The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the expectation values for the hyperfine splittings of the 5d96s2 2D3/2 and 5d96s2 2D5/2 levels of atomic gold. One-, two-, and three-body electron correlation effects involving all 79 electrons have been included in a systematic manner. The approximation employed in this study is equivalent to a Complete Active Space (CAS) approach. Calculated electric field gradients, together with experimental values of the electric quadrupole hyperfine structure constants, allow us to extract a nuclear electric quadrupole moment Q(197Au)=521.5(5.0) mb.
The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p ^3 P_0 $ state through 2-photon E1M1 and hyperfine induced channels is also studied.
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 ionization from the groundstate for photon energies in the non-sequential regime, and compare them to direct solutions of the Schrödinger equation using the time-dependent (full) Configuration Interaction method (TDCI). We find that the single-ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI.
We are reinvestigating the hyperfine structure of sodium using a fully relativistic multiconfiguration approach. In the fully relativistic approach, the computational strategy somewhat differs from the original nonrelativistic counterpart used in Jönsson et al. (Phys. Rev. A 53 (1996) 4021). Numerical instabilities force us to use a layer-by-layer approach that has some broad unexpected effects. Core correlation is found to be significant and therefore requires to be described in an adequate orbital basis. The natural-orbital basis provides an interesting alternative to the orbital basis from …
Large-scale calculations of atomic structures and radiative properties have been carried out for singly, doubly- and trebly ionized cerium. For this purpose, the purely relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method was used, taking into account the effects of valence-valence and core-valence electronic correlations in detail. The results obtained were then used to calculate the expansion opacities characterizing the kilonovae observed as a result of neutron star mergers. Comparisons with previously published experimental and theoretical studies have shown that the results p…
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.
The multiconfiguration Dirac-Hartree-Fock (MCDHF) method has been employed to calculate atomic electric dipole moments (EDM) of 225^Ra, 199^Hg, and 171^Yb. For the calculations of the matrix elements we extended the relativistic atomic structure package GRASP2K. The extension includes programs to evaluate matrix elements of (P, T)-odd e-N tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole interaction, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions were accoun…
Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic dipole (M1) transition probabilities are reported for transitions between levels of 3d^5 in [Fe IV]. The accuracy of the ab initio energy levels and the agreement in the length and velocity forms of the line strength for the E2 transitions are used as indicators of accuracy. The present E2 and M1 transition probabilities are compared with earlier Breit-Pauli results and other theories. An extensive set of transition probabilites with indicators of accuracy are reported in Appendices A and B. Recommended values of A(E2)…
We use the multiconfiguration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach (GRASP2K) to provide a consistent set of transition energies and radiative transition data for the lower $n =3$ states in all Cl-like ions of astrophysical importance, from \ion{Cr}{8} to \ion{Zn}{14}. We also provide excitation energies calculated for \mbox{Fe X} using the many-body perturbation theory (MBPT, implemented within FAC). The comparison of the present MCDHF results with MBPT and with the available experimental energies indicates that the theoretic…
The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $ 4s 4p \,\, ^3 \! P^o_{1} $ and $ 4s 4p \,\, ^3 \! P^o_{2} $ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $ Q(^{67}{\rm Zn}) = 0.122(10) $ b. The error bar has been evaluated in a q…
The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set of transitions between low-lying states in neutral zinc. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Within this computational approach, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope shift factors…
The multi-configuration Dirac-Hartree-Fock method was employed to calculate the total and excitation energies, oscillator strengths and hyperfine structure constants for low-lying levels of Sm I. In the first-order perturbation approximation, we systematically analyzed correlation effects from each electrons and electron pairs. It was found that the core correlations are of importance for physical quantities concerned. Based on the analysis, the important configuration state wave functions were selected to constitute atomic state wave functions. By using this computational model, our excitatio…
The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of isotope shifts for several well-known transitions in neutral magnesium. Relativistic normal and specific mass shift factors as well as the electronic probability density at the origin are calculated. Combining these electronic quantities with available nuclear data, energy and transition level shifts are determined for the $^{26}$Mg$-^{24}$Mg pair of isotopes. Different models for electron correlation are adopted. It is shown that although valence and core-valence models provide accurate valu…
Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the $2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and $2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference (SD-MR) expansions. The largest components of the single reference MCHF wave functions are selected to …
The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set of transitions between low-lying states in neutral aluminium. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Two computational approaches are adopted for the estimation of the mass- and field shift factors. Within these approaches, different models for electron correlation are explored in a systematic way to determine a reliabl…
In this paper, we used the multiconfiguration Dirac-Fock method to compute with high precision the influence of the hyperfine interaction on the $[Ar]3d^{10} 4s4p ^3P_0$ level lifetime in Zn-like ions for stable and some quasi-stable isotopes of nonzero nuclear spin between Z=30 and Z=92. The influence of this interaction on the $[Ar]3d^{10} 4s4p ^3P_1 - [Ar]3d^{10} 4s4p ^3P_0$ separation energy is also calculated for the same ions.
The multiconfiguration Dirac-Hartree-Fock theory (MCDHF) has been employed to calculate the electric dipole moment of the 7s6d 3D2 state of radium induced by the nuclear Schiff moment. The results are dominated by valence and core-valence electron correlation effects. We show that the correlation effects can be evaluated in a converged series of multiconfiguration expansions.
The $K$-shell level radiative, non-radiative, and total widths, $K$-shell fluorescence yields and $K$-shell hole state lifetimes for atoms with 20$\le$Z$\le$30 have been calculated in fully-relativistic way using the extensive multiconfiguration Dirac-Fock calculations with the inclusion of the Breit interaction and QED corrections and also using multiconfiguration Dirac-Hartree-Slater calculations.
Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^4 3d$, $3s 3p^2 3d^2$, $3s 3p^3 4p$, $3s 3p^4$, $3s^2 3d^3$, $3s^2 3p^2 3d$, $3s^2 3p^2 4d$, $3s^2 3p^2 4s$, $3p^3 3d^2$, $3p^5$, $3s 3p 3d^3$, $3s 3p^3 3d$, $3s 3p^3 4s$, $3s^2 3p 3d^2$, %$3s^2 3p^2 4f$, $3s^2 3p^2 4p$, $3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states an…
We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation (HHG) of H2 and H2O. The present implementation will open a way to the first-principle theoretical study of intense-field and attosecond-pulse induced ultrafast phenomena in general molecules.
Hyperfine structure parameters are calculated for the 2p2(3P)3s 4P_J, 2p2(3P)3p 4Po_J and 2p2(3P)3p 4Do_J levels, using the ab initio multiconfiguration Hartree-Fock method. The theoretical hyperfine coupling constants are in complete disagreement with the experimental values of Jennerich et al. (EPJD 40(2006), 81) deduced from the analysis of the near-infrared Doppler-free saturated absorption spectra.
In previous work devoted to {\it ab initio} calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic $LS$-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms $2p^4(^3\!P) 3…
The fully relativistic multiconfiguration Dirac--Hartree--Fock method is used to compute excitation energies and lifetimes for the 143 lowest states of the $3s^23p^3$, $3s3p^4$, $3s^23p^23d$, $3s3p^33d$, $3p^5$, $3s^23p3d^2$ configurations in P-like ions from Cr X to Zn XVI. Multipole (E1, M1, E2, M2) transition rates, line strengths, oscillator strengths, and branching fractions among these states are also given. Valence-valence and core-valence electron correlation effects are systematically accounted for using large basis function expansions. Computed excitation energies are compared with t…
A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation o…
Regarding trapped-ion microwave-frequency standards, we report on the determination of hyperfine splittings and Landé $g_J$ factors of $^{111,113}$Cd$^+$. The hyperfine splittings of the $5p~^2P_{3/2}$ state of $^{111,113}$Cd$^+$ ions were measured using laser-induced fluorescence spectroscopy. The Cd$^+$ ions were confined in a linear Paul trap and sympathetically cooled by Ca$^+$ ions. Furthermore, the hyperfine splittings and Landé $g_J$ factors of the $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ levels of $^{111,113}$Cd$^+$ were calculated with greater accuracy using the multiconfiguration Dirac-…
Multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations were performed for 28 and 78 states in neutral and singly ionized aluminium, respectively. In Al I, the configurations of interest are $3s^2nl$ for $n=3,4,5$ with $l=0$ to $4$, as well as $3s3p^2$ and $3s^26l$ for $l=0,1,2$. In Al II, the studied configurations are, besides the ground configuration $3s^2$, $3snl$ with $n=3$ to $6$ and $l=0$ to $5$, $3p^2$, $3s7s$, $3s7p$ and $3p3d$. Valence and core-valence electron correlation effects are systematically accounted for through large confi…
We use relativistic Hartree-Fock and correlation potential methods to calculate nuclear spin-dependent parity non-conserving amplitudes (dominated by the nuclear anapole moment) between hyperfine structure components of the ground state of odd isotopes of K, Rb, Cs, Ba+, Yb+, Tl, Fr, and Ra+. The results are to be used for interpretation of current and future measurements.
Employing two state-of-the-art methods, multiconfiguration Dirac--Hartree--Fock and second-order many-body perturbation theory, highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the $2s^{2} 2p^{3}$, $2s 2p^{4}$, $2p^{5}$, $2s^{2} 2p^{2} 3l$~($l=s,p,d$), $2s 2p^{3}3l$ ($l=s,p,d$), and $2p^{4} 3l$ ($l=s,p,d$) configurations in nitrogen-like Ge XXVI. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé $g_{J}$-factors, and E1, E2, M1, M2 line strengths, oscillator strengths, and trans…
Large-scale $\textit{ab initio}$ calculations of the electric field gradient, which constitutes the electronic contribution to the electric quadrupole hyperfine constant $B$, were performed for the $5s^25p6s$ $^{1,3}\!P^{\rm o}_1$ excited states of tin, using three independent computational strategies of the variational multiconfiguration Dirac-Hartree-Fock method and a fourth approach based on the configuration interaction Dirac-Fock-Sturm theory. For the $5s^25p6s$ $^{1}\!P^{\rm o}_1$ state, the final value of $B/Q =703(50)$ MHz/b differs by $0.4\%$ from the one recently used by Yordanov ${\…
We present highly correlated multi-configuration Hartree-Fock (MCHF) calculations of the hyperfine structure of the 3p5 2Po_J levels of {33}S- and {35,37}Cl. We obtain a good agreement with observation. The hyperfine structure of the neutral sulfur {33}S 3p4 3P_J lowest multiplet that has never been measured to the knowledge of the authors, is also estimated theoretically. We discuss some interesting observations made on the description of the atomic core in MCHF theory.
In the framework of the multiconfiguration Dirac-Hartree-Fock method, we investigate the transition properties of four excited states in the $2p^53s$ configuration of neutral neon. The electron correlation effects are taken into account systematically by using the active space approach. The effect of higher-order correlation on fine structures is shown. We also study the influence of the Breit interaction and find that it reduces the oscillator strength of the $^3P^o_1 - ^1S_0$ transition by 17%. It turns out that the inclusion of the Breit interaction is essential even for such a light atomic…
The hyperfine interaction constants of the 2p4(3P)3p 2Do_{3/2,5/2}, 4Do_{1/2-7/2} and 4Po_{1/2-5/2} levels in neutral fluorine are investigated theoretically. Large-scale calculations are carried out using the multiconfiguration Hartree-Fock (MCHF) and Dirac-Hartree-Fock (MCDHF) methods. In the framework of the MCHF approach, the relativistic effects are taken into account in the Breit-Pauli approximation using non relativistic orbitals. In the fully relativistic approach, the orbitals are optimized using the Dirac-Coulomb Hamiltonian with correlation models inspired by the non relativistic ca…
Relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) are carried out for the $^{1}S_{0}$ and $^{3}P_{0,1}^o$ states in neutral ytterbium by use of the available GRASP2018 package. From the resultant atomic state functions and the RIS4 extension, we evaluate the mass and field shift parameters for the $^{1}S_{0}-\,^{3}P_{0}^o$ (clock) and $^{1}S_{0}-\,^{3}P_{1}^o$ (intercombination) lines. We present improved estimates of the nuclear charge parameters, $λ^{A,A'}$, and differences in mean-square charge radii, $δ\langle r^2\rangle^{A,A'}$, an…
We have systematically investigated the ground-state hyperfine structure for alkali-metal atoms ^{87}Rb, ^{133}Cs, ^{211}Fr and alkali-metal-like ions ^{135}Ba^+, ^{225}Ra^+, which are of particular interest for parity violation studies. The quantum electrodynamic one-loop radiative corrections have been rigorously evaluated within an extended Furry picture employing core-Hartree and Kohn-Sham atomic potentials. Moreover, the effect of the nuclear magnetization distribution on the hyperfine structure intervals has been studied in detail and its uncertainty has been estimated. Finally, the theo…
Theoretical approaches to the photoionization of few-electron atoms are discussed. These include nonequilibrium Greens functions and wave function based approaches. In particular, the Multiconfiguration Time-Dependent Hartree-Fock method is discussed and applied to a model one-dimensional atom with four electrons. We compute ground state energies and the time-dependent photoionization by the field a strong laser pulse with two different frequencies in the ultraviolet.
Atomic quadrupole moments and hyperfine constants of the metastable $^2 D_{3/2, 5/2}$ states of Ca$^+$, Sr$^+$, Ba$^+$, Yb$^+$, and Hg$^+$ are calculated by the multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods. For Hg$^+$, the configuration is $5d^9 6s^2$. For the other ions, the configuration consists of a single $d$-electron outside a set of closed shells. Current interest in the quadrupole moments of these states is due to the fact that optical transitions of these ions may be useful as references for frequency standards. Energy shifts of the metastab…
To search for the temporal variation of the fundamental constants one needs to know dependence of atomic transition frequencies on these constants. We study the dependence of the hyperfine structure of atomic $s$-levels on nuclear radius and, via radius, on quark masses. An analytical formula has been derived and tested by the numerical relativistic Hartree-Fock calculations for Rb, Cd$^+$, Cs, Yb$^+$ and Hg$^+$. The results of this work allow the use of the results of past and future atomic clock experiments and quasar spectra measurements to put constrains on time variation of the quark mass…
This work is an ab initio study of the 2p3 4So_3/2, and 2Do_{3/2,5/2} states of C- and 2p2 3P_{0,1,2}, 1D_2, and 1S_0 states of neutral carbon. We use the multi-configuration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all C- detachment thresholds, including correlation effects to about 0.5%. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intra-configuration transition probabilities are also estimated.
State-of-the-art relativistic multiconfiguration Dirac-Hartree-Fock calculations have been performed to evaluate the electronic field and mass isotope shift factors of the Cu~I resonance line at $λ= 324.8$~nm. A linear correlation between the mass factors and the transition energy is found for elaborate correlation models, allowing extrapolation to the observed frequency limit. The relativistic corrections to the recoil operator reduces the transition mass factor by 5~\%.
Removal energies and hyperfine constants of the lowest four $ns, np_{1/2}$ and $np_{3/2}$ states in Na, K, Rb and Cs are calculated; removal energies of the n=7--10 states and hyperfine constants of the n=7 and 8 states in Fr are also calculated. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock (DHF) wave functions are included to all-orders in perturbation theory. Using SD wave functions, accurate values of removal energies, electric-dipole matrix elements and static polarizabilities are obtained, howe…
This work is aimed at the multiconfigurational Hartree-Fock calculations of the Er ionization energy. Authors have used the ATSP MCHF version in which there are new codes for calculation of spin-angular parts written on the basis of the methodology Gaigalas, Rudzikas and Froese Fischer, based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin) and graphical technique of spin-angular ntegrations. They allow the study of configurations with open f-shells without any restrictions and lead to fairly accurate values of spectros…
The multiconfiguration Dirac-Hartree-Fock method is applied to study the electron affinities of At and its homologous elements Cl, Br, and I. Our method of calculation is validated through the comparison with the available experimental electron affinities of Cl, Br, I, and other theoretical values. The agreement between our predicted electron affinities and the available experimental values for Cl, Br, and I is within 0.2%, which is an improvement of more than a factor of 10 over previous theoretical studies. Applying the same method to At, the electron affinity of At is predicted to be 2.3729…
We calculated the magnetic dipole and the electric quadrupole hyperfine interaction constants of 3s3p $^{3,1}P^o_1$ states and the isotope shift, including mass and field shift, factors for transitions from these two states to the ground state 3s$^2~^1S_0$ in Al$^+$ ions using the multiconfiguration Dirac-Hartree-Fock method. The effects of the electron correlations and the Breit interaction on these physical quantities were investigated in detail based on the active space approach. It is found that the CC and the higher-order correlations are considerable for evaluating the uncertainties of t…
We present extensive multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations including 106 states in doubly ionized silicon (Si III) and 45 states in triply ionized silicon (Si iv), which are important for astrophysical determination of plasma properties in different objects. These calculations represents an important extension and improvement of earlier calculations especially for Si IV. The calculations are in good agreement with available experiments for excitation energies, transition properties, and lifetimes. Important deviations from the NIST-databa…
Relativistic Calculation of Energies, Transition Parameters Hyperfine Structure, Landé g$_J$ and Isotope shifts factors for Ar$^{7+}$, Kr$^{25+}$ and Xe$^{43+}$ ions
The values of nuclear electric quadrupole moment are different by about 7% for 87Sr nucleus between the recommended value [N. J. Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); P. Pyykko, Mol. Phys. 116, 1328 (2018)] and earlier results [e.g. A. M. Matensson-Pendrill, J. Phys. B: At. Mol. Opt. Phys. 35, 917 (2002); K. Z. Yu et al., Phys. Rev. A 70, 012506 (2004)]. In this work, we reported a new value, Q(87Sr) = 328(4) mb, making use of our calculated electric field gradients produced by electrons at nucleus in combination with experimental values for hyperfine structures of the 5s5p 3P1,…
Neutral uranium (U I) is a very difficult atom for theoretical calculations due to a large number of valence electrons, six, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can treat efficiently valence-core correlations and relativistic effects, but because the formalism was developed for Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for +6 charge of such a potential. Much more efficient is…
The Dirac-Hartree-Fock plus many-body perturbation theory (DHF+MBPT) method has been used to calculate hyperfine structure constants for Fr. Calculated hyperfine structure anomaly for hydrogen-like ion has been shown to be in good agreement with analytical expressions. It has been shown that the ratio of the anomalies for $s$ and $p_{1/2}$ states is weakly dependent on the principal quantum number. Finally, we estimate Bohr--Weisskopf corrections for several Fr isotopes. Our results may be used to improve experimental accuracy for the nuclear $g$ factors of short-lived isotopes.
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasi-degenerate 2P_{1/2} levels which are removed from the 2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift and the hyperfine effects. The van der Waals shift becomes commensurate with the 2S-2P_{3/2} fine-structure splitting only for close approach (R < 100 a_0, where a_0 is the Bohr radius) and one may thus restrict the discussion to the levels with n=2 and J=1/2 to good approximati…
We present the time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory as a new framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of…
