One‐particle density matrix functional for correlation in molecular systems

Based on the analysis of the general properties for the one‐ and two‐particle reduced density matrices, a new natural orbital functional is obtained. It is shown that by partitioning the two‐particle reduced density matrix in an antisymmeterized product of one‐particle reduced density matrices and a correction Γ^c we can derive a corrected Hartree–Fock theory. The spin structure of the correction term from the improved Bardeen–Cooper–Schrieffer theory is considered to take into account the correlation between pairs of electrons with antiparallel spins. The analysis affords a nonidempotent condition for the one‐particle reduced density matrix. Test calculations of the correlation energy and the dipole moment of several molecules in the ground state demonstrate the reliability of the formalism. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 317–323, 2003     

On a new partitioning of the Hamiltonian in many-body calculation of pair-correlation energies in closed-shell systems

We introduce here a new partitioning of the Hamiltonian in calculating pair-correlation energies using many-body perturbation theory, by which we are able to eliminate the off-diagonal particle–hole (p–h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle–particle (p–p) and hole–hole ladders exactly to all orders. The effect of the off-diagonal p–p ladders has been estimated for each pair by computing the third-, foruth- and fifth-order energies. For highly symmetric systems the present partitioning yields in general symmetry-broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p–h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π-electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed.     

The non-N-representability of the Colle–Salvetti second-order reduced density matrix

The Colle–Salvetti second-order reduced density matrix (2-matrix) is an approximation to the 2-matrix obtained from a wave function that is a product of a reference wave function containing little or no correlation times a product of correlation factors that are functions of the coordinates of pairs of electrons. A formal proof is given for the non-N-representability for the Colle–Salvetti 2-matrix using the nonnegativity condition of the 2-matrix. The nonnegativity condition of the particle-hole overlap matrix (G matrix) is also not satisfied. The proof is valid for Colle–Salvetti 2-matrices obtained from both the Hartree–Fock and small multiconfigurational-self-consistent-field wave functions. Even though the Colle–Salvetti 2-matrix is not N-representable, it does satisfy the Pauli principle component of the G-matrix condition because it reduces to an N-representable first-order reduced density matrix. © 1993 John Wiley & Sons, Inc.     

Density matrix expansions and their application in the theory of the many-electron systems

A method of calculation of the correlation energy is proposed, which includes the superposition of configurations and the two particle approach. This method is based on the density matrix formalism. The approximate, but N-representable expressions for the reduced density matrices are used. The correlation energy of the beryllium atom is calculated as an example.     

The conflict between hole delocalisation and static plus dynamic polarisation in molecular cations: illustration on Mg n + clusters

In a filled band problem, like an alkaline earth or a rare gas cluster, the positive ion is stabilised by both the hole delocalisation and by polarisation effects. The variational monoelectronic pictures take into account the first factor and the static polarisation, disregarding the dynamic or instantaneous polarisation, which is a correlation effect. This unbalance of SCF treatments underestimates the binding energy and unduly favors the structures in which the hole is concentrated on an atom surrounded by numerous neighbors. Taking into account the dynamic polarisation through CI or effective VB approaches restores the relative stability of structures where the hole is spread over a large number of atoms, as illustrated on the Mg ₄ ⁺ problem. This remark is shown to have general implications for covalent molecules.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Generalized density-functional theory: Conquering the N -representability problem with exact functionals for the electron pair density and the second-order reduced density matrix

Using the constrained search and Legendre-transform formalisms, one can derive “generalized” density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, theN-representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set ofN-representable densities sheds some light on the significance of this work.     

Density matrix approach to orbital relaxation dynamics in ionization

Dynamical response of electrons to a hole generated during ionization is formulated in time domain with the density matrix equations in the time‐dependent unrestricted Hartree–Fock approximation. Time evolutions of orbital energies and electron‐density distributions are computed for K‐shell and M‐shell ionizations of a Na atom by taking into account nonlinear coupling of density matrices beyond linear response. When the hole is generated so slowly that the adiabatic theorem is satisfied, the simulation eventually converges to the state of a fully relaxed Na⁺ ion. A rapid generation of a K‐shell hole (within about 1 fs) leads to a breakdown of the adiabatic theorem, triggering a collective oscillation of the electrons with the period of sub‐femtoseconds. The shake‐up effect associated with strong orbital relaxation in inner‐shell ionization is manifested as a mixing of occupied and unoccupied states in the density matrix.     

Single determinant N‐representability and the kernel energy method applied to water clusters

The Kernel energy method (KEM) is a quantum chemical calculation method that has been shown to provide accurate energies for large molecules. KEM performs calculations on subsets of a molecule (called kernels) and so the computational difficulty of KEM calculations scales more softly than full molecule methods. Although KEM provides accurate energies those energies are not required to satisfy the variational theorem. In this article, KEM is extended to provide a full molecule single‐determinant N‐representable one‐body density matrix. A kernel expansion for the one‐body density matrix analogous to the kernel expansion for energy is defined. This matrix is converted to a normalized projector by an algorithm due to Clinton. The resulting single‐determinant N‐representable density matrix maps to a quantum mechanically valid wavefunction which satisfies the variational theorem. The process is demonstrated on clusters of three to twenty water molecules. The resulting energies are more accurate than the straightforward KEM energy results and all violations of the variational theorem are resolved. The N‐representability studied in this article is applicable to the study of quantum crystallography. © 2017 Wiley Periodicals, Inc.     

Superelectrophilicity of 1,2‐Azaborine: Formation of Xenon and Carbon Monoxide Adducts

The BN analogue of ortho‐benzyne, 1,2‐azaborine, is shown to bind carbon monoxide and a xenon atom under matrix isolation conditions, demonstrating its strongly Lewis acidic superelectrophilic nature. The Lewis acid–base complexes involving CO and Xe can be cleaved photochemically and reformed by mildly annealing the matrices. The interaction energy of 1,2‐azaborine with Xe is 3 kcal mol^?1 according to quantum chemical computations, and is similar to that of the superelectrophilic carbene difluorovinylidene.     

On parametrization of orthogonal and unitary matrices with respect to their use in the description of molecules

The parametrization of a general N-dimensional unitary matrix is derived. A theorem is proved which permits a considerable reduction of the number of independent variational parameters when parametrization of orthogonal or unitary matrices is used in the energy expression of the LCAO MO and similar methods. As a numerical illustration the CO molecule is described in terms of complex molecular orbitals.     

Addendum to “variational principle for obtaining approximate analytical solutions of the temperature-perturbed Thomas–Fermi equation for compressed atoms”

In the present work the total energy of a Ne atom at T = 0 K is calculated as a function of a spherical container radius. The calculation is based on the Thomas–Fermi (TF ) equation, which is solved approximately by an equivalent variational principle. The effect of an approximate exchange correction on the variational TF energy values is investigated.     

Symmetric-group algebraic variational solutions for Heisenberg models at finite temperature

The Heisenberg spin Hamiltonian for a collection of N spin-1/2 sites is viewed, as favored by Professor Matsen, to be an element of the group algebra of the symmetric group ??_N. Several computationally tractable, variational group–algebraic approximations for the finite-temperature density matrix are made so as to minimize the Gibb's free–energy functional. Relations to previous quite differently motivated approximations are identified, though improvements are noted with the present approach.     

三原子分子振转激发态的理论研究

三原子分子振转激发态的理论研究谢代前,鄢国森,田安民（四川大学化学系,成都,６１００６４）关键词振转激发态,三原子分子,变分法能级较高的振转激发态通常包含大振幅运动,其波函数分布于很广的势能面区域内,传统的正则模理论已不适合于解决这类问题．近年来,Ｈ...     

New MALDI matrices based on lithium salts for the analysis of hydrocarbons and wax esters

Lithium salts of organic aromatic acids (lithium benzoate, lithium salicylate, lithium vanillate, lithium 2,5‐dimethoxybenzoate, lithium 2,5‐dihydroxyterephthalate, lithium α‐cyano‐4‐hydroxycinnamate and lithium sinapate) were synthesized and tested as potential matrices for the matrix‐assisted laser desorption/ionization (MALDI)‐mass spectrometry analysis of hydrocarbons and wax esters. The analytes were desorbed using nitrogen laser (337.1 nm) and ionized via the attachment of a lithium cation, yielding [M + Li]⁺ adducts. The sample preparation and the experimental conditions were optimized for each matrix using stearyl behenate and n‐triacontane standards. The performance of the new matrices in terms of signal intensity and reproducibility, the mass range occupied by matrix ions and the laser power threshold were studied and compared with a previously recommended lithium 2,5‐dihydroxybenzoate matrix (LiDHB) (Cva?ka and Svato?, Rapid Commun. Mass Spectrom. 2003, 17, 2203). Several of the new matrices performed better than LiDHB. Lithium vanillate offered a 2–3 times and 7–9 times higher signal for wax esters and hydrocarbons, respectively. Also, the signal reproducibility improved substantially, making this matrix a suitable candidate for imaging applications. In addition, the diffuse reflectance spectra and solubility of the synthesized compounds were investigated and discussed with respect to the compound's ability to serve as MALDI matrices. The applicability of selected matrices was tested on natural samples of wax esters and hydrocarbons. Copyright © 2014 John Wiley & Sons, Ltd.