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.     

Multidimensional time-dependent discrete variable representations in multiconfiguration Hartree calculations

In the multiconfiguration time-dependent Hartree (MCTDH) approach, the wave function is expanded in time-dependent basis functions, called single-particle functions, to increase the efficiency of the wave-packet propagation. The correlation discrete variable representation (CDVR) approach, which is based on a time-dependent discrete variable representation (DVR), can be employed to evaluate matrix elements of the potential energy. The efficiency of the MCTDH method can be further enhanced by using multidimensional single-particle functions. However, up to now the CDVR approach could not be used in MCTDH calculations employing multidimensional single-particle functions, since this would require a general multidimensional non-direct-product DVR scheme. Recently, Dawes and Carrington presented a practical scheme to implement general non-direct-product multidimensional DVRs [R. Dawes and T. Carrington, Jr., J. Chem. Phys. 121, 726 (2004)]. The present work utilizes their scheme in the MCTDH/CDVR approach. The accuracy is tested using the photodissociation of NOCl as example. The results show that the CDVR scheme based on multidimensional time-dependent DVRs allows for an accurate evaluation of the potential in MCTDH calculations with multidimensional single-particle functions.     

改进的相对论量子化学计算ZORA方法

提出一种改进的ZORA(Zeroth-OrderRegularApproximationtotheDiracEquation)方法,其单电子方程为：[σ·p(c^2/2c^2-V~0)σ·p+V(r)]ψ=εψ。式中V~0为空间限域的势能函数：V~0(r=~A∑V~0^A(r~A),r~A=|r-R~A|,V~0^A(r~A)=V^A(r~A){1+exp[α(r~A-r~0^A]}^-^1。其中A表示分子的某个组成原子,R~A为A原子的位置矢量,V^A(r~A)为自由A原子的势函数,α和r~0^A为参数。改进的ZORA方法具有原来方法的所有优点,避免了原有ZORA方法因不满足标度变换不变性带来的缺陷,而且计算过程简单。具体计算表明,通过适当选择参数α和r~0^A,用本研究提出来的方法,在计算分子几何结构和键合能时,基本上消除了ZORA方法由于标度变换依赖性产生的误差。     

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.     

A fragment energy assembler method for Hartree-Fock calculations of large molecules

We present a fragment energy assembler approach for approximate Hartree-Fock (HF) calculations of macromolecules. In this method, a macromolecule is divided into small fragments with appropriate size, and then each fragment is capped by its neighboring fragments to form a subsystem. The total energy of the target system is evaluated as the sum of the fragment energies of all fragments, which are available from conventional HF calculations on all subsystems. By applying the method to a broad range of molecules, we demonstrate that the present approach could yield satisfactory HF energies for all studied systems.     

Unrestricted Hartree-Fock instabilities in nuclear spin-spin coupling calculations. The MNDO method

The MNDO wavefunction is used to calculate the Fermi contact term of nuclear spin-spin coupling constants. Owing to the presence of non-singlet unrestricted Hartree-Fock instabilities of the wavefunction, convergence problems arise in a rather large set of molecules, especially those containing molecular orbitals. A special technique to cope with this situation is presented. The MNDO and transmitted components of the coupling constants in the ethylene molecule are also calculated and compared with those previously obtained with the INDO and INDO/S methods.Part of a Ph.D. thesis (G.E.S.) to be presented to the University of Buenos Aires.Commission of Scientific Research (CIC, Pcia. Bs. As.) fellow.Argentine National Research Council (CONICET) fellow.Member of the Argentine National Research Council (CONICET).     

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.     

Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method.     

Photoabsorption in H2O: Stieltjes-Tchebycheff calculations in the time-dependent Hartree-Fock approximation

Total and partial-channel photoabsorption cross-section calculations in H₂O are reported employing the time-dependent Hartree-Fock approximation and Stieltjes-Tchebycheff imaging procedures, and comparisons are made with the corresponding results of recent (e, 2e), (e, e + ion), and synchrotron-radiation dipole oscillator-strength studies.     

Spline methods for multiconfiguration Hartree–Fock calculations

The earlier numerical multiconfiguration Hartree–Fock atomic structure package was not designed with high-performance computers in mind. In this paper, some new algorithms based on spline–Galerkin methods are described that are appropriate for concurrent/vector architectures. The goal is to improve the level of numerical accuracy by several orders of magnitude using fewer basis functions than points in a numerical grid. Of critical importance is the robustness of the code: The most serious problems in the numerical implementation were associated with orthogonality constraints. In a spline basis approach, the orthogonality requirements can be integrated into quadratically convergent update procedures. These procedures are evaluated for a number of cases.     

A method and program for mass quantum chemical calculations of protein—ligand docking complexes

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root-mean-square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 418–420, February, 2008.     

Direct one-index transformations in multiconfiguration response calculations

The evaluation of gradient vectors of a general operator with one-index, double-one-index, or higher-order one-index transformed integrals is a key operation in multiconfiguration response theory calculations. We describe an integral-driven direct algorithm that carries out this operation efficiently without pretransforming the integrals. The use of this algorithm leads to a considerable reduction in disk space and timing. © 1994 by John Wiley & Sons, Inc.     

Calculations of frequency-dependent molecular magnetizabilities with quasi-relativistic time-dependent generalized unrestricted Hartree-Fock method

The time-dependent generalized unrestricted Hartree-Fock (TDGUHF) method combined with a two-component quasi-relativistic Hamiltonian generated from the Douglas-Kroll-Hess (DKH) transformation was developed to calculate frequency-dependent molecular magnetizabilities, which are the linear response quantity of a molecule to an external magnetic field. By calculating the magnetizabilities of H(2)X (X = O, S, Se, and Te), the noble gases (He, Ne, Ar, Kr, and Xe) and small open shell molecules (CH(2), CH(3), and O(2)), we found that scalar relativistic terms affect mainly the diamagnetic magnetizability and spin-orbit (SO) interaction affects the paramagnetic magnetizability.     

A new algorithm for molecular fragmentation in quantum chemical calculations

In this study, we present a "black-box" method for fragmenting a molecule with a well-defined Kekulé or valence-bond structure into a significant number of smaller fragment molecules that are more amenable to high level quantum chemical calculations. By taking an appropriate linear combination of the fragment energies, we show that it is possible in many cases to obtain highly accurate total energies when compared to the total energy of the full molecule. Our method is derived from the approach reported by Deev and Collins, but it contains significant unique elements, including an isodesmic approach to the fragmentation process. Using a method such as that described in this work it is in principle possible to obtain very accurate total energies of systems containing hundreds, if not thousands, of atoms as the approach is subject to massive parallelization.     

Real space Hartree-Fock configuration interaction method for complex lateral quantum dot molecules

We present unrestricted Hartree-Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in quasi-two-dimensional quantum dot molecules. The method employs real space finite difference method, incorporating strong magnetic field, for calculating single particle states. The Hartree-Fock method is employed for the calculation of direct and exchange interaction contributions to the ground state energy. The effects of correlations are included in energies and directly in the many-particle wave functions via CI method using a limited set of excitations above the Fermi level. The URHF-CI method and its performance are illustrated on the example of ten electrons confined in a two-dimensional quantum dot molecule.     

Convergence of the Rayleigh—Ritz method in self-consistent-field and multiconfiguration self-consistent-field calculations

We investigate the analytical convergence of SCF and MCSCF calculations, when the dimension of the subspaces to which the orbitals are restricted tends to infinity. We show that the completeness only inL ²(R ³;C ²) of the orbital bases does not ensure the convergence of the Ritz-energy, neither in SCF nor in MCSCF calculations, but that this convergence — as well as the convergence of the Ritz-orbitals in SCF calculations — is on the contrary guaranteed if the orbital bases are complete in the Sobolev spaceW ^1,2(R ³;C ²). Some consequences on the choice of the orbital exponents of Slater and Gauss functions are also discussed.