X-ray thomson scattering spectrum simulation method based on first principle

Abstract

The application provides a first-principle-based X-ray Thomson scattering spectrum simulation method, which decomposes the scattering spectrum of a warm dense matter into an elastic part and an inelastic part based on quantum perturbation theory, wherein the elastic part is calculated by first-principle molecular dynamics and finite-temperature density functional theory, the inelastic part is calculated by a perturbation formula of time-dependent density functional theory, and the calculated elastic part and inelastic part are integrated to obtain a complete X-ray Thomson scattering spectrum of the warm dense matter. The method uses first principles to accurately simulate the internal environment of the warm dense matter, ensures that the finally simulated X-ray Thomson scattering spectrum truly reflects the internal environment of the warm dense matter, facilitates accurate spectrum decomposition operation on the actually measured scattering spectrum, and improves the research reliability of the warm dense matter.

Description

Technical Field

[0001] This invention relates to the technical field of X-ray diagnostics of dense materials, and particularly to a first-principles-based X-ray Thomson scattering spectroscopy simulation method. Background Technology

[0002] X-ray Thomson scattering (XTS) is primarily used for diagnosing the state of warm, dense matter. It can penetrate the interior of such matter, providing comprehensive and precise information on temperature, density, ionization degree, and ionic structure. It has been widely applied in laboratory astrophysics, planetary physics, and inertial confinement fusion research. However, existing conventional modeling methods cannot adequately handle dense plasma environments and are ill-suited for extracting state parameters from high-precision experimental data. With preliminary X-ray Thomson scattering experiments underway in China, establishing a corresponding theoretical model is crucial. First-principles methods can effectively simulate partially dissociated, ionized, and degenerate warm, dense environments; however, no first-principles method has yet been developed to predict the complete X-ray Thomson scattering spectrum, making accurate and complete first-principles modeling and prediction of the X-ray Thomson scattering spectrum for warm, dense matter impossible. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a first-principles X-ray Thomson scattering spectrum simulation method. Based on quantum perturbation theory, it decomposes the scattering spectrum of warm, dense materials into elastic and inelastic components. The calculation of the elastic component is achieved using first-principles molecular dynamics and finite-temperature density functional theory, while the calculation of the inelastic component is achieved using perturbation formulas from time-dependent density functional theory. The calculated elastic and inelastic components are then integrated to obtain the complete X-ray Thomson scattering spectrum of the warm, dense material. This method utilizes first-principles calculations to perform a complete and accurate simulation of the internal environment of the warm, dense material, ensuring that the final simulated X-ray Thomson scattering spectrum truly reflects the internal environment of the material. This facilitates accurate spectral interpretation of the actual measured scattering spectrum, improving the reliability of research on warm, dense materials.

[0004] This invention provides a first-principles-based method for simulating X-ray Thomson scattering spectra, comprising the following steps:

[0005] Step S1: Simulate the ionic state of a warm-dense substance under specific electron and ion temperature densities using first-principles molecular dynamics to obtain a series of equilibrium ionic configurations; then, simulate the equilibrium ionic configurations according to finite temperature density functional theory to obtain the total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum of the warm-dense substance.

[0006] Step S2: Simulate the equilibrium ion configuration using finite-temperature density functional theory to obtain the corresponding ground-state wavefunction; calculate the time-dependent density functional theory perturbation formula based on the ground-state wavefunction to obtain the electronic response function χ(q,q',ω) corresponding to different equilibrium ion configurations; and then obtain the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum of the dense material based on the electronic response function χ(q,q',ω).

[0007] Step S3: Based on the total integrated intensity S1(q) of the elastic part and the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum, the complete total intensity S(q,ω) of the X-ray dense material's X-ray Thomson scattering spectrum is obtained.

[0008] Further, in step S1, the equilibrium ion configuration is simulated according to finite-temperature density functional theory to obtain the total intensity S1(q,ω) of the elastic component of the X-ray Thomson scattering spectrum of the dense material, including:

[0009] The equilibrium ionic configuration was analyzed to obtain the corresponding static ionic structure factor S. ii (q);

[0010] Simulations based on finite-temperature density functional theory yielded the atomic shape factor N(q) of partially equilibrium ionic configurations and the elastic X-ray scattering intensity caused by partially ionized bound electrons.

[0011] According to the ionic static structure factor S ii (q) and the atomic shape factor N(q) are used to obtain the elastic X-ray scattering intensity caused by spatial fluctuations in electron density.

[0012] The elastic X-ray scattering intensity caused by the spatial fluctuations in electron density and the intensity of elastic X-ray scattering caused by partial ionization The total integrated intensity S1(q) of the elastic component of the X-ray Thomson scattering spectrum of a warm, dense material is obtained, i.e.

[0013] Furthermore, in step S1, according to the ionic static structure factor S ii (q) and the atomic shape factor N(q) are used to obtain the elastic X-ray scattering intensity caused by spatial fluctuations in electron density. include:

[0014] Using the following formula (1), based on the ionic static structure factor S ii(q) and the atomic shape factor N(q) are used to obtain the elastic X-ray scattering intensity caused by spatial fluctuations in electron density.

[0015]

[0016] In the above formula (1), N i Indicates the number of ions.

[0017] Furthermore, step S1 also includes:

[0018] The atomic shape factor N(q) is obtained using the following formula (2).

[0019] N(q) = <ρ e (q) / ρ i (q)> (2)

[0020] In the above formula (2), ρ e (q) represents the electron density ρ e Fourier transform of (r); ρ i (q) represents the ion density ρ i Fourier transform of (r); <> represents the calculation of ensemble average; the meaning of the above formula (2) is that N(q) is equal to the electron density ρ e Fourier transform ρ of (r) e (q) divided by the ion density ρ i Fourier transform ρ of (r) i The ensemble mean of (q);

[0021] The static structure factor S of the ion is obtained using the following formula (3). ii (q),

[0022] S ii (q)=<|ρ i (q)| 2 > / N i (3)

[0023] In the above formula (3), ρ i (q) represents the ion density ρ i Fourier transform of (r); || denotes the modulus operation; <> denotes the ensemble average operation; N i Indicates the number of ions.

[0024] Furthermore, in step S1, the ionic states of warm-dense substances at specific electron and ion temperature densities are simulated using first-principles molecular dynamics to obtain a series of equilibrium ionic configurations, including:

[0025] Based on the modulus conservation and projected embellishment wave methods, different cutoff radii are selected to construct pseudopotentials suitable for warm and dense materials, thereby obtaining modulus conservation pseudopotentials and projected embellishment wave pseudopotentials.

[0026] Based on the projected pseudopotential, the ionic state of a dense substance at a specific electron and ion temperature density is simulated using first-principles molecular dynamics, thereby obtaining a series of equilibrium ionic configurations including a first number of atoms and an equilibrium ionic configuration including a second number of atoms; wherein the first number of atoms is greater than the second number of atoms.

[0027] Further, in step S2, a simulation of the equilibrium ion configuration using finite-temperature density functional theory is performed to obtain the corresponding ground-state wavefunction, including:

[0028] The extracted portion includes the equilibrium ion configuration with the second atomic number. Simulations based on finite-temperature density functional theory are performed on the extracted equilibrium ion configuration to obtain the corresponding ground state wavefunction and its corresponding eigenenergy and occupation number.

[0029] Further, in step S2, based on the ground state wavefunction, a time-dependent density functional theory perturbation formula is used to calculate the electronic response function χ(q,q',ω) corresponding to different equilibrium state ion configurations, including:

[0030] Based on the ground state wavefunction, determine the corresponding single-electron eigenstate ψ. n (r);

[0031] According to the single-electron eigenstate ψ n (r), the intrinsic energy ε n and the number of occupancy f n Determine the non-interacting electronic response function χ. 0 (q,q',ω);

[0032] Based on the Dyson equation for the electronic response function and the aforementioned non-interacting electronic response function χ... 0 (q,q',ω) yields the electronic response function χ(q,q',ω) corresponding to different equilibrium state ion configurations.

[0033] Further, in step S2, the total intensity S2(q,ω) of the inelastic portion of the X-ray Thomson scattering spectrum of the warm, dense material is obtained according to the electronic response function χ(q,q',ω), including:

[0034] The electronic response function χ(q,q',ω) is expanded with an ensemble average to obtain the average value <χ(q,q',ω)>. The average value <χ(q,q',ω)> is then converted into the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum of a warm and dense material using the fluctuation dissipation theorem.

[0035] Further, in step S3, based on the total integrated intensity S1(q) of the elastic portion and the total intensity S2(q,ω) of the inelastic portion of the X-ray Thomson scattering spectrum, the complete total intensity S(q,ω) of the X-ray Thomson scattering spectrum of the warm-dense material is obtained, including:

[0036] After broadening the total integrated intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum, the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum is obtained.

[0037] The sum of the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum and the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum is taken as the complete total intensity S(q,ω) of the X-ray Thomson scattering spectrum, that is, S(q,ω)=S1(q,ω)+S2(q,ω).

[0038] Further, in step S3, after broadening the total integrated intensity S1(q) of the elastic portion of the X-ray Thomson scattering spectrum, the total intensity S1(q,ω) of the elastic portion of the X-ray Thomson scattering spectrum is obtained, including:

[0039] The total integrated intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum is broadened by the experimentally measured instrument function g(ω) to obtain the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum, that is, S1(q,ω)=S1(q)g(ω).

[0040] Compared to existing technologies, this first-principles X-ray Thomson scattering spectroscopy simulation method decomposes the scattering spectrum of warm-dense materials into elastic and inelastic components based on quantum perturbation theory. The calculation of the elastic component is achieved through first-principles molecular dynamics and finite-temperature density functional theory, while the calculation of the inelastic component is achieved through perturbation formulas of time-dependent density functional theory. The calculated elastic and inelastic components are then integrated to obtain the complete X-ray Thomson scattering spectrum of the warm-dense material. It uses first-principles to perform a complete and accurate simulation of the internal environment of the warm-dense material, ensuring that the final simulated X-ray Thomson scattering spectrum truly reflects the internal environment of the warm-dense material. This facilitates accurate spectral interpretation of the scattering spectrum obtained from actual measurements and improves the reliability of research on warm-dense materials.

[0041] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0042] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 A schematic flowchart of the X-ray Thomson scattering spectrum simulation method based on first principles provided by the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] See Figure 1 This is a schematic flowchart of the X-ray Thomson scattering spectroscopy simulation method based on first principles provided in an embodiment of the present invention. The X-ray Thomson scattering spectroscopy simulation method based on first principles includes the following steps:

[0047] Step S1: Using first-principles molecular dynamics, the ionic state of a warm-dense substance under specific electron and ion temperature densities is simulated to obtain a series of equilibrium ionic configurations. Then, based on finite-temperature density functional theory, the equilibrium ionic configurations are simulated to obtain the total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum of the warm-dense substance.

[0048] Step S2: Simulate the equilibrium ion configuration using finite-temperature density functional theory to obtain the corresponding ground-state wavefunction; based on the ground-state wavefunction, perform time-dependent density functional theory perturbation calculations to obtain the electronic response function χ(q,q',ω) corresponding to different equilibrium ion configurations; then, based on the electronic response function χ(q,q',ω), obtain the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum of the dense material.

[0049] Step S3: Based on the total integrated intensity S1(q) of the elastic part and the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum, the complete total intensity S(q,ω) of the X-ray Thomson scattering spectrum of the warm and dense material is obtained.

[0050] The beneficial effects of the above technical solution are as follows: This first-principles X-ray Thomson scattering spectroscopy simulation method decomposes the scattering spectrum of warm and dense matter into elastic and inelastic components based on quantum perturbation theory. The calculation of the elastic component is achieved through first-principles molecular dynamics and finite-temperature density functional theory, while the calculation of the inelastic component is achieved through perturbation formulas of time-dependent density functional theory. The calculated elastic and inelastic components are then integrated to obtain the complete X-ray Thomson scattering spectrum of warm and dense matter. It uses first-principles to perform a complete and accurate simulation of the internal environment of warm and dense matter, ensuring that the final simulated X-ray Thomson scattering spectrum truly reflects the internal environment of warm and dense matter. This facilitates accurate spectral interpretation of the scattering spectrum obtained from actual measurements and improves the reliability of research on warm and dense matter.

[0051] According to quantum perturbation theory, under a specific momentum transfer q, the total intensity S(q,ω) of the X-ray Thomson scattering spectrum related to the photon frequency ω received by the detector can be expanded in the particle number representation by a set of orthogonal and complete single-particle energy eigenstates |n>, thus decomposing into an elastic part S1(q,ω) and an inelastic part S2(q,ω), i.e.

[0052] in, ρ e (q) represents the electron density ρ e Fourier transform of (r); f n =1 / {exp[(ε n -μ) / T e ]+1} is the occupancy number of the wave function |n>, ε n Let T be the energy eigenvalue of the wave function |n>, μ be the chemical potential, and T be the energy eigenvalue of the wave function |n>. e Let be the electronic temperature, <> represent the ensemble average over the ionic state, and δ(ω) be the Dirac delta function, i.e., satisfying . and Matrix element <n|e -iq·r |n> is represented as ψ n (r) represents the wave function |n> in coordinate space. Represents ψ n The complex conjugate of (r); It can be obtained directly through finite temperature density functional theory.

[0053] The inelastic portion S2(q,ω) of the X-ray Thomson scattering spectrum can be transformed into the response function χ(q,q',ω) using the fluctuation dissipation theorem, i.e.

[0054]

[0055] In the above formula, Im[] represents the imaginary part operation; q' = q means that two momentums are transferred q', and q is equal; V represents the volume of the system.

[0056] The response function can be obtained using finite-temperature density functional theory, commonly used in condensed matter spectroscopy, thus theoretically constructing a complete first-principles simulation method for X-ray Thomson scattering spectra. Here, the Dyson equation χ(q,q',ω)=χ is adopted. 0 (q,q',ω)+Σ q”q”' χ 0 The function (q,q”,ω)K(q”,q”',ω)χ(q”',q',ω) is used to calculate the response function, simplifying the computation. The kernel K(q,q',ω) simultaneously includes contributions from the Coulomb potential and the commutative correlation.

[0057] K(q,q',ω)=v c (q)δ qq' δ(ω)+f xc (q,q',ω)

[0058] In the above formula, v c (q) is the Fourier transform of the Coulomb potential, f xc (q,q',ω) represents the exchange-correlation kernel in density functional theory; δ qq’ It is the Kronecker delta function, i.e. χ 0 (q,q',ω) represents the non-interacting electronic response function, and its expression is as follows: Among them, matrix elements <n|e -iq·r |m> represents ψ m (r) represents the wave function |m> in coordinate space. The wave function |n> is expressed in coordinate space as ψ. nComplex conjugate of (r); matrix element <m|e -iq'·r |n> is represented as ψ n (r) represents the wave function |n> in coordinate space. The wave function |m> is expressed in coordinate space as ψ. m The complex conjugate of (r); f n =1 / {exp[(ε n -μ) / T e ]+1} is the occupancy number of the wave function |n>, ε n f represents the energy eigenvalues ​​of the wave function |n>. m =1 / {exp[(ε m -μ) / T e ]+1} represents the occupancy number of the wave function |m>, ε m Let be the energy eigenvalue of the wave function |m>; η represents the adiabatic factor, which is an infinitesimal positive number approaching 0.

[0059] Preferably, in step S1, the equilibrium ion configuration is simulated according to the finite temperature density functional theory to obtain the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum of the dense material, including:

[0060] The equilibrium ionic configuration was analyzed to obtain the corresponding static ionic structure factor S. ii (q);

[0061] Simulations based on finite-temperature density functional theory yielded the atomic shape factor N(q) of partially equilibrium ionic configurations and the elastic X-ray scattering intensity caused by partially ionized bound electrons.

[0062] Based on the ion static structure factor S ii Using (q) and atomic shape factor N(q), the elastic X-ray scattering intensity caused by spatial fluctuations in electron density is obtained.

[0063] Elastic X-ray scattering intensity caused by spatial fluctuations in electron density and the intensity of elastic X-ray scattering caused by partial ionization The total integrated intensity S1(q) of the elastic component of the X-ray Thomson scattering spectrum of a warm, dense material is obtained, i.e.

[0064] The beneficial effects of the above technical solution are as follows: by using the above method, only some equilibrium ion configurations need to be analyzed and processed, and it is not necessary to analyze all equilibrium ion configurations, which effectively reduces the computational workload of equilibrium ion configurations and improves the computational efficiency of the elastic part of X-ray Thomson scattering spectrum.

[0065] Preferably, in step S1, based on the ionic static structure factor S ii Using (q) and atomic shape factor N(q), the elastic X-ray scattering intensity caused by spatial fluctuations in electron density is obtained. include:

[0066] Using the following formula (1), based on the ionic static structure factor S ii Using (q) and atomic shape factor N(q), the elastic X-ray scattering intensity caused by spatial fluctuations in electron density is obtained.

[0067]

[0068] In the above formula (1), N i Indicates the number of ions.

[0069] The beneficial effects of the above technical solution are: in order to obtain accurate... High-precision pseudopotentials and a large number of ion configurations are required for ensemble averaging, the computational cost of which is beyond the capacity of existing first-principles simulations. Therefore, it is decomposed into the contribution S of ion structure. ii The contribution of (q) and the electron density distribution N(q) near each ion is reduced, thus decreasing the impact on The computational load.

[0070] Preferably, step S1 further includes:

[0071] Using the formula (2) below, the atomic shape factor N(q) is obtained.

[0072] N(q) = <ρ e (q) / ρ i (q)> (2)

[0073] In the above formula (2), ρ e (q) represents the electron density ρ e Fourier transform of (r); ρ i (q) represents the ion density ρ i Fourier transform of (r); <> represents the calculation of ensemble average; the meaning of the above formula (2) is that N(q) is equal to the electron density ρ e Fourier transform ρ of (r) e (q) divided by the ion density ρ i Fourier transform ρ of (r) i The ensemble mean of (q);

[0074] Using the following formula (3), the ionic static structure factor S is obtained. ii (q),

[0075] Sii (q)=<|ρ i (q)| 2 > / N i (3)

[0076] In the above formula (3), ρ i (q) represents the ion density ρ i Fourier transform of (r); || denotes the modulus operation; <> denotes the ensemble average operation; N i Indicates the number of ions.

[0077] The beneficial effects of the above technical solution are: S ii The calculation of N(q) requires a large number of ion configurations to be averaged, and the requirements for pseudopotential accuracy are relatively low; while the calculation of N(q) requires high-precision pseudopotentials, but only a small number of ion configurations. The above decomposition method will greatly save computational resources.

[0078] Preferably, in step S1, the ionic states of a warm-dense substance at a specific electron and ion temperature density are simulated using first-principles molecular dynamics to obtain a series of equilibrium ionic configurations, including:

[0079] Based on the modulus conservation and projected embellishment wave methods, different cutoff radii are selected to construct pseudopotentials suitable for warm and dense materials, thereby obtaining modulus conservation pseudopotentials and projected embellishment wave pseudopotentials.

[0080] Based on the projected augmented wave pseudopotential, and through first-principles molecular dynamics, the ionic states of warm-dense substances at specific electron and ion temperature densities are simulated, thereby obtaining a series of equilibrium ionic configurations including a first number of atoms and an equilibrium ionic configuration including a second number of atoms; wherein the first number of atoms is greater than the second number of atoms. The equilibrium ionic configuration including the first number of atoms corresponds to the equilibrium ionic configuration of a large system, and the equilibrium ionic configuration including the second number of atoms corresponds to the equilibrium ionic configuration of a small system.

[0081] The beneficial effects of the above technical solution are as follows: the corresponding ion density distribution ρ of the above series of equilibrium ion configurations including the first number of atoms and the equilibrium ion configurations including the second number of atoms. i (r) is: ρ i (r)=Σ j δ(rr j ), where r j Indicates the position of each ion, δ(rr) j ) represents the Dirac delta function, which is the same as the definition of the Dirac delta function mentioned above. For a series of large systems, ρ i (r) Perform a Fourier transform to obtain ρ i (q), and further according to formula Sii (q)=<|ρ i (q)| 2 > / N i Calculate S ii (q). A small number of ion configurations are extracted from the first-principles simulation results of the equilibrium ion configurations of a large system, and the single-electron eigenstates ψ are obtained by using the finite-temperature density functional theory method based on the mode-conserving pseudopotential. n (r) and the corresponding number of occupancy f n According to the formula ρ e (r)=Σ n f n |ψ n (r)| 2 The electron density ρ was obtained. e (r).

[0082] Then according to the formula Calculated matrix elements <n|e -iq·r |n> is represented as ψ n (r) represents the wave function |n> in coordinate space. Represents ψ n The complex conjugate of (r).

[0083] Preferably, in step S2, a simulation of the equilibrium ion configuration using finite-temperature density functional theory is performed to obtain the corresponding ground-state wavefunction, including:

[0084] The extracted portion includes the equilibrium ion configuration with the second atomic number. Simulations based on finite-temperature density functional theory are performed on the extracted equilibrium ion configuration to obtain the corresponding ground state wavefunction and its corresponding eigenenergy and occupation number.

[0085] The beneficial effects of the above technical solution are as follows: through the above method, the ground state wave of the corresponding equilibrium ion configuration can be analyzed and processed, providing a reliable basis for the subsequent determination of the electronic response function of different equilibrium ion configurations.

[0086] Preferably, in step S2, based on the ground state wavefunction, a time-dependent density functional theory perturbation formula is used to calculate the electronic response function χ(q,q',ω) corresponding to different equilibrium state ion configurations, including:

[0087] Based on the ground state wavefunction, determine the corresponding single-electron eigenstate ψ. n (r);

[0088] Based on the single-electron eigenstate ψ n (r), intrinsic energy ε n and the number of occupants f n Determine the non-interacting electronic response function χ.0 (q,q',ω);

[0089] Based on the Dyson equation for the electronic response function and the non-interacting electronic response function χ... 0 (q,q',ω) yields the electronic response function χ(q,q',ω) corresponding to different equilibrium state ion configurations.

[0090] The beneficial effects of the above technical solution are: non-interacting electronic response function χ 0 The expression for (q,q',ω) is as follows: Among them, matrix elements <n|e -iq·r |m> represents ψ m (r) represents the wave function |m> in coordinate space. The wave function |n> is expressed in coordinate space as ψ. n Complex conjugate of (r); matrix element <m|e -iq ' ·r |n> is represented as ψ n (r) represents the wave function |n> in coordinate space. The wave function |m> is expressed in coordinate space as ψ. m The complex conjugate of (r); f n =1 / {exp[(ε n -μ) / T e ]+1} is the occupancy number of the wave function |n>, ε n f represents the energy eigenvalues ​​of the wave function |n>. m =1 / {exp[(ε m -μ) / T e ]+1} represents the occupancy number of the wave function |m>, ε m Let be the energy eigenvalue of the wave function |m>; η represents the adiabatic factor, which is an infinitesimal positive number approaching 0.

[0091] According to the Dyson equation for the electronic response function, χ(q,q',ω)=χ 0 (q,q',ω)+Σ q”q”' χ 0 (q,q”,ω)K(q”,q”',ω)χ(q”',q’,ω), the response function χ(q,q’,ω) is obtained by calculating the perturbation formula of time-dependent density functional theory, where the kernel K(q,q’,ω) simultaneously includes the contributions of the Coulomb potential and the exchange correlation, i.e.

[0092] K(q,q',ω)=v c (q)δ qq' δ(ω)+f xc (q,q',ω)

[0093] Here, v c (q) is the Fourier transform of the Coulomb potential, f xc (q,q',ω) represents the exchange-correlation kernel in density functional theory; δ qq’ It is the Kronecker delta function, i.e.

[0094] Preferably, in step S2, the total intensity S2(q,ω) of the inelastic portion of the X-ray Thomson scattering spectrum of the dense material is obtained according to the electronic response function χ(q,q',ω), including:

[0095] The ensemble average of the electronic response function χ(q,q',ω) is expanded to obtain the average value <χ(q,q',ω)>. The average value <χ(q,q',ω)> is then transformed into the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum of warm and dense matter by the fluctuation dissipation theorem.

[0096] The beneficial effect of the above technical solution is that, through the above method, the total intensity of the inelastic part of the X-ray Thomson scattering spectrum of a dense material can be accurately calculated.

[0097] Preferably, in step S3, the complete total intensity S(q,ω) of the X-ray Thomson scattering spectrum of a warm, dense material is obtained based on the total integrated intensity S1(q) of the elastic component and the total intensity S2(q,ω) of the inelastic component of the X-ray Thomson scattering spectrum, including:

[0098] After broadening the total integrated intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum, the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum is obtained.

[0099] Then, the sum of the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum and the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum is taken as the complete total intensity S(q,ω) of the X-ray Thomson scattering spectrum, that is, S(q,ω)=S1(q,ω)+S2(q,ω).

[0100] The beneficial effects of the above technical solution are as follows: In actual calculations, the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum can be convolved with the instrument function g(ω) to obtain the experimentally observable inelastic part of the X-ray Thomson scattering spectrum ∫dω'S2(q,ω')g(ω-ω'). Combining S1(q,ω) and S2(q,ω), the complete first-principles calculation result of the X-ray Thomson scattering spectrum is obtained: S(q,ω)=S1(q)g(ω)+∫dω'S2(q,ω')g(ω-ω').

[0101] Preferably, in step S3, broadening the total integrated intensity S1(q) of the elastic component of the X-ray Thomson scattering spectrum to obtain the total intensity S1(q,ω) of the elastic component of the X-ray Thomson scattering spectrum includes:

[0102] The total integrated intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum is broadened by the experimentally measured instrument function g(ω) to obtain the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum, that is, S1(q,ω)=S1(q)g(ω).

[0103] The beneficial effects of the above technical solution are as follows: In actual calculations, broadening the total integrated intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum and the instrument function g(ω) can ensure the accuracy of the total intensity S1(q,ω) of the elastic part of the X-ray Thomson scattering spectrum.

[0104] As can be seen from the above embodiments, this first-principles X-ray Thomson scattering spectroscopy simulation method decomposes the scattering spectrum of warm-dense materials into elastic and inelastic components based on quantum perturbation theory. The calculation of the elastic component is achieved through first-principles molecular dynamics and finite-temperature density functional theory, while the calculation of the inelastic component is achieved through perturbation formulas of time-dependent density functional theory. The calculated elastic and inelastic components are then integrated to obtain the complete X-ray Thomson scattering spectrum of the warm-dense material. It uses first-principles to perform a complete and accurate simulation of the internal environment of the warm-dense material, ensuring that the final simulated X-ray Thomson scattering spectrum truly reflects the internal environment of the warm-dense material. This facilitates accurate spectral interpretation of the scattering spectrum obtained from actual measurements and improves the reliability of research on warm-dense materials.

[0105] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for simulating X-ray Thomson scattering spectrum based on first principles, comprising the following steps: S1, simulating ion states of a warm-dense matter at a specific electron and ion temperature density by first-principles molecular dynamics to obtain a series of equilibrium ion configurations, and simulating the equilibrium ion configurations according to a finite-temperature density functional theory to obtain a total integral intensity S1(q) of an elastic part of an X-ray Thomson scattering spectrum of the warm-dense matter; Step S2, performing simulation on the equilibrium ion configuration about finite temperature density functional theory to obtain a corresponding ground state wave function; according to the ground state wave function, performing time-dependent density functional theory perturbation formula calculation to obtain an electronic response function χ(q,q ,ω) corresponding to different equilibrium ion configurations; and then according to the electronic response function χ(q,q ,ω), obtaining the total intensity S2(q,ω) of the inelastic part of the X-ray Thomson scattering spectrum of the warm dense matter; wherein, q' and q each represent a momentum transfer; and ω represents a photon frequency received by a detector; S3, obtaining a complete total intensity S(q, ω) of the X-ray Thomson scattering spectrum of the warm-dense matter according to the total integral intensity S1(q) of the elastic part and a total intensity S2(q, ω) of a non-elastic part of the X-ray Thomson scattering spectrum, comprising: obtaining a total intensity S1(q, ω) of the elastic part of the X-ray Thomson scattering spectrum after broadening the total integral intensity S1(q) of the elastic part; The sum of the total intensity S1(q, ω) of the elastic part of the X-ray Thomson scattering spectrum and the total intensity S2(q, ω) of the inelastic part of the X-ray Thomson scattering spectrum is taken as the complete total intensity S(q, ω) of the X-ray Thomson scattering spectrum, i.e. . 2.The method for simulating X-ray Thomson scattering spectrum based on first principles according to claim 1, wherein: in the step S1, the total intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum of the warm-dense matter is obtained by simulating the equilibrium ion configurations according to the finite-temperature density functional theory, comprising: The equilibrium ionic configuration is analyzed to obtain the corresponding ionic static structure factor S ii (q); Based on the simulation of finite temperature density functional theory, the atomic shape factor N(q) of the partially equilibrium ion configuration and the elastic X-ray scattering intensity caused by the partially ionized bound state electrons are obtained (q); from the ion static structure factor S(q) ii (q) and the atomic shape factor N(q), the elastic X-ray scattering intensity caused by the spatial fluctuation of electron density (q); elastic x-ray scattering intensity due to spatial fluctuations of the electron density (q) and partial ionization (q), to obtain the total integrated intensity S1(q) of the elastic part of the x-ray Thomson scattering spectrum of the warm dense matter, i.e. (q) + (q)2 (q)2. 3.The method for simulating X-ray Thomson scattering spectrum based on first principles according to claim 2, wherein: In said step S1, the ion static structure factor S(q) is determined from the measured intensity I(q) of the elastic X-ray scattering ii (q) and the atomic shape factor N(q), obtaining the elastic X-ray scattering intensity I(q) caused by the spatial fluctuations of the electron density (q), comprising: Using the following equation (1), the elastic X-ray scattering intensity ii (q) caused by the spatial fluctuation of the electron density is obtained from the ion static structure factor S (q), （1） In the above formula (1), N i represents the number of ions. 4.The method for simulating X-ray Thomson scattering spectrum based on first principles according to claim 3, wherein: in the step S1, further comprising: obtaining the atomic shape factor N(q) by using the following formula (2), （2） In the above equation (2), ρ e (q) represents the Fourier transform of the electron density ρ e (r); ρ i (q) represents the Fourier transform of the ion density ρ i (r); denotes the ensemble average operation; the meaning of the above equation (2) is equal to the ensemble average of the Fourier transform of the electron density ρ e (r) divided by the Fourier transform of the ion density ρ e (r); and i (q) divided by the Fourier transform of the ion density ρ i (q). The ionic static structure factor S(q) is obtained using the following equation (3) ii (q), S ii (q)= (3) In the above equation (3), p i (q) denotes the Fourier transform of the ion density p i (r); denotes a modulo operation; denotes an ensemble average operation; N i denotes the number of ions. 5.The method for simulating X-ray Thomson scattering spectrum based on first principles according to claim 4, wherein: in the step S1, the ion states of the warm-dense matter at the specific electron and ion temperature density are simulated by the first-principles molecular dynamics to obtain the series of equilibrium ion configurations, comprising: selecting different cutoff radii to construct pseudo-potentials suitable for the warm-dense matter based on the plane-wave basis set method and the projector augmented wave method, so as to obtain the pseudo-potentials of the plane-wave basis set and the projector augmented wave; simulating the ion states of the warm-dense matter at the specific electron and ion temperature density by the first-principles molecular dynamics according to the pseudo-potentials of the projector augmented wave, so as to obtain a series of equilibrium ion configurations including a first atomic number and a series of equilibrium ion configurations including a second atomic number; wherein the first atomic number is greater than the second atomic number. 6.The method for simulating X-ray Thomson scattering spectrum based on first principles according to claim 5, wherein: in the step S2, the simulation on the finite-temperature density functional theory is carried out on the equilibrium ion configurations to obtain corresponding ground state wave functions, comprising: extracting part of the equilibrium ion configurations including the second atomic number, and carrying out the simulation on the finite-temperature density functional theory on the extracted equilibrium ion configurations to obtain corresponding ground state wave functions, and corresponding eigen-energies and occupation numbers.

7. The first-principles based X-ray Thomson scattering spectrum simulation method of claim 6, wherein the step S2 is performed by: calculating the total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum according to the formula: S1(q) = 4π2e2m2c2n(q)2. In the step S2, according to the ground state wave function, a time-dependent density functional theory perturbation formula calculation is carried out to obtain the electronic response function χ(q, q , ω) corresponding to different equilibrium ion configurations, including: According to the ground state wave function, a corresponding single electron eigenstate ψ is determined n (r); According to the single-electron eigenstate ψ n (r), the eigenenergy ε n , and the occupation number f n , a non-interacting electron response function χ 0 (q, q , ω) is determined; According to the Dyson equation of the electronic response function and the non-interacting electronic response function χ 0 (q,q ,ω), the electronic response functions χ(q,q ,ω) corresponding to different equilibrium ionic configurations are obtained.

8. The first-principles based X-ray Thomson scattering spectrum simulation method of claim 7, wherein the step S2 is performed by: calculating the total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum according to the formula: S1(q) = 4π2e2m2c2n(q)2. In the step S2, the total intensity S2(q, ω) of the inelastic part of the X-ray Thomson scattering spectrum of the warm dense matter is obtained according to the electronic response function χ(q, q , ω), including: expanding the electronic response function χ(q, q , ω) over an ensemble average, obtaining an average value , transforming the average value into the total intensity S2(q, ω) of the inelastic part of the X-ray Thomson scattering spectrum of the warm-dense matter by the fluctuation dissipation theorem.

9. The first-principles based X-ray Thomson scattering spectrum simulation method of claim 1, wherein the step S2 is performed by: calculating the total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum according to the formula: S1(q) = 4π2e2m2c2n(q)2. In the step S3, the total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum is broadened to obtain the total intensity S1(q, ω) of the elastic part of the X-ray Thomson scattering spectrum, including: The total integral intensity S1(q) of the elastic part of the X-ray Thomson scattering spectrum is broadened by the instrument function g(ω) measured by experiment to obtain the total intensity S1(q, ω) of the elastic part of the X-ray Thomson scattering spectrum, that is, S1(q, ω) = S1(q)g(ω).

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