Time-dependent Hartree-Fock Method Research Articles

Carbon monoxide ionization in femtosecond bicircular laser pulses

The CO ionization by 7.8 fs bicircular laser field consisting of the coherent superposition of two coplanar circularly polarized laser pulses is studied in the framework of the time-dependent Hartree–Fock method. Six different superpositions composed of a near-infrared pulse with wavelength of 780 nm and an ultraviolet pulse with wavelength ranging from 244 to 390 nm are considered. The intensity of the near-infrared laser pulse is 1.0 × 1014 W cm−2 and the intensity of the ultraviolet laser pulse runs from 5.0 × 1013 to 2.0 × 1014 W/cm2. Numerical results reveal that the ionization probabilities for counter-rotating field are enhanced compared to the ionization probabilities for co-rotating field only for the coherent superposition of 780 and 390 nm circularly polarized laser pulses. Our computations also emphasize that the highest occupied molecular orbital mainly contributes to CO ionization. The contribution of the inner valence molecular orbitals can be significantly increased by adjusting the intensity ratio and the relative phase between the two colors. Note that the co-rotating laser field consisting of the coherent superposition of two circularly polarized laser pulses of wavelengths 780 and 390 nm yields higher ionization probability when the positive direction of the electric field component along molecular axis points to the O nucleus.

Role of excited states in helium-like ions on high-order harmonic generation

We theoretically investigate high-order harmonic generation (HHG) of helium (He), lithium cation (Li+), and beryllium dication (Be2+) using the time-dependent Hartree–Fock method to solve the three-dimensional time-dependent Schrödinger equation. It is found that the intensity of the HHG increases significantly from a certain harmonic order below the ionization threshold, and the initial position of the enhancement does not depend on the intensity or the wavelength of the driving laser field. Further analysis shows that excited states play an important role on this enhancement, consistent with the excited-state tunneling mechanism [Phys. Rev. Lett. 116 123901 (2016)]. Our results unambiguously show that excited-state tunneling is essential for understanding the enhancement of HHG. Accordingly, a four-step model is herein proposed to illustrate the multiphoton excitation effect in helium-like ions, which enriches the physics of HHG enhancement.

Efficient simulation of multielectron dynamics in molecules under intense laser pulses: implementation of the multiconfiguration time-dependent Hartree–Fock method based on the adaptive finite element method

We present an implementation of the multiconfiguration time-dependent Hartree–Fock method based on the adaptive finite element method for molecules under intense laser pulses. For efficient simulations, orbital functions are propagated by a stable propagator using the short iterative Arnoldi scheme and our implementation is parallelized for distributed memory computing. This is demonstrated by simulating high-harmonic generation from a water molecule and achieves a simulation of multielectron dynamics with overwhelmingly less computational time, compared to our previous work [Sawada, R. et al. Phys. Rev. A, 2016, 93, 023434].

Investigation of the multielectron dynamics of CO in intense laser fields by the effective potential analysis of natural orbitals

We simulated the multielectron dynamics of CO in multicolor pulses of a near-IR fundamental ω and harmonics up to 4ω by using the multiconfiguration time-dependent Hartree-Fock method. The dynamics were analyzed in terms of effective potentials that govern the time evolution of molecular orbitals. The effective potential for the highest occupied orbital has a hump barrier responsible for anisotropic ionization of CO and the shape of a hump significantly changes at different internuclear distances. The electronic response became nonadiabatic when a 4ω-field was included, resulting in the enhancement in ionization and the extension of the high-order harmonic generation cutoff.

Time-dependent optimized coupled-cluster method with doubles and perturbative triples for first principles simulation of multielectron dynamics.

We report the formulation of a new, cost-effective approximation method in the time-dependent optimized coupled-cluster (TD-OCC) framework [T. Sato et al., J. Chem. Phys. 148, 051101 (2018)] for first-principles simulations of multielectron dynamics in an intense laser field. The method, designated as TD-OCCD(T), is a time-dependent, orbital-optimized extension of the “gold-standard” CCSD(T) method in the ground-state electronic structure theory. The equations of motion for the orbital functions and the coupled-cluster amplitudes are derived based on the real-valued time-dependent variational principle using the fourth-order Lagrangian. The TD-OCCD(T) is size extensive and gauge invariant, and scales as O(N 7) with respect to the number of active orbitals N. The pilot application of the TD-OCCD(T) method to the strong-field ionization and high-order harmonic generation from a Kr atom is reported in comparison with the results of the previously developed methods, such as the time-dependent complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and the time-dependent Hartree-Fock (TDHF) methods.

Multielectron effects in CO ionization by orthogonal two-color laser fields

We study the single ionization of CO molecule in orthogonally polarized two-color laser fields using time-dependent Hartree–Fock method. Employing the coherent superposition consisting of a fundamental field and its second harmonic, we consider different wavelengths (780 and 390nm) and intensities (1×1014, 1.5×1014 and 2×1014 W/cm2) of the fundamental field for which different ionization mechanisms are involved. Our numerical results reveal that the contributions of the three highest occupied molecular orbitals are strongly influenced by the intensity ratio and time delay between the two components of the bichromatic field. At the fundamental wavelength of 780nm and intensity of 2×1014 W/cm2, the two outermost molecular orbitals display a dominant response to the orthogonal two-color laser field when the second harmonic field is stronger than the fundamental field.

High-order harmonic generation from stretched C2H2 molecules in intense laser fields

We investigate the high harmonic generation from stretched acetylene molecules subjected to intense laser fields employing time-dependent Hartree-Fock methods. It is found that as the C-C and C-H bonds are stretched, the harmonic efficiency increases significantly due to the increased ionization of inner valence $\ensuremath{\sigma}$ orbitals in the monochromatic field, while the harmonic yield will be limited by the strong depletion of the ground-state population under a certain bond length. Moreover, the harmonic emission is affected by the nonadiabatic electron dynamics from the multiorbital coupling effects. In addition, by introducing a two-color field scheme for different C-H bond configurations with the fixed C-C bond, the aforementioned harmonic efficiency will be further enhanced due to laser-induced strong excitation from inner valence orbitals to initially unoccupied orbitals. The above results would be helpful for further understanding multiorbital dynamics in the harmonic generation from polyatomic molecules.

Excited states of a phosphorus pair in silicon: Combining valley-orbital interaction and electron-electron interactions

Excitations of impurity complexes in semiconductors can not only provide a route to fill the terahertz gap in optical technologies, but can also connect local quantum bits to scale up solid-state quantum-computing devices. However, taking into account both the interactions among electrons/holes, and the host band structures, is challenging. Here we combine first-principles band-structure calculations with quantum-chemistry methodology to evaluate the ground and excited states of a pair of phosphorous donors in silicon within s single framework. We use a broken-symmetry Hartree-Fock approach, followed by a time-dependent Hartree-Fock method to compute the excited states. Our Hamiltonian for each valley includes an anisotropic kinetic energy term, which splits the 2p_0 and 2p_+- transitions of isolated donors by ~4 meV, in good agreement with experiments. Our single-valley calculations show the optical response is a strong function of the optical polarisation, and suggest the use of valley polarisation to control optics and reduce oscillations in exchange interactions. When taking into account all valleys, including valley-orbital interactions, we find a gap opens between the 1s to 2p transition and low-energy charge-transfer states within 1s manifolds (which become optically allowed because of inter-donor interactions). In contrast to the single-valley case, we find charge-transfer excited states also in the triplet sector, thanks to the valley degrees of freedom. These states have a qualitatively correct energy as compared with the previous experiments; additionally, we predict new excitations below 20 meV that have not been analysed previously. A statistical average of nearest-neighbour pairs at different separations suggests that THz radiation could be used to excite pairs spin-selectively. Our approach can readily be extended to other donors and to other semiconducting hosts.

Manipulation of Multielectron Dynamics of Molecules by Fourier-Synthesized Intense Laser Pulses: Effective Potential Analysis of CO

We present a theoretical investigation as to how multielectron dynamics of CO are manipulated by Fourier-synthesized intense laser pulses. The pulses used are assumed to be comprised of harmonics up to the fourth order. The multiconfiguration time-dependent (TD) Hartree-Fock (MCTDHF) method, where the multielectron wavefunction Ψ(t) is expressed as a linear combination of various electron configurations, is employed to simulate the dynamics of CO interacting with Fourier-synthesized pulses. The multielectron nature such as electron correlation is quantified by using our effective potential approach. To begin with, the time-dependent natural orbitals {ϕj(r,t)} which diagonalize the first order reduced density matrix are obtained from Ψ(t), where r is the one-electron coordinate. The effective potentials υjeff(r,t) that determine the dynamics of ϕj(r,t) are then derived from the equations of motion for {ϕj(r,t)}. υjeff(r,t) consists of the one-body part υ1(t) including the interaction with the laser electric field ε(t) and the two-body part υ2,j(t) originating from electron-electron interaction. In this way, the role of electron correlation can be quantified by comparing υjeff(r,t) with those obtained by the TDHF method, where Ψ(t) is approximated by a single Slater determinant. We found a very similar profile in υ5σeff(r,t) of the 5σ highest occupied molecular orbital for both near-infrared one-color (ω) and directionally asymmetric ω+2ω two-color pulses; when ε(t) points from the nucleus C to O, a hump appears in υ5σeff(r,t) only 2 bohrs outward from C. The hump formation, which originates from the field-induced change in υ2,5σ(t) (especially, due to electron correlation), is responsible for preferential electron ejection from the C atom side (experimentally observed anisotropic ionization). A coherent superposition of ω and 2ω fields with an appropriate relative phase thus works as a one-color pulse of which either positive or negative peaks are filtered out. More sophisticated manipulation is possible by adding higher harmonics to a synthesized field. We show that the 5σ orbital can be squeezed toward the inside of the potential valley in υ5σeff(r,t), which encloses the molecule at a radius of ∼7 bohrs (semicircle in the region of z <0), by adjusting the phases of a ω+2ω+3ω+4ω field. The hump and valley formation in υ5σeff(r,t) are closely correlated with domains of increasing and decreasing electron density, respectively.

Hydrogen-molecule spectrum by the many-body GW approximation and the Bethe-Salpeter equation

We check the ab initio GW approximation and Bethe-Salpeter equation (BSE) many-body methodology against the exact solution benchmark of the hydrogen molecule H$_2$ ground state and excitation spectrum, and in comparison with the configuration interaction (CI) and time-dependent Hartree-Fock methods. The comparison is made on all the states we could unambiguously identify from the excitonic wave functions' symmetry. At the equilibrium distance $R = 1.4 \, a_0$, the GW+BSE energy levels are in good agreement with the exact results, with an accuracy of 0.1~0.2 eV. GW+BSE potential-energy curves are also in good agreement with the CI and the exact result up to $2.3 \, a_0$. The solution no longer exists beyond $3.0 \, a_0$ for triplets ($4.3 \, a_0$ for singlets) due to instability of the ground state. We tried to improve the GW reference ground state by a renormalized random-phase approximation (r-RPA), but this did not solve the problem.

Giant dipole resonance in Sm isotopes within TDHF method

In this work, we have studied the isovector giant dipole resonance (IVGDR) in even-even Sm isotopes within time-dependent Hartree–Fock (TDHF) with four Skyrme forces SLy6, SVbas, SLy5 and UNEDF1. The approach we have followed is somewhat similar to the one we did in our previous work in the region of neodymium (Nd, \(Z=60\)) [Physica Scripta (2020)]. We have calculated the dipole strength of \( ^{128-164}\text {Sm}\) and compared with the available experimental data. An overall agreement between them is obtained. The dipole strength in neutron-deficient \( ^{128-142}\text {Sm}\) and in neutron-rich \(^{156-164}\text {Sm}\) isotopes is predicted. Shape phase transition and shape coexistence in Sm isotopes are also investigated in the light of IVGDR. In addition, the correlation between the quadrupole deformation parameter \(\beta _{2}\) and the splitting \(\Delta E/ \bar{E}_{m}\) of the giant dipole resonance spectra is studied. The results confirm that \(\Delta E/ \bar{E}_{m}\) is proportional to quadrupole deformation \(\beta _{2}\).

Effects of intrachain disorder on photoexcitation in conjugated polymer chains

The luminescence efficiency of conjugated polymers has been a central topic in the study of light emitting. The effect of disorder plays an important role in generating excitons after the conjugated polymers have been excited by photons. In this paper, by using the Su-Schriffer-Heeger model, which has been modified to include intrachain disorder and electron correlation, we investigate the effects of disorder on the photoexcitation, especially on the yield of excitons in a conjugated polymer chain. We adopt the multi-configurational time-dependent Hartree–Fock method to solve the multi-electron time-dependent Schrödinger equation and the Newtonian equation of motion for the lattice vibration. The results show that after the photoexcitation relaxation process, the products of the disordered polymer chain are qualitatively distinct from those of the pure polymer chain. While the pairs of polarons can be generated directly after the photoexcitation in a pure polymer chain, the disorder favors excitons as the products of the photoexcitation, and the yield of excitons depends crucially on the kind and strength of the disorder. Furthermore, the influences of the electron correlation and the conjugation length on the yield of excitons are also discussed. Specifically, we find that in the case of diagonal disorder, when the conjugation length is short and the diagonal disorder is weak, the excitons are mainly generated by the recombination of two lattice defects with a high yield of excitons which will be reduced as the conjugation length increases. The excitons tend to be generated directly with a low yield of excitons which is enlarged as the disorder gets stronger when the conjugation length is long or the diagonal disorder is strong. The on-site Coulomb repulsion favors the generation of excitons as well. The case of off-diagonal disorder is similar to that of diagonal disorder except that the on-site Coulomb potential favors the generation of excitons in the weak disorder regime but depresses the generation of excitons in the strong disorder regime. When both diagonal and off-diagonal disorders are considered, the yield of excitons is dominated by the off-diagonal disorder. We hope that our investigations can provide useful guidance and help for designing organic photoelectric materials and devices.

Synthesis, physicochemical properties and computational study of donor–acceptor polymer for optical limiting application

A new donor–acceptor configured π-conjugated polymer P1 with alkoxy pendant groups having cyclic diimide and thiophene core moieties in polymer backbone were efficiently synthesized via polycondensation reaction. The incorporation of cyclic diimide in polymer increased the rigidity and thermal stability of polymer backbone aided by its high Tg value. These chromophores assisted in reducing the steric interaction of bulky alkoxy pendants which supported lowering the bandgap. The donor and acceptor moieties along with π spacers were particularly chosen to enhance the π-conjugation length in the polymer thereby increasing its nonlinear optical absorption i.e. two-photon absorption. The various structure–property relationships of the polymer were characterized by UV–Vis absorption, fluorescence emission, cyclic voltammetry, and density functional theory studies. The molecular nonlinear properties were theoretically evaluated through the calculation of polarizabilities and hyperpolarizabilities using time-dependent Hartree–Fock method. The polymer showed enhanced effective two-photon absorption with an absorption coefficient ( $$\beta_{eff}$$ ) of 2.031 × 10−10 m/W obtained from open aperture Z-scan analysis which is in good agreement with theoretical study.

Ionization of carbon monoxide in intense infrared femtosecond laser pulses

Using the time-dependent Hartree-Fock method, the CO ionization in intense femtosecond laser pulses at infrared wavelengths has been investigated. We have considered a laser intensity domain (4 × 1013–1.4 × 1014 W/cm2) in which the tunneling ionization mechanism plays an important role in the intense field ionization of CO. A dominant contribution of the highest occupied molecular orbital was found.

Study of laser-driven multielectron dynamics of Ne atom using time-dependent optimised second-order many-body perturbation theory

We calculate the high-harmonic generation (HHG) spectra, strong-field ionisation, and time-dependent dipole-moment of Ne using explicitly time-dependent optimised second-order many-body perturbation method (TD-OMP2) where both orbitals and amplitudes are time-dependent. We consider near-infrared (800 nm) and mid-infrared (1200 nm) laser pulses with very high intensities (, , and ), required for strong-field experiments with the high-ionisation potential (21.6 eV) atom. We compare the result of the TD-OMP2 method with the time-dependent complete-active-space self-consistent field method and the time-dependent Hartree-Fock method. Further, we report the implementation of the TD-CC2 method within the chosen active space, which is also a second-order approximation to the TD-CCSD method, and present results of time-dependent dipole-moment and HHG spectra with an intensity of at a wavelength of 800 nm. It is found that the TD-CC2 method is not stable in the case with a higher laser intensity, and it does not provide a gauge-invariant description of the physical properties, which makes TD-OMP2 a superior choice to reach out to larger chemical systems, especially for the study of strong-field dynamics. The obtained results indicate that the TD-OMP2 method shows moderate performance, overestimating the response of Ne, while TDHF underestimates it..

Time-dependent generator coordinate method for many-particle tunneling

It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering of two α particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.

Time-dependent optimized coupled-cluster method for multielectron dynamics. III. A second-order many-body perturbation approximation.

We report successful implementation of the time-dependent second-order many-body perturbation theory using optimized orthonormal orbital functions called time-dependent optimized second-order many-body perturbation theory to reach out to relatively larger chemical systems for the study of intense-laser-driven multielectron dynamics. We apply this method to strong-field ionization and high-order harmonic generation of Ar. The calculation results are benchmarked against ab initio time-dependent complete-active-space self-consistent field, time-dependent optimized coupled-cluster double, and time-dependent Hartree-Fock methods, as well as a single active electron model to explore the role of electron correlation.

Excited states of molecular and crystalline acetylene: application of TDHF and BSE via density fitting methods

Low-lying states in small, multiply bonded hydrocarbon molecules may be divided into valence and Rydberg excitations. Excited states of the cubic phase of the acetylene molecular crystal are calculated using the time-dependent Hartree–Fock (TDHF) method. TDHF and Bethe–Salpeter equation (BSE) calculations are performed on molecular CH in order to interpret these excited states. Computationally inexpensive TDHF and BSE methods are compared to previous CASPT2, MRCI and EOM-CCSD calculations and experiment. Localised, lowest energy excited states in the CH molecular crystal mirror those in the gas phase. In the next lowest excitations the electron and hole separate over one or two shells of molecular neighbours. A density fitting method for calculating the Coulomb matrix elements which arise in time-dependent Hartree Fock theory (TDHF) in periodic systems is implemented in the Exciton code and described briefly.

Excited-state populations in the multiconfiguration time-dependent Hartree–Fock method

We study time-dependent populations in the excited states of many-electron atoms and molecules with the multiconfiguration time-dependent Hartree–Fock method and reveal the non-stationary behavior of the excited-state populations during field-free propagation originating from the nonlinear character of the equations of motion. We calculate the time-dependent populations of the three lowest singlet S states in a helium atom for two different cases of intense laser-atom interaction. In the first case, He is excited by a VUV pulse with the central wavelength of 108 nm, which is two-photon resonant with the transition. In the second case, He is excited by an off-resonant UV laser pulse with the central wavelength of 200 nm. We obtain the stationary wave functions of the excited states by imaginary time propagation and show that the populations oscillate as a function of time even after the laser pulse has vanished. The time-dependent variations in the populations in the respective eigenstates can be sufficiently suppressed when the number of orbitals adopted in the expansion of the wave function exceeds eight.

Giant dipole resonance and shape evolution in Nd isotopes within TDHF method

The isovector giant dipole resonance (IVGDR) in even–even Nd isotopes from A = 124 to A = 160 is studied in the framework of time-dependent Hartree–Fock (TDHF) with Skyrme forces SkI3, SVbas, SLy5 and SLy6. The dipole strength is calculated and compared with the experimental data on photon absorption cross section σγ. An overall agreement between them is obtained. The dipole strengths in 124–140Nd and 152–160Nd are predicted. In addition, the correlation between the quadrupole deformation parameter β2 and the splitting of the giant dipole resonance (GDR) spectra is studied. The results confirm that is proportional to β2. Shape phase transition in Nd isotopes is also investigated in the light of IVGDR.