Method and device for drawing two-dimensional projection drawing of delocalized electronic structure of spherical molecule, medium and product
By projecting the π orbital wavefunctions of spherical conjugated molecules onto a two-dimensional plane using the Hückel molecular orbital method and the Mollweide projection method, the problem of visualizing delocalized π orbitals of spherical molecules is solved, generating an intuitive two-dimensional projection diagram. This overcomes the limitations of existing methods and achieves accurate visualization of spherical molecules.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHENGZHOU UNIV
- Filing Date
- 2026-01-14
- Publication Date
- 2026-04-21
AI Technical Summary
Existing methods cannot effectively draw two-dimensional projection diagrams of delocalized π orbitals of spherical conjugated molecules, which limits the visualization research and teaching of non-planar conjugated molecules.
The Hückel molecular orbital method is used to calculate the atomic orbital combination coefficients of π molecular orbitals in spherical conjugated molecules. Combined with equal-area projection methods such as Mollweide projection, the wave function values of π orbitals on the three-dimensional plotted sphere are projected onto a two-dimensional plane. Data processing tools such as Excel are used to generate two-dimensional projection diagrams of π molecular orbitals.
It achieves accurate visualization of the delocalized π orbitals of spherical conjugated molecules, breaking through the limitations of existing methods, and generates intuitive and standardized two-dimensional projection diagrams that reflect the overall symmetry of the spherical molecular orbitals and the spatial distribution of wave function values.
Smart Images
Figure CN121904205A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of two-dimensional projection mapping technology, and in particular to a method, apparatus, medium, and product for mapping two-dimensional projections of the delocalized electronic structure of a spherical molecule. Background Technology
[0002] The delocalized π orbitals of conjugated molecules determine their optical and chemical properties. Therefore, a deep understanding of the composition and characteristics of π orbitals is crucial for exploring the optical properties and chemical transformations of molecules. Visualizing π molecular orbitals using computer software is one of the most effective ways to study orbital properties and is widely used in both teaching and research. In recent years, experimental design and practical training related to molecular orbital visualization have attracted attention. Inspired by previous work, our team previously reported an experimental design suitable for undergraduate students, guiding them to combine π molecular orbital data obtained from Hückel molecular orbital (HMO) theory with the plotting functions of commonly used office software like Excel to draw sectional contour plots of π orbitals in planar conjugated molecules such as butadiene and benzene. The teaching effect was good. Unfortunately, this method mainly reduces the dimension of the π molecular orbital sectional contour plot by setting one of the x, y, or z coordinate directions to a fixed value. However, it is clearly not suitable for dimensionality reduction plotting of π molecular orbitals (wave functions) with spherical sectional surfaces, thus it is not suitable for non-planar conjugated molecules (such as C). 20 C 60 B 12 H 12 2- The limited ability to construct two-dimensional diagrams of delocalized orbitals in spherical conjugated molecules restricts the widespread adoption of methods for drawing planar images of such π molecular orbitals. Furthermore, current chemistry curriculum primarily focuses on introducing the π-delocalized structures of butadiene, benzene rings, and their homologous fused-ring compounds, which significantly restricts students' understanding of the depth and breadth of delocalized molecular structures. Summary of the Invention
[0003] The purpose of this application is to provide a method, apparatus, medium, and product for drawing two-dimensional projection maps of the delocalized electronic structure of spherical molecules, which can be applied to drawing two-dimensional projection maps of the delocalized π orbitals of spherical molecules.
[0004] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule, including: Determine the drawing sphere of the spherical conjugated molecule; Based on the drawing sphere, determine the atomic orbital wavefunction of each atom in the spherical conjugated molecule on the drawing sphere. The atomic orbital combination coefficients of each atom in the π molecular orbitals of the spherical conjugated molecule are calculated using the Hückel molecular orbital method, and the wave function values of the π molecular orbitals on the plotted sphere are determined based on the atomic orbital expressions. Using the equal-area projection method, the wave function values of the π molecular orbitals on the drawing sphere are projected onto a two-dimensional plane to obtain the projection function of the π molecular orbitals on the two-dimensional plane; Based on the projection function, a two-dimensional projection diagram of the π molecular orbitals of the spherical conjugated molecule is generated by using data processing tools for visualization.
[0005] Optionally, determining the drawing sphere of the spherical conjugated molecule specifically includes: The sphere in the drawing is a sphere with the center of the spherical conjugated molecule as its center and a radius of R; wherein the radius R is equal to the radius r of the sphere formed by the atomic coordinates of the spherical conjugated molecule plus... a 0 / 3, a 0 represents the Bohr radius.
[0006] Optionally, the i-th atom of the spherical conjugated molecule is located at any point on the drawing sphere. x s , y s , z s ) at 2 p z The expression for the atomic orbital wavefunction is: ; Among them, (x i ,y i ,z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.
[0007] Optionally, the step of calculating the atomic orbital combination coefficients of each atom in the π molecular orbitals of the spherical conjugated molecule using the Hückel molecular orbital method, and determining the wavefunction values of the π molecular orbitals on the plotted sphere based on the atomic orbital expressions, specifically includes: The secular equations of the spherical conjugated molecule were established using the Hückel molecular orbital method. Solving the secular equations yields the atomic orbital combination coefficient matrix for each atom in the π molecular orbitals of the spherical conjugated molecule. By combining the atomic orbital combination coefficient matrix with the atomic orbital expression, the wavefunction values of the π molecular orbitals at each point on the plotted sphere are calculated. ; ; in, Let i be the atomic orbital wavefunction of the i-th atom. c ik denoted as , where is the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital of a spherical conjugated molecule, n is the total number of atomic orbitals, and g is the total number of molecular orbitals.
[0008] Optionally, the equal-area projection method is the Mollweide projection method; the step of using the equal-area projection method to project the wavefunction values of the π molecular orbitals on the drawing sphere onto a two-dimensional plane to obtain the projection function of the π molecular orbitals on the two-dimensional plane specifically includes: Establish a coordinate transformation relationship between points on the drawing sphere and points on the two-dimensional projection plane; the coordinate transformation relationship is based on the Mollweide projection. The wave function value of the π molecular orbital is converted into a function on the two-dimensional projection plane through the coordinate transformation relationship, thus obtaining the projection function of the π molecular orbital on the two-dimensional plane.
[0009] Optionally, the data processing tool is spreadsheet software; based on the projection function, the data processing tool is used for visualization processing to generate a two-dimensional projection diagram of the π molecular orbitals of the spherical conjugated molecule, specifically including: In spreadsheet software, the cell array is simulated as grid points on a two-dimensional projection plane, and the planar coordinates corresponding to each cell are determined according to the projection range; In each cell, the value of the projection function corresponding to the cell coordinates is calculated using the formula function of the spreadsheet software; Using the contour plotting function of the spreadsheet software, a two-dimensional contour projection map of the π molecular orbital is generated based on the value of the projection function corresponding to the coordinates of each cell.
[0010] Optionally, using the contour plotting function of the spreadsheet software, a two-dimensional contour projection map of the π molecular orbital is generated based on the value of the projection function corresponding to each cell coordinate, specifically including: Using the IF function of the spreadsheet software, cells that are outside the effective projection range of the projection method are assigned a preset value that is outside the actual value range of the π molecular orbital wave function. Using the contour plotting function of the spreadsheet software, a two-dimensional contour projection map of the π molecular orbital is generated based on the value of the projection function corresponding to the coordinates of each cell; wherein, the area corresponding to the preset value is set as the background color.
[0011] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for drawing a two-dimensional projection map of the delocalized electronic structure of a spherical molecule as described above.
[0012] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for drawing a two-dimensional projection map of the delocalized electronic structure of a spherical molecule as described above.
[0013] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method for drawing a two-dimensional projection map of the delocalized electronic structure of a spherical molecule as described above.
[0014] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method, apparatus, medium, and product for drawing a two-dimensional projection map of the delocalized electronic structure of a spherical molecule. The method includes: determining a drawing sphere of the spherical conjugated molecule; determining the atomic orbital wavefunction expression of each atom in the spherical conjugated molecule on the drawing sphere based on the drawing sphere; calculating the atomic orbital combination coefficient of each atom in the π molecular orbitals of the spherical conjugated molecule using the Hückel molecular orbital method, and determining the wavefunction value of the π molecular orbital on the drawing sphere based on the atomic orbital expression; projecting the wavefunction value of the π molecular orbital on the drawing sphere onto a two-dimensional plane using the equal-area projection method to obtain the projection function of the π molecular orbital on the two-dimensional plane; and performing visualization processing using data processing tools based on the projection function to generate a two-dimensional projection map of the π molecular orbitals of the spherical conjugated molecule. This application proposes the concept of a drawing sphere and derives the wavefunction expression of atomic orbitals on this sphere. This fundamentally overcomes the limitation of existing methods that can only draw planar cross-sectional diagrams by fixing a single spatial coordinate (dimensional reduction), making it possible to visualize the delocalized π orbitals of approximately spherical non-planar conjugated molecules and solving the technical challenge of visualizing orbitals in spherical conjugated molecules. This application introduces and adapts the Mollweide equal-area projection method to systematically and accurately transform the calculated π orbital wavefunction values distributed on the three-dimensional drawing sphere to two-dimensional planar coordinates. This method preserves the area characteristics of the projection region, resulting in a standardized and intuitive two-dimensional projection diagram that facilitates observation and analysis of the overall symmetry of spherical molecular orbitals and the spatial distribution of wavefunction values (phase and magnitude). Furthermore, this application relies heavily on the fundamental principles of quantum chemistry (Hückel's molecular orbital theory) and the precise form of atomic orbital wave functions. By solving the secular equations of a specific molecule, precise combination coefficients are obtained. Combined with precise projection coordinate transformation, this ensures that the final generated two-dimensional projection diagram can realistically and quantitatively reflect the intrinsic characteristics of the delocalized π orbitals of the spherical molecule, rather than a simple qualitative schematic diagram. Attached Figure Description
[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is an application environment diagram of a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to an embodiment of this application.
[0017] Figure 2 This is a flowchart illustrating a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule, as provided in an embodiment of this application.
[0018] Figure 3 This is a schematic diagram showing the selection of the sphere for drawing spherical conjugated molecular orbitals according to an embodiment of this application.
[0019] Figure 4 One embodiment of this application provides a method for drawing a sphere C using Excel. 20 A schematic diagram of the projection of molecular π orbitals.
[0020] Figure 5 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation
[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0022] This application proposes the concept of dimension-reduction projection of π molecular orbitals (wave functions) on the surface of a spherical skin to create a two-dimensional map, using spherical molecules C 20 Taking this example, a method for drawing two-dimensional projection diagrams of delocalized π orbitals of spherical molecules is proposed to provide support for related teaching or research activities.
[0023] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0024] The method for drawing two-dimensional projection diagrams of the delocalized electronic structure of spherical molecules provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on other servers.
[0025] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.
[0026] In one exemplary embodiment, such as Figure 2 As shown, a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 208. Wherein: S1. Determine the drawing sphere of the spherical conjugated molecule.
[0027] The sphere used in the drawing is a sphere with the center of the spherical conjugated molecule as its center and a radius of R; where the radius R is equal to the radius r of the sphere formed by the atomic coordinates of the spherical conjugated molecule plus... a 0 / 3, a 0 represents the Bohr radius.
[0028] Specifically, such as Figure 3 As shown, for a spherical conjugated molecule, all atoms are located at the center of the sphere, with a radius of 1. On the spherical surface (red). Taking a carbon-based spherical molecule as an example, take the surface of each carbon atom. p z Linear combinations of orbitals form delocalized π molecular orbitals with radii of . The sphere is the drawing sphere (green), and the direction from the center of the sphere to the carbon atom is set as the z-axis direction of that carbon atom. It can be seen from the following equation (1) that... 2 for carbon atoms p z The value of the spherical polar coordinate variable r when the orbital has a maximum value. Industry convention generally holds that main group atoms pass through a plane (x,y) shaped molecule. p z The linear combination of wavefunctions corresponding to atomic orbitals forms delocalized π molecular orbitals. Therefore, this section uses the carbon atom as an example. p z The relevant content is illustrated using the track as an example.
[0029] S2. Based on the drawn sphere, determine the atomic orbital wavefunction of each atom in the spherical conjugated molecule on the drawn sphere.
[0030] 2 carbon atoms p z The orbital approximation is represented by a single-electron atom wavefunction, which is expressed in spherical polar coordinates as follows: (1) In polar coordinates, r, θ, and ϕ are three variables. A point in three-dimensional space is represented by three parameters: radial distance r, polar angle θ (sometimes called zenith angle or co-latitude angle), and azimuth angle ϕ (sometimes called longitude angle). θ refers to the angle rotated downwards from the positive z-axis (north pole direction) to the point's location, with a value range of 0 ≤ θ ≤ π radians.
[0031] The expression in the Cartesian coordinate system is: (2) In the formula a 0 Let be the Bohr radius, ( x i , y i , z i Let (x, y) be the spatial coordinates of the i-th carbon atom. Therefore, the orbital wavefunction of the i-th carbon atom at any point (x, y) on the plotting sphere... s ,y s ,z s The value at position ) can be expressed as: (3) Among them, (x i ,y i ,z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.
[0032] S3. Calculate the atomic orbital combination coefficient of each atom in the π molecular orbital of the spherical conjugated molecule using the Hückel molecular orbital method, and determine the wave function value of the π molecular orbital on the plotted sphere based on the atomic orbital expression.
[0033] In this embodiment, the secular equations of the spherical conjugated molecule are established using the Hückel molecular orbital method; the secular equations are solved to obtain the atomic orbital combination coefficient matrix of each atom in each π molecular orbital of the spherical conjugated molecule; the atomic orbital combination coefficient matrix is combined with the atomic orbital expression to calculate the π molecular orbital wavefunction values at each point on the plotted sphere. .
[0034] Specifically, the atomic orbital combination coefficients in each π molecular orbital are calculated using the HMO method, and the wave function values of the π molecular orbitals on the plotting sphere are determined by combining the atomic orbital expressions obtained above (Equation 3).
[0035] The Hückel molecular orbital (HMO) method is a semi-empirical quantum chemical calculation method that uses the principles of linear variational methods to solve for the large π-delocalized molecular orbitals of conjugated molecules. The HMO method assumes that π electrons move within the entire framework formed by the nucleus and σ bonds, allowing for the separate treatment of σ and π bonds. In this method, the σ-bond framework of the conjugated molecule remains unchanged, and the molecular properties are determined by the π-electron state. The Schrödinger equation describing the motion of the k-th π electron is: (4) in, This represents the Hamiltonian operator for the k-th π electron, which is the operator form corresponding to energy.
[0036] Suppose a conjugated molecule consists of n carbon atoms forming a conjugated system, with each carbon atom providing one p z Orbits, according to atomic orbitals ( Linear combination into molecular orbitals ( The k-th π molecular orbital can be... Expressed as a linear combination of the wave functions of each atomic orbital: ; (5) in, Let be the atomic orbital wave function of the i-th atom (as shown in equation (3)). c ik Let be the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital of a spherical conjugated molecule, where n is the total number of atomic orbitals and g is the total number of molecular orbitals. Based on the concept of linear combination of atomic orbitals into molecular orbitals (LCAO-MO), n atomic orbitals will linearly combine into g molecular orbitals. According to the variational principle, any possible state of a molecule... The energy average integral must be greater than or equal to the true ground state energy of the system. : (6) in, Integral for the average energy value, This is the integral form of the energy average. It is the reciprocal of the normalization coefficient of the wave function.
[0037] Therefore, based on the linear variational method, the combination coefficients can be obtained by integrating the energy-average value. The first derivative is equal to 0, which gives us the secular equations: (7) Among them, H uv For the Coulomb integral (when u=v) or the commutative integral (when u≠v), c iS represents the atomic orbital combination coefficients (i=1-n). uv For the overlap integral, u / v = 1 - n.
[0038] The HMO method further assumes that the α integral of each carbon atom is the same, the β integral of each adjacent carbon atom is also the same, and the β integral and overlap integral S of non-adjacent atoms are both 0, thus obtaining C 20 The simplified secular equations for the molecules are as follows: (8) in, , Let be the energy of the k-th π molecular orbital. From this, the combination coefficient matrix of the wavefunctions of each π molecular orbital can be obtained: (9) Substituting equations (2) and (5) into equation (3), we can calculate the molecular orbital wavefunctions at various points on the plotted sphere. The value.
[0039] S4. Using the equal-area projection method, the wave function value of the π molecular orbital on the drawing sphere is projected onto a two-dimensional plane to obtain the projection function of the π molecular orbital on the two-dimensional plane.
[0040] Wherein, the equal-area projection method is the Mollweide projection method; in this embodiment, a coordinate transformation relationship is established between points on the drawing sphere and points on the two-dimensional projection plane; the coordinate transformation relationship is a coordinate transformation relationship based on the Mollweide projection; the wave function value of the π molecular orbital is converted into a function on the two-dimensional projection plane through the coordinate transformation relationship, thereby obtaining the projection function of the π molecular orbital on the two-dimensional plane.
[0041] Mollweide projection is a commonly used equal-area projection method that projects a sphere onto a plane. It can project a specified sphere as a plane with an aspect ratio of 2:1 and is often used for world map drawing, star map drawing, etc. Let the radius of the sphere be R, and let any point (x, y) on the sphere be a point (x, y). s ,y s ,z s The projection coordinates of the point in the two-dimensional plane are (x, y).
[0042] The coordinate transformation relationship in this embodiment can be constructed through the following steps: Introducing intermediate variables ω : (10) Then the spherical latitude corresponding to that point and longitude They are respectively: (11) (12) Transform spherical latitude and longitude to a spatial rectangular coordinate system: (13) The combined formulas (10) to (13) can determine any point (x) on the drawing sphere. s ,y s ,z s The transformation relationship between the coordinates of each atom in the structure and its projected position (x, y) in a two-dimensional plane. i ,y i ,z i Substituting the above projection transformation relationship into equation (3), we determine the expression of the molecular orbital wavefunction in the projection plane. .
[0043] S5. Based on the projection function, use data processing tools to perform visualization processing to generate a two-dimensional projection diagram of the π molecular orbitals of the spherical conjugated molecule.
[0044] The data processing tool is a spreadsheet software. In this embodiment, the cell array is simulated as a grid on a two-dimensional projection plane in the spreadsheet software, and the planar coordinates corresponding to each cell are determined according to the projection range. The IF function of the spreadsheet software is used to assign a preset value that exceeds the actual value range of the π molecular orbital wavefunction to cells that are outside the effective projection range of the projection method.
[0045] In each cell, the value of the projection function corresponding to the cell coordinates is calculated using the formula function of the spreadsheet software; wherein, the area corresponding to the preset value is set as the background color.
[0046] Please see Figure 4 The basic principle of using Excel to draw molecular orbital projection contour maps is as follows: each cell in Excel is regarded as an evenly divided grid point on the drawing plane. The value of the corresponding point of each cell is calculated by editing the Excel formula, that is, the value of the projection of the π molecular orbital on the drawing plane at the cell position calculated by formula (17), and then according to... Figure 4 The process shown uses Excel's contour plotting function to draw the projection map.
[0047] First, the structure of the molecule was optimized using the Gaussian16 program and density functional theory (DFT) to obtain the coordinates (x, y, y) of each atom in the molecule. i , y i , z i And the circumscribed sphere radius r of the molecule. Based on Figure 3 As shown, select The radius R of the sphere being drawn.
[0048] Based on the spatial coordinates of each atom and the principle of the Mollweide projection method, the drawing range can be calculated. According to equation (12), the range of values for y is... to The upper and lower limits of x are twice the upper and lower limits of y, that is, the range of x is... to Let the distance between two adjacent cells in Excel be 0.04 Å (this can be adjusted appropriately depending on the molecular structure and plotting effect). Then the coordinates (x, y) of the point in the two-dimensional plane corresponding to the cell in row () and column () of column () can be expressed as ( .
[0049] For the Mollweide projection, from formulas (10) to (13), it can be seen that the projection range of the sphere onto the two-dimensional plane must satisfy: (14) Therefore, it is necessary to use the IF() function in Excel to exclude cells that do not meet equation (14). Based on the usage of the IF() function in Excel (IF(condition, output if condition is met, output if condition is not met)), the values of cells within the range that meet equation (14) are excluded by Ψ. k The actual calculated values show that the cell value that does not meet the requirements of equation (14) is assigned the value of 1.35. According to the Mollweide projection method, the projection of the spherical drawing surface is an elliptical plane with an aspect ratio of 2:1, so the projection function needs to be truncated. 1.35 is a value that no Ψk can reach. If the cell containing this value is set to white, an elliptical projection can be achieved. Therefore, the IF function expression should be: (15) In summary, the condition within the IF function in Excel code can be written as: (16) Based on this, molecular orbital expressions can be defined in Visual Basic. The value at cell (x, y): (17) Finally, set the colors. Set the color of the cell with the smallest value according to formula (15) to blue (RGB value is 0, 0, 255), and the color step size is set to the absolute value of the minimum value of the cell divided by 50. From the minimum value to 0.0000, the B value of RGB is always 255, and for each step increase, R and G are each increased by 5. When the wave function value is 0.0000, the RGB value is 255, 255, 255, which is white. The maximum value should be greater than 1.35 and be an integer multiple of the step size. From 0.0000 to the maximum value, the R value of RGB is always 255, and for each cell move, the G value and B value are each decreased by 5. When the wave function value is the maximum value, the RGB value is 255, 0, 0, which is red. For the remaining cells with values greater than 1.35, the RGB value is set to 255, 255, 255, which is pure white. Based on this, the projection diagram of the π molecular orbital can be obtained and points that do not conform to the projection range in the image can be avoided.
[0050] In existing technologies, the method for plotting contour maps based on the Hückel molecular orbital method is not suitable for processing spherical molecular systems. This application derives a formula for calculating delocalized orbitals in spherical cross-sections, and combines this with projection formulas and plotting tools to achieve image visualization of delocalized molecular orbitals in approximately spherical molecules. The delocalized electron wavefunctions (orbitals) of approximately spherical molecules can be plotted using the described method to create both three-dimensional cross-sections and two-dimensional projection maps. Theoretically, this method can also be applied to spherical molecules of other main group element types, requiring only further modification of the corresponding 2D projections for different types of atoms. p z The wave function form of the orbit is sufficient, and the radius of the spherical cross-section can be freely adjusted.
[0051] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 5 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and databases. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a method for drawing a two-dimensional projection map of the delocalized electronic structure of a spherical molecule.
[0052] Those skilled in the art will understand that Figure 5 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.
[0053] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.
[0054] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.
[0055] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Moreover, the collection, use and processing of the relevant data are carried out in compliance with the relevant data protection laws and policies of the country where the location is located, and with the authorization granted by the owner of the corresponding device.
[0056] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).
[0057] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.
[0058] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0059] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule, characterized in that, include: Determine the drawing sphere of the spherical conjugated molecule; Based on the drawing sphere, determine the atomic orbital wavefunction of each atom in the spherical conjugated molecule on the drawing sphere. The atomic orbital combination coefficients of each atom in the π molecular orbitals of the spherical conjugated molecule are calculated using the Hückel molecular orbital method, and the wave function values of the π molecular orbitals on the plotted sphere are determined based on the atomic orbital expressions. Using the equal-area projection method, the wave function values of the π molecular orbitals on the drawing sphere are projected onto a two-dimensional plane to obtain the projection function of the π molecular orbitals on the two-dimensional plane; Based on the projection function, a two-dimensional projection diagram of the π molecular orbitals of the spherical conjugated molecule is generated by using data processing tools for visualization.
2. The method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to claim 1, characterized in that, The determination of the drawing sphere for the spherical conjugated molecule specifically includes: The sphere in the drawing is a sphere with the center of the spherical conjugated molecule as its center and a radius of R; wherein the radius R is equal to the radius r of the sphere formed by the atomic coordinates of the spherical conjugated molecule plus... a 0 / 3, a 0 represents the Bohr radius.
3. The method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to claim 1, characterized in that, The i-th atom of the spherical conjugated molecule is located at any point on the drawn sphere. x s , y s , z s ) at 2 p z The expression for the atomic orbital wavefunction is: ； Among them, (x i ,y i ,z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.
4. The method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to claim 1, characterized in that, The calculation of the atomic orbital combination coefficients of each atom in the π molecular orbitals of the spherical conjugated molecule using the Hückel molecular orbital method, and the determination of the wavefunction values of the π molecular orbitals on the plotted sphere based on the atomic orbital expressions, specifically includes: The secular equations of the spherical conjugated molecule were established using the Hückel molecular orbital method. Solving the secular equations yields the atomic orbital combination coefficient matrix for each atom in the π molecular orbitals of the spherical conjugated molecule. By combining the atomic orbital combination coefficient matrix with the atomic orbital expression, the wavefunction values of the π molecular orbitals at each point on the plotted sphere are calculated. ; ； in, Let i be the atomic orbital wavefunction of the i-th atom. c ik denoted as , where is the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital of a spherical conjugated molecule, n is the total number of atomic orbitals, and g is the total number of molecular orbitals.
5. The method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to claim 1, characterized in that, The equal-area projection method is the Mollweide projection method; the process of using the equal-area projection method to project the wave function values of the π molecular orbitals on the drawing sphere onto a two-dimensional plane to obtain the projection function of the π molecular orbitals on the two-dimensional plane specifically includes: Establish a coordinate transformation relationship between points on the drawing sphere and points on the two-dimensional projection plane; the coordinate transformation relationship is based on the Mollweide projection. The wave function value of the π molecular orbital is converted into a function on the two-dimensional projection plane through the coordinate transformation relationship, thus obtaining the projection function of the π molecular orbital on the two-dimensional plane.
6. The method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to claim 1, characterized in that, The data processing tool is spreadsheet software; based on the projection function, the data processing tool is used for visualization processing to generate a two-dimensional projection diagram of the π molecular orbitals of the spherical conjugated molecule, specifically including: In spreadsheet software, the cell array is simulated as grid points on a two-dimensional projection plane, and the planar coordinates corresponding to each cell are determined according to the projection range; In each cell, the value of the projection function corresponding to the cell coordinates is calculated using the formula function of the spreadsheet software; Using the contour plotting function of the spreadsheet software, a two-dimensional contour projection map of the π molecular orbital is generated based on the value of the projection function corresponding to the coordinates of each cell.
7. The method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to claim 6, characterized in that, Using the contour plotting function of the spreadsheet software, a two-dimensional contour projection map of the π molecular orbital is generated based on the value of the projection function corresponding to each cell coordinate. Specifically, this includes: Using the IF function of the spreadsheet software, cells that are outside the effective projection range of the projection method are assigned a preset value that is outside the actual value range of the π molecular orbital wave function. Using the contour plotting function of the spreadsheet software, a two-dimensional contour projection map of the π molecular orbital is generated based on the value of the projection function corresponding to the coordinates of each cell; wherein, the area corresponding to the preset value is set as the background color.
8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule according to any one of claims 1-7.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule as described in any one of claims 1-7.
10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements a method for drawing a two-dimensional projection diagram of the delocalized electronic structure of a spherical molecule as described in any one of claims 1-7.