The electronic mean-field configuration interaction method. I. Theory and integral formulas

In this article, we introduce a new method for solving the electronic Schrodinger equation. This new method follows the same idea followed by the mean-field configuration interaction method already developed for molecular vibrations; i.e., groups of electronic degrees of freedom are contracted together in the mean field of the other degrees. If the same partition of electronic degrees of freedom is iterated, a self-consistent field method is obtained. Making coarser partitions (i.e., including more degrees in the same groups) and discarding the high energy states, the full configuration interaction limit can be approached. In contrast with the usual group function theory, no strong orthogonality condition is enforced. We have made use of a generalized version of the fundamental formula defining a Hopf algebra structure to derive Hamiltonian and overlap matrix element expressions which respect the group structure of the wave function as well as its fermionic symmetry. These expressions are amenable to a recursive computation.     

Energetics of proton transfer in liquid water. I. Ab initio study for origin of many-body interaction and potential energy surfaces

The energetics of proton transfer in liquid water investigated by using ab initio calculation. The molecular electronic interaction of hydrated proton clusters in classified into many-body interaction elements by a new energy decomposition method. It is found that up to three-body molecular interaction is essential to describe the potential energy surface. The three-body effect mainly arises from the (non-classical) charge transfer and strongly depends on their configuration. Higher than three-body effects are small enough to be neglected. To simulate the liquid state reactions, two cluster models including all water molecules up to the second shell in the proton transfer reactions are employed. It is shown that these proton transfer reactions only involve small potential energy barriers of a few kcal/mol or less when structural rearrangement of the solvent is induced along the proton movement.     

Simultaneous ab initio calculations of isoelectronic diatomic molecules

Large gaussian basis sets are employed in simultaneous configuration interaction calculations for the ground states of isoelectronic diatomic molecules. The resulting potential energy curves for three members respectively of four different isoelectronic molecule sequences show the applicability of the method. Comparisons with available results of standard configuration interaction calculations for selected molecules are given. Using our method we often get lower upper bounds for the electronic energy, save computer time and treat physically totally different molecules simultaneously.     

Optimized Jastrow-Slater wave functions for ground and excited states: application to the lowest states of ethene

A quantum Monte Carlo method is presented for determining multideterminantal Jastrow-Slater wave functions for which the energy is stationary with respect to the simultaneous optimization of orbitals and configuration interaction coefficients. The approach is within the framework of the so-called energy fluctuation potential method which minimizes the energy in an iterative fashion based on Monte Carlo sampling and a fitting of the local energy fluctuations. The optimization of the orbitals is combined with the optimization of the configuration interaction coefficients through the use of additional single excitations to a set of external orbitals. A new set of orbitals is then obtained from the natural orbitals of this enlarged configuration interaction expansion. For excited states, the approach is extended to treat the average of several states within the same irreducible representation of the pointgroup of the molecule. The relationship of our optimization method with the stochastic reconfiguration technique by Sorella et al. is examined. Finally, the performance of our approach is illustrated with the lowest states of ethene, in particular with the difficult case of the 1(1)B(1u) state.     

Spin-orbit configuration interaction study of the electronic structure of the 5f (2) manifold of U(4+) and the 5f manifold of U(5+)

The energy levels of the 5f configuration of U(5+) and 5f(2) configuration of U(4+) have been calculated in a dressed effective Hamiltonian relativistic spin-orbit configuration interaction framework. Electron correlation is treated in the scalar relativistic scheme with either the multistate multireference second-order multiconfigurational perturbation theory (MS-CASPT2) or with the multireference single and double configuration interaction (MRCI) and its size-extensive Davidson corrected variant. The CASPT2 method yields relative energies which are lower than those obtained with the MRCI method, the differences being the largest for the highest state (1)S(0) of the 5f(2) manifold. Both valence correlation effects and spin-orbit polarization of the outer-core orbitals are shown to be important. The satisfactory agreement of the results with experiments and four-component correlated calculations illustrates the relevance of dressed spin-orbit configuration interaction methods for spectroscopy studies of heavy elements.     

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.     

Electronic states of NiFe. Anab initio HF-CI study

Ab initio Hartree-Fock and configuration interaction methods have been employed in describing the interaction between a Ni and an Fe atom. The chemical bond between the atoms is due to a 4sσ molecular orbital. The 3d orbitals merely cause small splittings between the potential energy curves. Equilibrium distance, dissociation energy and vibrational frequency are predicted for the ground state of the molecule.     

Quantum Monte Carlo study of ground and first excited state of C,N, O,F, and Ne atoms using Slater-Jastrow-Backflow wave function

All-electron fixed-node diffusion quantum Monte Carlo energies of the two lowest-lying states of C, N, O, F, and Ne atoms are reported. The Slater-Jastrow form is used as the trial wave function. We will use single- and multideterminant wave functions as the Slater part. The single-determinant wave function has been computed by the Hartree-Fock method and the multideterminant wave functions have been computed by the complete active space self-consistent field, configuration interaction with single and double excitation, configuration interaction with single, double, triple, and quadruple excitation and second-order configuration interaction. For the ground- and first excited states, the multideterminant wave functions have computed more than 99% of the correlation energy. Significant improvements have been achieved using the backflow transformations and up to 99.8% of the correlation energy has been recovered. A very good agreement with the experimental data has been obtained for the excitation energies.     

Correlation energy extrapolation by intrinsic scaling. V. Electronic energy, atomization energy, and enthalpy of formation of water

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390+/-0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh.     

Molecular ordering of a cyano compound at a displacive transition temperature: a statistical analysis based on quantum mechanics and computer simulations

A statistical analysis has been carried out to determine the configurational preference of a pair of 4-cyanophenyl 4-n-pentylbenzoate (CPPB) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Configurational energy has been computed using the Rayleigh—Schodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using the Maxwell—Boltzmann formula. An attempt has been made to identify the most probable configuration at the phase transition temperature. Further, the flexibility of various configurations has been studied in terms of variation of probability due to small departures from the most probable configuration. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pair have been considered. The results are discussed in the light of experimental as well as theoretical observations. The nature of the mesophase has been correlated with the parameter introduced in this paper.     

Molecular ordering of a cyano compound at a displacive transition temperature: a statistical analysis based on quantum mechanics and computer simulations

A statistical analysis has been carried out to determine the configurational preference of a pair of 4-cyanophenyl 4- n -pentylbenzoate (CPPB) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Configurational energy has been computed using the Rayleigh-Schodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using the Maxwell-Boltzmann formula. An attempt has been made to identify the most probable configuration at the phase transition temperature. Further, the flexibility of various configurations has been studied in terms of variation of probability due to small departures from the most probable configuration. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pair have been considered. The results are discussed in the light of experimental as well as theoretical observations. The nature of the mesophase has been correlated with the parameter introduced in this paper.     

完全活性空间组态相互作用能量的拟合和外推

完全活性空间组态相互作用计算与完全活性空间中的活性电子数和活性轨道数有关,但完全活性空间组态相互作用的能量不是活性电子数和活性轨道数的单调递减函数,因此活性轨道数和活性电子数不能用来外推完全活性空间组态相互作用的能量。为此,我们定义了一个新的变量:活性空间中的最大未占满轨道数。我们对一系列单重态、双重态和三重态分子进行了完全活性空间组态相互作用的计算,并利用活性空间中的活性电子数和最大未占满轨道数这两个变量,对这些基态能量进行了拟合和外推,拟合的均方根误差都在10~(-6)数量级。外推能量的精度优于MP4,对小分子体系,其精度高于CCSD。外推的完全的组态相互作用(FCI)能量值和实际计算的FCI值也很接近。另外,我们还利用外推能量来优化双原子分子的平衡键长,并计算谐振频率,其精度优于CASSCF。     

Gradients for configuration interaction energies with spin-orbit coupling in a semiempirical framework

We present a method for the analytical evaluation of the molecular energy gradient for a semiempirical configuration interaction (CI) wavefunction, taking into account the spin-orbit coupling. We show how to proceed in the simplest case where all the wavefunctions belonging to the CI subspace considered are mixed by the spin-orbit interaction, and we develop an original procedure for the more complex case where only a limited number of CI eigenvectors of the spin-free Hamiltonian are mixed.     

A note on the treatment of quadruple excitations in configuration interaction

Perturbation theory is used to justify the approximation in configuration interaction of the coefficients of quadruple excitations as products of coefficients of double excitations. Corresponding energy expressions are presented and tested in a simple application to the beryllium atom. The ideas are likely to be of most use in connection with large configuration interaction calculations.     

Explicitly correlated configuration interaction studies using spherical Gaussians. II. Exploratory studies on LiH

Ab initio self-consistent-field and configuration interaction studies have been carried out on the ground state of the LiH molecule at its equilibrium distance. Floating spherical Gaussian basis orbitals (FSGO ) were employed, along with spherical Gaussian correlation factors, using the procedure described in the preceding paper. A near-Hartree–Fock function was found using only 13 FSGO . Exploratory configuration interaction studies recovered approximately 73% of the inner shell correlation energy and approximately 56% of the total correlation energy with five configurations plus the Hartree–Fock configuration. These studies indicate that, by using spherical Gaussian correlation factors, direct introduction of interelectronic coordinates into trial wave functions can be accomplished for molecular systems. It was also shown that correlating configurations need not utilize the full Hartree–Fock basis, but may use substantially smaller bases and still recover correlation energy effectively. Finally, the results indicate that, in spite of their improper cusp behavior, FSGOS and spherical Gaussian correlation factors can be used for construction of high accuracy wave functions.     

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

The recently introduced method of correlation energy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F(2) molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 A to 8 A, the equilibrium distance being 1.412 A. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.     

Calculation of one-electron properties using limited configuration interaction techniques

One-electron properties may be evaluated by configuration interaction methods using analytical differentiation of the total energy with respect to an external perturbation parameter. Dipole moments are reported using such a method for CO and H₂CO. Inclusion of single substitutions does not change calculated dipole moments appreciably with this method. The differences between this method and the direct evaluation of an expectation value are discussed.     

Generation of potential energy curves for the X1Sigma(+)g, B1Delta(+)g, and B'1Sigma(+)g states of C2 using the effective valence shell Hamiltonian method

Calculations of the ground and excited state potential energy curves of C2 using the third-order effective valence Hamiltonian (Hv3rd) method are benchmarked against full configuration interaction and other correlated single-reference perturbative and nonperturbative theories. The large nonparallelity errors (NPEs) exhibited even by state-of-art coupled cluster calculations through perturbative triples indicate a serious deficiency of these single-reference theories. The Hv method, on the other hand, produces a much reduced NPE, rendering it a viable approximate many-body method for accurately determining global ground and excited state potential energy curvessurfaces.     

The calculation of London coefficients by the variation-perturbation method

The London coefficients for the dispersion interaction between LiLi, BeBe and LiBe are calculated by the variation-perturbation method using the whole atomic hamiltonian as H₀ and the Hartree-Fock approximation for the upper turbed wavefunction ?₀. A single excited valence configuration with optimized orbital exponents gives accurate results for Li, whereas comparable accuracy for Be is obtained when part of the valence correlation energy in the ground as well as in the excited state is accounted for through a limited configuration interaction.     

Superconductivity and the effective electron–electron interaction mechanism in the light of the configuration interaction study

The effect of electron–phonon interactions, described by the effective electron–electron interaction mechanism, on the electronic structure of molecular systems has been investigated by the configuration interaction method. For systems with strongly quasi-degenerate electronic states near to the Fermi surface, this interaction mechanism, according to the BCS theory, results in the electronic ground-state energy lowering and in the gap formation. A more rigorous treatment of the configuration interaction method as applied in this paper confirms the electronic ground-state energy lowering, but the obtained results indicate that the effective electron–electron interaction term does not yield the experimentally detected temperature dependence of the gap. Accordingly, the two-particle mechanism seems not to be the key factor for the gap formation and for the microscopic mechanism of superconductivity, which agrees with the results of the molecular nonadiabatic theory of electron–vibrational interactions.