A comparison of efficiency and accuracy of two-electron integrals calculation between two methods in multi-configuration time-dependent hartree fock frame

An approach to the evaluation of the two-electron repulsion integrals exactly in sine finite basis representation is proposed. The two-electron coulomb potential integrals are calculated respectively in sine finite basis representation by using two-fold Gaussian quadrature rules and in discrete variable representation by using the natural potential expansion of coulomb potential $r_{12} $ . The efficiency and accuracy of two methods to calculate the two-electron repulsion integrals are compared. Some demonstrative calculations indicate that both the two ways are effective methods to do two-electron integrals calculations in the multi-configuration time-dependent hartree fock (MCTDHF) frame. By using the method to calculate the two-electron integrals in sine FBR, the working equations of MCTDHF are propagated in imaginary time. The ground state energy of helium atom obtained in the imaginary propagation is close to the Full Configuration interaction energy calculated by Molpro.     

Excitation energies,oscillator strengths,and frequency dependent polarizabilities of Be: Comparison of TDHF,EOM (second order), and MCTDHF

Low-lying excitation energies from the ground state of Be were calculated using a basis set of 61 Cartesian Gaussian functions. Three approximations were employed: the time-dependent Hartree–Fock (TDHF ), second-order equations-of-motion (EOM ), and multiconfigurational time-dependent Hartree–Fock (MCTDHF ). The TDHF excitation energies are 0.5–1.1 eV lower than experiment, and the EOM values are 0.3–1.2 eV lower than experiment, whereas the MCTDHF excitation energies deviate on the absolute average from experiment by only 0.03 eV. We found that in an MCTDHF calculation, any proper MCSCF stationary point is a good reference (i.e., initial) state, not just the ground state. Experimental values for oscillator strength are accurately known only for the 2s²X¹S → 2s2p¹P⁰ transition. The TDHF value and the MCTDHF value agree with experiment, but the EOM value does not. The agreement of the TDHF value with experiment seems to be coincidental, because for higher lying transitions the TDHF values differ by approximately a factor of two or more from the more accurate MCTDHF . Frequency independent polarizabilities, α(0), were also calculated with the TDHF , HRPA , and MCTDHF and frequency dependent polarizabilities, β(ω), were calculated with the MCTDHF . No experimental data for Be polarizabilities exist, but we expect the MCTDHF values to be among the most accurate calculations available.     

Time-dependent approach to electronically excited states of molecules with the multiconfiguration time-dependent Hartree-Fock method

In this paper the authors show how the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method can be used for the calculation of electronic properties of molecules associated with the population of excited states. In contrast to other methods for correlated electron dynamics, such as configuration interaction, MCTDHF does not rely on a solution of the electronic Schrodinger equation prior to the propagation. The authors apply this approach to the calculation of vertical excitation energies, transition dipole moments, and oscillator strengths for two test molecules, lithium hydride and methane.     

Two-photon ionization of helium studied with the multiconfigurational time-dependent Hartree-Fock method

The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is applied for simulations of the two-photon ionization of helium. We present results for the single and double ionizations from the ground state for photon energies in the nonsequential regime and compare them to direct solutions of the Schro?dinger equation using the time-dependent (full) configuration interaction (TDCI) method. We find that the single ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI.     

Unified view on multiconfigurational time propagation for systems consisting of identical particles

We show that the successful and formally exact multiconfigurational time-dependent Hartree method (MCTDH) takes on a unified and compact form when specified for systems of identical particles (MCTDHF for fermions MCTDHB for bosons). In particular the equations of motion for the orbitals depend explicitly and solely on the reduced one- and two-body density matrices of the system's many-particle wave function. We point out that this appealing representation of the equations of motion opens up further possibilities for approximate propagation schemes.     

多组态含时自旋非限制HartreeFock理论

基于自旋非限制HartreeFock理论,发展了自旋非限制多组态含时HartreeFock理论方法来研究激光场中的多电子相关动力学．自旋向上和自旋向下的自旋轨道分别在他们各自的子空间内传播;并通过约化密度矩阵和平均场算符相互作用．分别利用了自旋限制和非限制的多组态含时HartreeFock方法虚时和实时传播计算氦原子基态能量和电离几率．自旋非限制的计算结果与其他报道相吻合．     

Origin of electronic structure and time-dependent state averaging in the multi-configuration time-dependent Hartree–Fock approach to electron dynamics

In this Letter, we discuss problems that can arise in the interpretation of results obtained by quantum dynamical simulations with the multi-configuration time-dependent Hartree–Fock (MCTDHF) method. In particular, we show that an effect, which can be seen as the time-dependent version of the state averaging known from standard quantum chemistry, can modify the electronic structure as derived from such a simulation. We illustrate our findings with numerical calculations for the laser excitation of a water molecule, with a Gaussian Type Orbital basis set.     

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor–corrector time integration schemes. The Coulomb contribution to the Kohn–Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.     

Photoabsorption spectra of boron nitride fullerenelike structures

Optical absorption spectra have been calculated for a series of boron nitride fullerenelike cage structures BnNn of sizes n=12-36. The method used is a real-time, real-space implementation of the time-dependent density-functional theory, involving the full time propagation of the time-dependent Kohn-Sham equations. The spectra are found to be a possible tool for distinguishing between different boron nitride fullerene species and isomers. The trends and differences in the spectra are found to be related to the general geometry of the molecules. Comparison between local-density and generalized-gradient approximations for electron exchange-correlation functionals shows that both of them produce essentially the same spectral characteristics.     

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.     

Theoretical study of excitations in furan: spectra and molecular dynamics

The excitation spectra and molecular dynamics of furan associated with its low-lying excited singlet states 1A2(3s), 1B2(V), 1A1(V'), and 1B1(3p) are investigated using an ab initio quantum-dynamical approach. The ab initio results of our previous work [J. Chem. Phys. 119, 737 (2003)] on the potential energy surfaces (PES) of these states indicate that they are vibronically coupled with each other and subject to conical intersections. This should give rise to complex nonadiabatic nuclear dynamics. In the present work the dynamical problem is treated using adequate vibronic coupling models accounting for up to four coupled PES and thirteen vibrational degrees of freedom. The calculations were performed using the multiconfiguration time-dependent Hartree method for wave-packet propagation. It is found that in the low-energy region the nuclear dynamics of furan is governed mainly by vibronic coupling of the 1A2(3s) and 1B2(V) states, involving also the 1A1(V') state. These interactions are responsible for the ultrafast internal conversion from the 1B2(V) state, characterized by a transfer of the electronic population to the 1A2(3s) state on a time scale of approximately 25 fs. The calculated photoabsorption spectrum of furan is in good qualitative agreement with experimental data. Some assignments of the measured spectrum are proposed.     

Ultrasoft pseudopotentials in time-dependent density-functional theory

We describe an efficient formulation allowing the use of ultrasoft pseudopotentials (USPPs) in plane wave based time-dependent density-functional theory. The practical steps required to implement USPP functionality within real time propagation schemes and linear-response schemes based on Lanczos algorithms are provided. The functioning of the methodology is demonstrated by calculations of the optical absorption spectra of the fullerene C(60), using both real time propagation and the Lanczos/linear-response approaches. Comparisons between the rates of convergence of the optical spectra with the number of applications of the Hamiltonian required in calculations with ultrasoft pseudopotentials and norm-conserving pseudopotentials show clearly the benefits provided by the use of USPP.     

Self-trapping of the N-H vibrational mode in alpha-helical polypeptides

Recent calculations on the formation of self-trapped amide group vibrational states in alpha-helical polypeptides [J. Chem. Phys. 124, 134907 (2006)] are extended to the amide N-H normal mode vibrations. First, the adiabatic N-H vibrational single- and two-exciton states are examined by treating the longitudinal chain coordinates as parameters. Then, in using the multiconfiguration time-dependent Hartree method coupled exciton-chain vibrational quantum dynamics are accounted for. Based on the respective exciton-chain vibrational wave function propagation the infrared transient absorption related to a sequential pump-probe experiment is calculated. The modulation of local amide vibrational energies by the longitudinal chain coordinates is found to have a pronounced effect on the broadening of absorption lines. Moreover, the ultrafast exciton transfer in the system is studied in order to characterize the dynamics of the self-trapped single-exciton states on a time scale below 10 ps.     

On the calculation of circular dichroism spectra using quantum wave-packet dynamics with an application to molecular dimers

Circular dichroism (CD) spectra are calculated from the Fourier transform of a time-correlation function. The latter can efficiently be evaluated by wave-packet propagation methods. This approach is similar to the time-dependent evaluation of absorption or Raman spectra. As an application, correlation functions and CD spectra for a molecular dimer are determined and compared to the case of absorption.