in block 240, the electronic device 120 determines an estimate 303 of the system energy of the molecular system based on the segment orbital spaces 302 of each segment 301. In some embodiments, the electronic device 120 may construct an embedded Hamiltonian based on the segment orbital spaces 302 of each segment 301, thereby describing the electronic behavior in the segment orbital spaces 302. (Refer to...) Figure 3A The electronic device 120 can construct an embedded Hamiltonian 304-1 based on the fragment orbital space 302-1, an embedded Hamiltonian 304-2 based on the fragment orbital space 302-2, and an embedded Hamiltonian 304-M based on the fragment orbital space 302-M. For ease of discussion, the embedded Hamiltonians 304-1, 304-2, and 304-M will be referred to individually or collectively as the embedded Hamiltonian 304. The electronic device 120 can then determine an estimate 303 of the system energy of the molecular system by solving for the embedded Hamiltonian 304 (e.g., using the linear response algorithm and / or quantum many-body algorithm mentioned below). In some embodiments, the embedded Hamiltonian 304 can be constructed using the fragment orbital space 302 and density fitting integrals. In some embodiments, the electronic device 120 can utilize a first acceleration module 305 to assist in the construction of the embedded Hamiltonian 304, thereby supporting efficient large-scale simulations. In some embodiments, the first acceleration module may be implemented based on Message Passing Interface (MPI) parallel and / or Graphics Processing Unit (GPU) acceleration technologies.

[0093] In some embodiments, the electronic device 120 may utilize a linear response algorithm to determine an estimate 303 of the system energy of the molecular system. Alternatively, in some embodiments, the electronic device 120 may utilize a quantum many-body algorithm to determine an estimate 303 of the system energy of the molecular system. Alternatively, in some embodiments, the electronic device 120 may utilize both a linear response algorithm and a quantum many-body algorithm to determine an estimate 303 of the system energy of the molecular system. Specifically, for segment 301 among a plurality of segments 301, the electronic device 120 may use a linear response algorithm to determine an estimate (e.g., a first estimate) of the segment energy of segment 301 based on the segment orbital space 302 of segment 301. (Refer to...) Figure 3A The electronic device 120 can determine a first estimate 306-1 of the fragment energy of fragment 301-1, a first estimate 306-2 of the fragment energy of fragment 301-2, and a first estimate 306-M of the fragment energy of fragment 301-M. The electronic device 120 can determine an estimate (e.g., a second estimate) of the fragment energy of fragment 301 based on the fragment orbital space 302 of fragment 301 using a quantum many-body algorithm. The electronic device can determine a second estimate 307-1 of the fragment energy of fragment 301-1, a second estimate 307-2 of the fragment energy of fragment 301-2, and a second estimate 307-M of the fragment energy of fragment 301-M. Furthermore, the electronic device 120 can determine an estimate 303 of the system energy of the molecular system based on the first estimate 306-1 and the second estimate 306-2 determined for each of the multiple fragments 301. For ease of discussion, the first estimate 306-1, the first estimate 306-2, and the first estimate 306-M will be referred to individually or collectively as the first estimate 306, and the second estimate 307-1, the second estimate 307-2, and the second estimate 307-M will be referred to individually or collectively as the second estimate 307.

[0094] Linear response algorithms can refer to algorithms based on perturbation theory in quantum chemistry. They are used to handle the response behavior of a system to small perturbations. Examples of linear response algorithms include the stochastic phase approximation (RPA) algorithm and time-dependent density functional theory algorithms. Quantum many-body algorithms can refer to high-precision methods in quantum chemistry used to solve strongly correlated problems in multi-electron systems. Quantum many-body algorithms can include Auxiliary Field Quantum Monte Carlo (AFQMC) algorithms or density matrix renormalization group algorithms. Quantum many-body algorithms can handle complex cases such as strongly correlated, fractionally occupied, and gapless systems. By dividing the molecular system into multiple segments 301 and using linear response methods (such as RPA) and quantum many-body methods (such as AFQMC) to estimate the energy of each segment 301, the electronic device 120 can achieve high-precision system energy prediction while maintaining computational efficiency, thereby achieving efficient and accurate modeling of complex molecular systems.

[0095] In some embodiments, the linear response algorithm may include a stochastic phase approximation algorithm. The electronic excitation amplitude involved in the stochastic phase approximation algorithm may be determined at least based on a projection operator (e.g., a first projection operator). The first projection operator may indicate, during the determination of the electronic excitation amplitude, the influence of the partially occupied orbit based on the relationship between the partially occupied orbit and segment 301. Alternatively or additionally, in some embodiments, the quantum many-body method may include an auxiliary field quantum Monte Carlo algorithm. The Green's function involved in the auxiliary field quantum Monte Carlo algorithm may be determined at least based on a first projection operator. The first projection operator may indicate, during the determination of the Green's function, the influence of the partially occupied orbit based on the relationship between the partially occupied orbit and segment 301.

[0096] In the stochastic phase approximation algorithm, the electron excitation amplitude indicates the intensity of the electron's excitation from the occupied orbit to the virtual orbit. The first projection operator can introduce the influence of partially occupied orbits in the determination of the electron excitation amplitude, thus considering the effect of orbits with a fractional number of occupants when dealing with systems such as metals. In the auxiliary field quantum Monte Carlo algorithm, the Green's function indicates the propagation of the electron between the occupied and virtual orbits. The first projection operator can introduce the influence of partially occupied orbits in the determination of the Green's function, thus considering the effect of orbits with a fractional number of occupants when dealing with systems such as metals.

[0097] In some embodiments, the first projection operator may be indicated to determine the effect of the partially occupied orbit during the determination of the electronic excitation amplitude if the partially occupied orbit is one of multiple orbits of segment 301. Alternatively or additionally, the first projection operator may be indicated to determine the effect of the partially occupied orbit during the determination of the Green's function if the partially occupied orbit is one of multiple orbits of segment 301.

[0098] The following section explains the determination process of the first estimate 306 using formulas, and introduces how the first projection operator introduces the influence of the partially occupied track. First, electronic device 120 can determine the correlation energy of the direct random phase approximation (dRPA) within the framework of the Adiabatic Connection Fluctuation Dissipation Theorem (ACFDT). dRPA related energy This can be expressed by formula (20):

[0099]

[0100] Where χ0(iω) represents the non-interacting density-density response function (e.g., the Lindhard function), Represents the Coulomb interaction nucleus, and Tr represents the relationship between spatial coordinates r and r v The trace. In some embodiments, the electronic device 120 may utilize the electron repulsion integral under the density fitting approximation. In this case, dRPA related energy It can be expressed by formula (21):

[0101]

[0102] Where ∏(ω) is the dielectric matrix. In numerical calculations, using the determinant form (ln det) is more stable and efficient than directly calculating the matrix logarithm (ln). This is because the matrix logarithm tends to diverge when approaching singularity, while the determinant form guarantees that 1-Π(ω) is a real number when it is positive semi-definite. In this case, formula (22) holds:

[0103] Tr[ln(1-∏(ω))+∏(ω)]=Tr[ln(1-Π)(ω)]+Tr[Π(ω)]=ln[det(1-Π(ω))]+Tr[Π(ω)]. (twenty two)

[0104] For a restricted mean-field, under a space orbital basis, the dielectric matrix Π can be expressed by formula (23):

[0105]

[0106] Where χ 0,ia (ω) is the density response kernel, which can be represented by formula (24):

[0107]

[0108] If a molecular system contains orbitals with a fractional occupancy (e.g., in metallic systems, such orbitals can also be called partially occupied or fractionally occupied orbitals), then a broadening function needs to be introduced to handle these partially occupied orbitals. In this case, the response kernel will be modified, which can be expressed by equation (25):

[0109]

[0110] Where f ia =f i -f a f i and f a f represents the number of orbitals occupied. ia This represents the occupancy difference. It's important to note that the indices i and a here are summed across all orbitals, not just occupied and virtual orbitals. This includes intraband transitions. ia It is sparse.

[0111] Figure 3B The occupancy difference f is shown according to some embodiments of the present disclosure. ia A schematic diagram of the relevant matrix 300B. (Refer to...) Figure 3B In matrix 300B, o, f, and v represent occupied, fractional, and virtual tracks, respectively. In matrix 300B, f represents the fully occupied-occupied (oo) block 310-1 and the fully virtual-virtual (vv) block 310-2. ia It is 0. And f ia It is antisymmetric, that is, f ia =-f ai These properties are utilized in practical implementations to improve computational efficiency and numerical stability.

[0112] In some embodiments, the first estimate This can be expressed by formula (26):

[0113]

[0114] in This indicates the electronic excitation amplitude (e.g., double excitation amplitude) involved in RPA, derived from ACFDT-RPA. This represents the form of the electron repulsion integral (ERI) in the segment orbital space 302. It can be expressed by formula (27):

[0115]

[0116] in Represents the projection operator. This represents the global electronic excitation amplitude (e.g., a dual excitation amplitude). In some embodiments, the first projection operator may be based on the coefficient matrix C in the embedded basis set. xi To construct it. This process can be represented by formula (28):

[0117]

[0118] To handle partially occupied orbits (coexisting with fully occupied or unoccupied orbits), one can... Perform block diagonalization to obtain the first diagonalized projection operator P. F It can be expressed by formula (29):

[0119]

[0120] in Suitable for fully occupying the orbit. This is the first projection operator, applicable to partially occupied orbits. Therefore, it can be used to generate electronically excited amplitudes. In the process of determining, through the first projection operator Introducing the effects of partially occupied orbits.

[0121] The determination process of the second estimate 307 will be explained below in conjunction with the formula, and in this process, we will introduce how the first projection operator introduces the influence of the partially occupied track. In some embodiments, the AFQMC correlation energy can be expressed by formula (30):

[0122] E corr =∑ i,j,a,b G ia G jb [2(ia|jb) - (ib|ja)); (30)

[0123] Among them G iaThe Green's function is the mean-field single-unit Green's function, which is strictly zero if the system has an energy gap. To introduce a broadening effect, a broadened Green's function can be introduced. The broadened Green's function can be expressed by formula (31):

[0124]

[0125] in Let represent the diagonal occupancy matrix used for broadening trials. For gapless systems, index i includes fully occupied and partially occupied orbitals, and index a includes partially occupied and unoccupied orbitals. Therefore, an extra term is introduced due to the "double counting" of partially occupied orbitals. This extra term can be expressed by formula (32):

[0126]

[0127] In a system with a band gap, G ia =0, and However, in a gapless system, this term is not zero and must therefore be subtracted from the correlation energy expression. In this case, the final correlation energy of AFQMC (i.e., the second estimate) This can be expressed by formula (33):

[0128]

[0129] Based on this, the Green function The first projection operator mentioned above can be used. To determine. In some embodiments, the Green's function can be expressed by formula (34):

[0130]

[0131] Therefore, in the Green function In the process of determining, through the first projection operator Introducing the effect of partially occupied orbits.

[0132] In some embodiments, the electronic device 120 may be based on a first estimate. Second estimate Determine the segment energy compensation for each segment 301 in the multiple segments 301. (Refer to...) Figure 3AIn example architecture 300A, electronic device 120 can determine the fragment energy compensation 308-1 for fragment 301-1, the fragment energy compensation 308-2 for fragment 301-2, and the fragment energy compensation 308-M for fragment 301-M. For ease of discussion, fragment energy compensation 308-1, fragment energy compensation 308-2, and fragment energy compensation 308-M will be referred to individually or collectively as fragment energy compensation 308 below. Electronic device 120 can then determine an estimate 303 of the system energy of the molecular system based on the fragment energy compensation 308 for each fragment 301. Specifically, for fragment 301 among multiple fragments 301, electronic device 120 can determine the fragment energy compensation 308 of fragment 301 based on the difference between a first estimate 306-1 and a second estimate 306-2. Electronic device 120 can then adjust the reference system energy of the molecular system based on the fragment energy compensation 308 determined for each of the multiple fragments 301 to determine the estimate 303 of the system energy of the molecular system. In some embodiments, this process can be represented by formula (35):

[0133]

[0134] Where E represents the system energy of the molecular system. This indicates that the fragment energy compensation of fragment 301 is 308, E. RPA This represents the reference system energy determined based on RPA (also known as the global RPA energy). In this way, the electronic device 120 can determine the system energy of the molecular system by solving the embedded Hamiltonian 304 using both RPA and AFQMC algorithms. The difference between the RPA and AFQMC results defines a systematically controlled local correction, which, after being added to the global RPA energy, yields an estimate 303 of the system energy of the molecular system.

[0135] In some embodiments, to ensure scalability and high performance across large and complex systems, the electronic device 120 can introduce MPI parallelism and / or GPU acceleration at any stage of the above process to achieve more efficient processing. For example, the electronic device 120 can accelerate the calculation process of the first estimate 306 by means of a second acceleration module 309-1, which can be implemented based on MPI parallelism and / or GPU acceleration. As another example, the electronic device 120 can accelerate the calculation process of the second estimate 307 by means of a third acceleration module 309-2, which can be implemented based on MPI parallelism and / or GPU acceleration. Furthermore, the electronic device 120 can optimize for memory-intensive tensor operations occurring throughout the workflow. Specifically, the electronic device 120 can use GPU acceleration libraries and custom kernel-level optimizations to effectively handle key tensor shrinkage involved in computationally relevant energy contributions, reducing memory bottlenecks and improving throughput. The electronic device 120 can also combine a hybrid MPI+GPU strategy with distributed computation on k-point and Monte Carlo traversers to achieve efficient scaling across computing nodes for large-scale simulations of periodic and strongly correlated systems.

[0136] As can be clearly understood from the various embodiments described above, the embodiments of this disclosure construct a unified and systematically scalable quantum many-body computation framework. The embodiments of this disclosure can naturally incorporate partially occupied orbitals into multi-level computations from mean field to post-mean field (RPA and AFQMC), thus making them applicable to insulator and metallic systems. Through the fragment 301 embedding method, the embodiments of this disclosure can systematically converge energy results to those of conventional methods as the fragment 301 size increases. High accuracy is maintained even when there are a large number of partially occupied orbitals in the mean field. Furthermore, the embodiments of this disclosure utilize RPA at the global level to capture long-range nonlocal electronic correlations (especially applicable to metals), while accurately describing strong local correlation effects in the local embedding space through AFQMC. This achieves a unified description of local and nonlocal electronic correlations. In addition, to improve computational efficiency, for large material systems, GPU-accelerated algorithms can be introduced in multiple stages such as embedding construction, bath orbital expansion, RPA, and AFQMC solving, significantly enhancing the scalability and practicality of the method.

[0137] Embodiments of this disclosure provide a unified and systematically scalable fragment 301-based quantum embedding framework capable of simulating metal-insulator systems with high precision. These embodiments aim to overcome key limitations of existing embedding methods, particularly conventional methods that often rely on heuristic approximations or uncontrolled broadening techniques when dealing with gapless systems (such as metals). The embodiments of this disclosure are particularly suitable for applications such as surface chemistry, heterogeneous catalysis, data generation, and predictive modeling for AI-driven chemical discovery, where both local and extended electronic correlation effects must be accurately captured simultaneously. Compared to conventional methods, the embodiments of this disclosure can handle metals and insulators in a unified form without introducing heuristic assumptions or prior bandgap settings. The embodiments of this disclosure are architecture-agnostic, memory-efficient, and particularly suitable for periodic and transition-rich metal systems. Furthermore, by integrating AFQMC as a high-precision solver after embedding, the embodiments of this disclosure provide a systematically controllable and tunable path for predicting strongly correlated processes such as bond breaking or catalytic reactions on metal surfaces, thereby achieving accurate modeling of complex multi-electron behavior.

[0138] Embodiments of this disclosure also provide corresponding apparatus for implementing the above methods or processes. Figure 4 A schematic structural block diagram of an apparatus 400 for determining the energy of a molecular system according to some embodiments of the present disclosure is shown. Apparatus 400 may be implemented as or included in electronic device 120. Various modules / components in apparatus 400 may be implemented by hardware, software, firmware, or any combination thereof.

[0139] Reference Figure 4The device 400 includes an orbit determination module 410, a spatial mapping module 420, a fragment orbital space construction module 430, and a system energy estimation module 440. The orbit determination module 410 is configured to determine multiple orbits associated with a fragment among multiple fragments of the molecular system. These multiple orbits include at least one fragment orbital of the fragment, at least one first environment orbital strongly coupled to the fragment, and at least one second environment orbital weakly coupled to the fragment. The spatial mapping module 420 is configured to map the multiple orbits to a first orbital space or a second orbital space based on their respective occupancy states. For fragment orbitals, first environment orbitals, and second environment orbitals mapped to the same orbital space, the occupancy state of the second environment orbital differs from that of the fragment orbital and the first environment orbital. The fragment orbital space construction module 430 is configured to select a set of target orbitals from the multiple orbitals to construct the fragment orbital space of the fragment using reference information related to electronic excitation determined based on the first and second orbital spaces. The system energy estimation module 440 is configured to determine an estimate of the system energy of the molecular system based on the fragment orbital spaces of each fragment among the multiple fragments.

[0140] In some embodiments, the space mapping module 420 is further configured to: extract a track in an unoccupied state from at least one segment track and at least one first environment track to obtain at least one first virtual track; extract a track in an occupied state from at least one segment track and at least one first environment track to obtain at least one first occupied track; map at least one second occupied track in an occupied state from at least one first virtual track and at least one second environment track to a first track space; and map at least one second virtual track in an unoccupied state from at least one first occupied track and at least one second environment track to a second track space.

[0141] In some embodiments, at least one first virtual track and at least one first occupied track are both represented by embedded track features, and at least one second occupied track and at least one second virtual track are both represented by track coefficient features.

[0142] In some embodiments, the fragment orbit space of a fragment is constructed from at least one fragment orbit, at least one first environment orbit, at least one first reference orbit, and at least one second reference orbit; and wherein at least one first reference orbit is selected from at least one second occupied orbit based on reference information, and at least one second reference orbit is selected from at least one second virtual orbit based on reference information.

[0143] In some embodiments, the reference information includes a first electron excitation amplitude determined based on a first orbital space and a second electron excitation amplitude determined based on a second orbital space, and at least one first reference orbital and at least one second reference orbital are selected by: determining an estimate of a first occupancy number for each of the at least one second occupancy orbitals based on the first electron excitation amplitude; selecting, from the at least one second occupancy orbitals, a second occupancy orbital whose estimated first occupancy number is greater than a first predetermined occupancy number as one of the at least one first reference orbitals; determining an estimate of a second occupancy number for each of the at least one second virtual orbitals based on the second electron excitation amplitude; and selecting, from the at least one second virtual orbitals, a second virtual orbital whose estimated second occupancy number is less than a second predetermined occupancy number as one of the at least one second reference orbitals.

[0144] In some embodiments, the system energy estimation module 440 is further configured to: for a segment among a plurality of segments, determine a first estimate of the segment energy of the segment based on the segment orbital space of the segment using a linear response algorithm; determine a second estimate of the segment energy of the segment based on the segment orbital space of the segment using a quantum many-body algorithm; and determine an estimate of the system energy of the molecular system based on the first estimate and the second estimate determined for the plurality of segments respectively.

[0145] In some embodiments, the system energy estimation module 440 is further configured to: determine a segment energy compensation for a segment among a plurality of segments based on the difference between a first estimate and a second estimate; and determine an estimate of the system energy of the molecular system by adjusting the reference system energy of the molecular system based on the segment energy compensation determined for each of the plurality of segments.

[0146] In some embodiments, the linear response algorithm includes a stochastic phase approximation algorithm, wherein the electronic excitation amplitude involved in the stochastic phase approximation algorithm is determined at least based on a first projection operator, which indicates that the influence of the partially occupied orbit is determined based on the relationship between the partially occupied orbit and the segment during the determination of the electronic excitation amplitude; and / or the quantum many-body method includes an auxiliary field quantum Monte Carlo algorithm, wherein the Green's function involved in the auxiliary field quantum Monte Carlo algorithm is determined at least based on a first projection operator, which further indicates that the influence of the partially occupied orbit is determined based on the relationship between the partially occupied orbit and the segment during the determination of the Green's function.

[0147] In some embodiments, the first projection operator further instructs at least one of the following: for a partially occupied orbit, if the partially occupied orbit is one of multiple orbits in a segment, to determine the influence of the partially occupied orbit during the determination of the electronic excitation amplitude, or if the partially occupied orbit is one of multiple orbits in a segment, to determine the influence of the partially occupied orbit during the determination of the Green's function.

[0148] In some embodiments, at least one second environmental orbital is determined by: acquiring a plurality of candidate environmental orbitals that are weakly coupled to the fragment in the molecular system; and selecting, from the plurality of candidate environmental orbitals, a candidate environmental orbital that meets a predetermined degree requirement in terms of overlap with a reference region of the molecular system as one of at least one second environmental orbital.

[0149] In some embodiments, the degree of overlap between the candidate environmental orbits and the reference region among the plurality of candidate environmental orbits is determined by projecting the plurality of candidate environmental orbits onto the reference region using a second projection operator to determine a first overlap feature representation, the first overlap feature representation indicating the degree of overlap between the candidate environmental orbits and the reference region among the plurality of candidate environmental orbits.

[0150] In some embodiments, the second projection operator is determined based on: local orbitals in the molecular system, and a second overlap feature representation indicating the degree of overlap between at least one orbital in the molecular system belonging to the reference region and other orbitals in the molecular system.

[0151] In some embodiments, multiple candidate environmental orbits are represented by orbit coefficients, and the first overlap feature is represented by an overlap matrix. The orbit determination module 410 is further configured to: determine, based on the product of the orbit coefficients and the diagonalized overlap matrix, the candidate environmental orbits among the multiple candidate environmental orbits that meet a predetermined degree requirement in terms of overlap with the reference region.

[0152] Figure 5 A block diagram is shown of an electronic device 500 in which one or more embodiments of the present disclosure may be implemented. The electronic device 500 may, for example, be used to implement... Figure 1 The electronic device 120 shown or such Figure 4 The device 400 shown. It should be understood that, Figure 5 The electronic device 500 shown is merely exemplary and should not be construed as limiting the functionality and scope of the embodiments described herein.

[0153] Reference Figure 5Electronic device 500 is in the form of a general-purpose electronic device. Components of electronic device 500 may include, but are not limited to, one or more processors 510, memory 520, storage device 530, one or more communication units 540, one or more input devices 550, and one or more output devices 560. Processor 510 may be a physical or virtual processor and is capable of performing various processes according to programs stored in memory 520. In a multiprocessor system, multiple processors execute computer-executable instructions in parallel to improve the parallel processing capability of electronic device 500.

[0154] Electronic device 500 typically includes multiple computer storage media. Such media can be any available media accessible to electronic device 500, including but not limited to volatile and non-volatile media, removable and non-removable media. Memory 520 can be volatile memory (e.g., registers, cache, random access memory (RAM)), non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. Storage device 530 can be removable or non-removable media and can include machine-readable media, such as flash drives, disks, or any other media capable of storing information and / or data and accessible within electronic device 500.

[0155] Electronic device 500 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not explicitly stated... Figure 5 As shown, disk drives for reading from or writing to removable, non-volatile disks (e.g., "floppy disks") and optical disk drives for reading from or writing to removable, non-volatile optical disks can be provided. In these cases, each drive can be connected to a bus (not shown) via one or more data media interfaces. Memory 520 may include computer program product 525 having one or more program modules configured to perform various methods or actions of various embodiments of this disclosure.

[0156] Communication unit 540 enables communication with other electronic devices via a communication medium. Additionally, the functionality of components of electronic device 500 can be implemented using a single computing cluster or multiple computing machines capable of communicating via communication connections. Therefore, electronic device 500 can operate in a networked environment using logical connections to one or more other servers, network personal computers (PCs), or another network node.

[0157] Input device 550 can be one or more input devices, such as a mouse, keyboard, trackball, etc. Output device 560 can be one or more output devices, such as a monitor, speaker, printer, etc. Electronic device 500 can also communicate with one or more external devices (not shown) via communication unit 540 as needed. These external devices include storage devices, display devices, etc., and can communicate with one or more devices that enable user interaction with electronic device 500, or with any device that enables electronic device 500 to communicate with one or more other electronic devices (e.g., network card, modem, etc.). Such communication can be performed via input / output (I / O) interface (not shown).

[0158] According to an exemplary implementation of this disclosure, a computer-readable storage medium is provided that stores computer-executable instructions thereon, wherein the computer-executable instructions are executed by a processor to implement the methods described above. According to an exemplary implementation of this disclosure, a computer program product is also provided, which is tangibly stored on a non-transitory computer-readable medium and includes computer-executable instructions, which are executed by a processor to implement the methods described above.

[0159] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatuses, devices, and computer program products implemented according to this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0160] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0161] Computer-readable program instructions can be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0162] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0163] Various implementations of this disclosure have been described above. The foregoing description is exemplary and not exhaustive, nor is it limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is determined to best explain the principles, practical applications, or improvements to technology in the market, or to enable others skilled in the art to understand the various implementations disclosed herein.

Claims

1. A method for determining the energy of a molecular system, comprising: For fragments in multiple segments of a molecular system, Determine multiple orbits associated with the segment, the multiple orbits including at least one segment orbital of the segment, at least one first environmental orbital strongly coupled to the segment, and at least one second environmental orbital weakly coupled to the segment; Based on the corresponding occupancy status of the multiple tracks, the multiple tracks are respectively mapped to a first track space or a second track space. For the segment track, the first environmental track and the second environmental track that are mapped to the same track space, the occupancy status of the second environmental track is different from the occupancy status of the segment track and the first environmental track. Using reference information related to electronic excitation determined based on the first orbital space and the second orbital space, a set of target orbitals is selected from the plurality of orbitals to construct the fragment orbital space of the fragment; as well as Based on the orbital space of each of the plurality of fragments, an estimate of the system energy of the molecular system is determined.

2. The method according to claim 1, wherein mapping the plurality of orbits to a first orbital space or a second orbital space comprises: Extract the unoccupied track from the at least one segment track and the at least one first environment track to obtain at least one first virtual track; Extract the occupied track from the at least one segment track and the at least one first environmental track to obtain at least one first occupied track; At least one second occupied track in the occupied state among the at least one first virtual track and the at least one second environmental track is mapped to the first track space; as well as At least one second virtual track in the unoccupied state among the at least one first occupied track and the at least one second environmental track is mapped to the second track space.

3. The method according to claim 2, wherein the at least one first virtual track and the at least one first occupied track are both represented by embedded track features, and the at least one second occupied track and the at least one second virtual track are both represented by track coefficient features.

4. The method of claim 2, wherein the segment orbit space of the segment is constructed by the at least one segment orbit, the at least one first environmental orbit, at least one first reference orbit, and at least one second reference orbit; and The at least one first reference track is selected from the at least one second occupied track based on the reference information, and the at least one second reference track is selected from the at least one second virtual track based on the reference information.

5. The method of claim 4, wherein the reference information includes a first electron excitation amplitude determined based on a first orbital space and a second electron excitation amplitude determined based on a second orbital space, and the at least one first reference orbit and the at least one second reference orbit are selected by: Based on the first electronic excitation amplitude, an estimate of the first occupancy number of each of the at least one second occupancy orbitals is determined; From the at least one second occupied track, select the second occupied track whose estimated first occupied number is greater than the first predetermined occupied number as one of the at least one first reference track; Based on the second electronic excitation amplitude, an estimate of the second occupancy number of each of the at least one second virtual orbits is determined; as well as From the at least one second virtual track, select a second virtual track whose estimated second occupancy number is less than a second predetermined occupancy number as one of the at least one second reference track.

6. The method of claim 1, wherein determining the estimate of the system energy of the molecular system comprises: For the segment among the plurality of segments, Based on the segment orbital space of the segment, a first estimate of the segment energy is determined using a linear response algorithm; Based on the orbital space of the fragment, a second estimate of the fragment energy is determined using the quantum many-body algorithm; as well as Based on the first estimate and the second estimate determined for the plurality of fragments respectively, an estimate of the system energy of the molecular system is determined.

7. The method of claim 6, wherein determining an estimate of the system energy of the molecular system based on the first estimate and the second estimate determined for the plurality of fragments respectively comprises: For the segment among the plurality of segments, Based on the difference between the first estimate and the second estimate, the fragment energy compensation of the fragment is determined; as well as An estimate of the system energy of the molecular system is determined by adjusting the reference system energy of the molecular system based on the segment energy compensation determined for each of the plurality of segments.

8. The method of claim 6, wherein the linear response algorithm comprises a stochastic phase approximation algorithm, wherein the electron excitation amplitude involved in the stochastic phase approximation algorithm is determined at least based on a first projection operator, the first projection operator indicating, during the determination of the electron excitation amplitude, the influence of the partially occupied orbit based on the relationship between the partially occupied orbit and the segment; and / or The quantum many-body method includes an auxiliary field quantum Monte Carlo algorithm, in which the Green's function is determined at least based on the first projection operator, which further indicates that, during the determination of the Green's function, the influence of the partially occupied orbit is determined based on the relationship between the partially occupied orbit and the segment.

9. The method of claim 8, wherein the first projection operator further indicates at least one of the following: Regarding the partially occupied track, If the partially occupied orbit is one of the plurality of orbits in the segment, the influence of determining the partially occupied orbit is considered during the determination of the electron excitation amplitude. If the partially occupied track is one of the plurality of tracks of the segment, the influence of the partially occupied track is determined during the determination of the Green's function.

10. The method of claim 1, wherein the at least one second environmental orbit is determined by: Obtain multiple candidate environmental orbitals in the molecular system that are weakly coupled to the fragment; and From the plurality of candidate environmental orbitals, a candidate environmental orbital that meets a predetermined degree requirement in terms of overlap with the reference region of the molecular system is selected as one of the at least one second environmental orbital.

11. The method of claim 10, wherein the degree of overlap between the candidate environmental orbits among the plurality of candidate environmental orbits and the reference region is determined by: By using a second projection operator, the plurality of candidate environmental orbits are projected onto the reference region to determine a first overlap feature representation, which indicates the degree of overlap between the candidate environmental orbits and the reference region.

12. The method of claim 11, wherein the second projection operator is determined based on: The local orbitals in the molecular system, and The second overlap feature indicates the degree of overlap between at least one orbital in the molecular system belonging to the reference region and other orbitals in the molecular system.

13. The method of claim 12, wherein the plurality of candidate environmental orbits are represented by orbit coefficients, the first overlap feature is represented by an overlap matrix, and selecting candidate environmental orbits that satisfy a predetermined degree requirement in overlap with the reference region comprises: Based on the product of the orbit coefficients and the overlap matrix after diagonalization, candidate environmental orbits among the plurality of candidate environmental orbits that meet the predetermined degree requirement in terms of overlap with the reference region are determined.

14. An apparatus for determining the energy of a molecular system, comprising: The orbital determination module is configured to determine multiple orbits associated with a segment of a molecular system, the multiple orbits including at least one segment orbital of the segment, at least one first environmental orbital strongly coupled to the segment, and at least one second environmental orbital weakly coupled to the segment. The space correspondence module is configured to correspond the multiple tracks to a first track space or a second track space based on the corresponding occupancy status of the multiple tracks. For the segment track, the first environmental track and the second environmental track that are corresponded to the same track space, the occupancy status of the second environmental track is different from the occupancy status of the segment track and the first environmental track. The fragment orbital space construction module is configured to select a set of target orbitals from the plurality of orbitals to construct the fragment orbital space of the fragment using reference information related to electronic excitation determined based on the first orbital space and the second orbital space; as well as The system energy estimation module is configured to determine an estimate of the system energy of the molecular system based on the orbital space of each of the plurality of segments.

15. An electronic device comprising: At least one processor; as well as At least one memory coupled to the at least one processor and storing instructions for execution by the at least one processor, the instructions causing the electronic device to perform the method according to any one of claims 1 to 13 when executed by the at least one processor.

16. A computer-readable storage medium having stored thereon computer-executable instructions that can be executed by a processor to implement the method according to any one of claims 1 to 13.

17. A computer program product comprising computer-executable instructions, wherein the computer-executable instructions, when executed by a processor, implement the method according to any one of claims 1 to 13.

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