New method of calculating idempotent density matrices and the total energy of many-electron systems

We have developed a method of successive approximations for the direct calculation of the density matrix and total energy of a many-electron system. The method can be used when the energy is a linear functional of the density matrix and the density matrix itself satisfies the idempotent conditions. A mathematical proof is given of the convergence of the successive approximations to the exact solution.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 1, pp. 1–5, January–February, 1990.The author thanks H. M. Mestechkina and I. V. Abarenkov for useful discussions.     

Information entropies of many-electron systems

The Boltzmann–Shannon (BS ) information entropy S_ρ = ∫ ρ(r)log ρ(r)dr measures the spread or extent of the one-electron density ρ(r), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically computed, not even for simple quantum mechanical systems such as, e.g., the harmonic oscillator (HO ) and the hydrogen atom (HA ) in arbitrary excited states. Here, we first review (i) the present knowledge and open problems in the analytical determination of the BS entropies for the HO and HA systems in both position and momentum spaces and (ii) the known rigorous lower and upper bounds to the position and momentum BS entropies of many-electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the BS entropies and various density functionals. Particular cases of these results are rigorous relationships of the BS entropies and some relevant density functionals (e.g., the Thomas–Fermi kinetic energy, the Dirac–Slater exchange energy, the average electron density) for finite many-electron systems. © 1995 John Wiley & Sons, Inc.     

Dissipative many-electron dynamics of ionizing systems

In this paper, we perform many-electron dynamics using the time-dependent configuration-interaction method in its reduced density matrix formulation (ρ-TDCI). Dissipation is treated implicitly using the Lindblad formalism. To include the effect of ionization on the state-resolved dynamics, we extend a recently introduced heuristic model for ionizing states to the ρ-TDCI method, which leads to a reduced density matrix evolution that is not norm-preserving. We apply the new method to the laser-driven excitation of H(2) in a strongly dissipative environment, for which the state-resolve lifetimes are tuned to a few femtoseconds, typical for dynamics of adsorbate at metallic surfaces. Further testing is made on the laser-induced intramolecular charge transfer in a quinone derivative as a model for a molecular switch. A modified scheme to treat ionizing states is proposed to reduce the computational burden associated with the density matrix propagation, and it is thoroughly tested and compared to the results obtained with the former model. The new approach scales favorably (～N(2)) with the number of configurations N used to represent the reduced density matrix in the ρ-TDCI method, as compared to a N(3) scaling for the model in its original form.     

Correlation effects in externally perturbed many-electron systems

Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self-consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many-electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many-body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree–Fock solution for the one-electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.     

New method for the direct calculation of electron density in many-electron systems. I. Application to closed-shell atoms

Analytical properties of hydrogen-like atomic orbitals (HAO ) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.     

Quantum chemistry of many-electron systems: high-priority aspects

The review generalizes the studies devoted to the development of a new quantum chemistry method representing an alternative to the Hartree–Fock approximation. Based on the hypothesis of prohibition of equipotential surfaces, which clarifies the physical sense of the Pauli exclusion principle, and taking account of the condition for antisymmetrical wave function of the triplet state (3S) of He atom, the Hartree–Fock approximation is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWFs) for the test systems traditionally used in quantum chemistry, namely, excited triplet state of H₂ molecule and the ground electronic states of Li atom and LiH molecule. The nodal surfaces of the wave functions corresponding to the minimum basis set of Slater orbitals in the Hartree–Fock approximation are constructed and analyzed. An alternative to the Hartree–Fock approximation is provided by the MWF quantum chemical method being developed by the authors. In the MWF method, the nodal surfaces for H₂(³Σ _u ^v ) and Li(²S) are specified a priori. Some aspects of geometric interpretation of the Pauli exclusion principle are discussed. Unlike the MWF method, the Hartree–Fock approximation is unsuitable for taking account of the dependence of the MWF nodal surfaces on the nuclear charges and on correlation effects related to the motion of electrons with antiparallel spins because such nodal surfaces are predefined by the mathematical properties of Slater determinants rather than by physically clear and more practically valuable algebraic products of electrostatic potential differences.     

Inner and outer radial density functions in many-electron atoms

When any two electrons are considered simultaneously, the radial density function D(r) in many-electron atoms is shown to be rigorously separated into inner D _<(r) and outer D _>(r) radial densities. Accordingly, radial properties such as the electron–nucleus attraction energy V _en and the diamagnetic susceptibility χ _d are the sum of the inner and outer contributions. The electron–electron repulsion energy V _ee has an approximate relation with the minus first moment of the outer density D _>(r). For the 102 atoms He through Lr in their ground states, different characteristics of local maxima in the radial densities D _<(r), D _>(r), and D(r) are reported based on the numerical Hartree-Fock wave functions. Relative contributions of the inner and outer components to V _en and are also discussed for these atoms.     

Model universal coulomb hole function for many-electron systems

In the framework of the homogeneous electron gas theory we give a model function G_c of the Coulomb hole that can be considered as an approximate universal correlation function for many-electron systems. The function G_c reflects the right asymptotic behavior of the correlation function of an electron gas in high and low density limits and enables one to reproduce experimental correlation energies of a number of atoms of the first and second periods in a local density approximation with the relative error 0.3–4.2%. The estimate of contributions of electrons with parallel or antiparallel spins into correlation energy shows that in the domain of densities typical for atoms of the first and second periods, the Coulomb correlation of electrons with parallel spins is in high extent suppressed by the Fermi correlation.     

A spin-dependent unitary group approach to many-electron systems

In this article we derive a segment-level formula for the matrix elements of the U(2n) generators in a basis symmetry adapted to the subgroup U(n) × U(2) (i.e., spin-orbit basis), for the representations appropriate to many-electron systems. This enables the direct evaluation of the matrix elements of spin-dependent Hamiltonians.     

Search for a density-based alternative quantum mechanics of many-electron systems

There are three reasons for seeking an alternative density-based quantum mechanics of many-electron systems, incorporating both interpretive and basic quantum mechanical aspects: (i) failure of popularad hoc chemical concepts underab initio scrutiny; (ii) failure ofab initio calculations to provide simple concepts; and (iii) highly attractive concepts and pictures generated by the electron density in three-dimensional space. At present the three interlinked pillars for such a density mechanics (in contrast to wave mechanics) are: (a) density functional theory; (b) quantum fluid dynamics; and (c) property densities in three-dimensional space. This article describes several studies dealing with these aspects. Although a density mechanics may well be an impossible ideal to realize, the search for it is indeed rejuvenating the whole of quantum chemistry.     

Correlation energy of many-electron systems: a modified Colle-Salvetti approach

The Colle and Salvetti approach [Theo. Chim. Acta 37, 329 (1975)] to the calculation of the correlation energy of a system is modified in order to explicitly include into the theory the kinetic contribution to the correlation energy. This is achieved by deducing from a many electrons wave function, including the correlation effects via a Jastrow factor, an approximate expression of the one-electron reduced density matrix. Applying the latter to the homogeneous electron gas, an analytic expression of the correlation kinetic energy is derived. The total correlation energy of such a system is then deduced from its kinetic contribution inverting a standard procedure. At variance of the original Colle-Salvetti theory, the parameters entering in both the kinetic correlation and the total correlation energies are determined analytically, leading to a satisfactory agreement with the results of Perdew and Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameter-free) expressions give rise to a modified-local-density approximation that can be used in self-consistent density-functional calculations. We have performed such calculations for a large set of atoms and ions and we have found results for the correlation energies and for the ionization potentials which improve those of the standard local-density approximation.