Transferability of the electronic structure characteristics of saturated molecules

The common quantum mechanical problem for the total class of saturated hydrocarbons has been stated and solved within the framework of the effective Hamiltonian method. A quantum mechanical substantiation of the transferability of the electronic structure characteristics (bond dipole moments, bond energies, and bond force constants) as well as the investigation of the origin of transferability have been considered for the stated class of chemical compounds.     

Electronic structure of saturated hydrocarbons in the semiempirical equivalent orbital method

The problem of matrix elements of the Hartree-Fock Hamiltonian for saturated hydrocarbons in the EO method is considered. It is stated, that all the proposed scales of such parameters are incomplete or lead to an incorrect band structure of diamond. It is shown that the data on the band structure of diamond may be useful to obtain the full scale of the parameters for the calculations of the electronic structure of hydrocarbons.     

L'utilisation d'orbitales localisées dans l'étude théorique des molécules

The five simplest alkanes have been studied in terms of localized orbitals. The transferability of the Fock matrix elements in this basis allows us to elaborate a simple parametric procedure adapted for saturated hydrocarbons. Some original applications of this procedure are performed.

     

Orthogonalized hybrid orbitals in the theoretical study of polyatomic systems

Ab initio calculations on simple saturated hydrocarbons have been carried out using a basis set of orthogonalized hybrid orbitals. We propose a simple parametric procedure based on the observed transferability of Fock matrix elements calculated in this basis set. Some applications are performed in order to test this simplified non empirical method.     

Additive components of heteroatom influence in substituted alkanes. Polarization and depolarization of bonds

The general expression for the common one-electron density matrix (DM) of saturated organic molecules obtained previously in the framework of the Hückel type model (V. Gineityte, J. Mol. Struct. (Theochem) 343 (1995) 183) has been applied to reveal the additive components of the heteroatom influence in substituted alkanes. To this end, the occupation number of a basis orbital has been expressed as a sum of three terms describing the polarization and depolarization of bonds and the intramolecular charge transfer. These terms, in turn, have been related to certain types of direct (through-space) and indirect (through-bond) interactions of bond orbitals (BOs). In particular, changes in the secondary polarization of C-C and C-H bonds under the influence of a heteroatom giving rise to their induced dipole moments has been related to differences in the indirect interaction between the two BOs of the given bond before and after substitution. Additive quantum-chemical analogues of the classical inductive and electron-donating effects have been established. The above-mentioned expressions for the occupation numbers have been also applied to substantiate the implicit postulates of the classical chemistry about additivity of the heteroatom influence in substituted alkanes.     

Research in the method of large molecular calculations utilizing transferability of LMO

The localized molecular orbitals of some saturated hydrocarbons and their derivatives have been formed using ab initio method and M. P. [1–2] localization procedure. Two models, SLMO and ELMO , a set of parameters of LMO Fock matrix elements, and a technique called “Group Effect” are proposed. Based on these, we developed a procedure to simulate the ab initio calculations on large molecules. Some test calculations have been done. The results are compared with those of the ab initio method. In general, absolute errors of orbital energies are about 10^?3 a.u., and the relative errors of total energies are about 10^?4. For the original applications, we applied this procedure to some large systems of alkane and their derivatives as well as three Crown-ether compounds. Satisfactory results are obtained.     

An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory

A fully atomic orbital (AO)-based reformulation of second-order M?ller-Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear. Our formulation avoids any transformation between the AO and the molecular orbital (MO) basis and employs pseudodensity matrices similar to the AO-MP2 energy expressions within the Laplace scheme for energies. The explicit computation of perturbed one-particle density matrices emerging in the new AO-based gradient expression is avoided by reformulating the Z-vector method of Handy and Schaefer [J. Chem. Phys. 81, 5031 (1984)] within a density matrix-based scheme.     

Decomposition of the first-order reduced density matrix: an isopycnic localization treatment

In this work, we propose a partitioning of the first-order reduced density matrix corresponding to an N-electron system into first-order reduced density matrices associated with regions defined in the real space (regional matrices). The treatment is based on an isopycnic orbital localization transformation that provides regional matrices that are diagonalized by identical localized orbitals, having many attributes associated with chemical concepts (appropriate localization in space, high transferability, etc.). Although the obtained numerical values are similar to those arising from previous studies, their interpretation is more rigorous and the computational cost is much lower.     

The explicit interactions of five-membered saturated heterocyclics containing one and two heteroatoms with single water molecule

In this article, the hydrogen bonding interaction between saturated five-membered heterocyclic molecules and water has been investigated. Molecular orbital and density functional theory methods have been used to evaluate the stabilization energies associated with the adduct formation between heterocyclic molecules and water. The hydrogen bond acceptor ability of O, S, Se, and N as members of five-membered ring has been analyzed. The effect of the presence of second heteroatom N in the ring on the hydrogen bond interaction has also been evaluated. Atoms in molecules theory calculations were carried out to characterize the hydrogen bond through the changes in electron density and Laplacian of electron density. A natural energy decomposition analysis and natural bond orbital analysis is also performed to understand the nature of hydrogen bonding interaction in monohydrated five-membered heterocyclic adducts.     

Molecular-orbital-free algorithm for the excited-state force in time-dependent density functional theory

Starting from the equation of motion in the density matrix formulation, we reformulate the analytical gradient of the excited-state energy at the time-dependent density functional theory level in the nonorthogonal Gaussian atom-centered orbital (AO) basis. Analogous to the analytical first derivative in molecular-orbital (MO) basis, a Z-vector equation has been derived with respect to the reduced one-electronic density matrix in AO basis, which provides a potential possibility to exploit quantum locality of the density matrix and avoids the matrix transformation between the AO and the MO basis. Numerical tests are finished for the excited-state geometry optimization and adiabatic excitation energy calculation of a series of small molecules. The results demonstrate the computational efficiency and accuracy of the current AO-based energy gradient expression in comparison with the MO-based scheme.     

L'utilisation d'orbitales localisées dans l'étude théorique des molécules

The systematical study of the localized orbitals and their properties has been extended to the unsaturated hydrocarbons. The six simplest alkenes have been studied and fairly good transferability of the bond orbitals and their associated matrix elements may be pointed out. The influence of the neighbourhoods as well as the relative orientation of the bonds is discussed. These results lead to the use of a simple parametric procedure expressing the molecular orbitals as a combination of bond orbitals (LCLO-SCF-MO). This procedure is applied to saturated and unsaturated hydrocarbons, even conjugated hydrocarbons may be treated. Some original applications show that the results obtained by our procedure are comparable with the full ab initio calculations.     

Heteroatom influence in substituted benzenes and pyridine-like heterocycles in terms of direct and indirect intramolecular interactions

The general expression for the one-electron density matrix obtained previously for saturated organic molecules (V. Gineityte, J. Mol. Struct. (Theochem), 343 (1995) 183) is shown to be applicable also to substituted benzenes and pyridine-like heterocycles. On this basis, a new interpretation of the influence of a heteroatom (substituent) upon the remaining fragment of an aromatic molecule is suggested. To this end, the occupation number of a 2p_z AO of the aromatic ring has been expressed as a sum of five terms, two of them describing the intramolecular charge transfer and the remaining ones representing the secondary (induced) dipole moments arising within the ring under the influence of heteroatom, viz. the so-called ipso–ortho (para–meta), para–ipso and ortho–meta dipole moments. Just the latter two moments proved to play the principal role in the formation of the observed picture of the electron density distribution, viz. of an increase (reduction) of occupation numbers of 2p_z AOs in the ortho and para positions after introducing an electron-donating (accepting) substituent. For pyridine-like heterocycles and substituted benzenes, these dipole moments are determined mostly by the direct and the indirect interactions, respectively, between the highest occupied and the lowest vacant MO of benzene. Orbitals of the heteroatom (substituent) play the role of mediators in the above-mentioned indirect interaction.     

Stark effect in X2Y4 molecules: Application to ethylene

We present a development of the dipole moment and polarizability operators of X₂Y₄ molecules, using a tensorial formalism analogous to the one developed for tetrahedral and octahedral molecules [V. Boudon, J.-P. Champion, T. Gabard, M. Loëte, F. Michelot, G. Pierre, M. Rotger, Ch. Wenger, M. Rey, J. Mol. Spectrosc. 228 (2004) 620–634]. These operators are involved in the calculation of the intensities of rovibrational transitions as well as in the calculation of the Stark effect. Expressions for the matrix elements are derived. A model for the study of the Stark effect in isolated bands of such molecules is proposed and has been used to predict the Stark spectra of the ν₁₂ band of ethylene. Values of the polarizability coefficients have been calculated using ab initio methods.     

Elements of irreducible tensorial matrices generated by finite groups with applications to ligand field Hamiltonians

Using symmetry to determine Hamiltonian matrix elements for quantum systems with finite group symmetry is a special case of obtaining group-generated irreducible tensorial matrices. A group-generated irreducible tensorial matrix transforms irreducibly under the group and is a linear combination of group transformations on a reference matrix. The reference matrix elements may be appropriate integrals or parameters. The methods of normalized irreducible tensorial matrices (NITM) are employed to express elements of the generated matrix in terms of those of the reference matrix without performing the actual transformations. Only NTTM components of the reference matrix with the same transformation properties as the group-generated matrix will contribute to its elements. The elements of invariant symmetry-generated matrices are proportional to simple averages of certain elements of the reference matrix. This relation is substantially more efficient than previous techniques for evaluating matrix elements of octahedral and tetragonal d-type ligand-field Hamiltonians.     

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     

Direct energy functional minimization under orthogonality constraints

The direct energy functional minimization problem in electronic structure theory, where the single-particle orbitals are optimized under the constraint of orthogonality, is explored. We present an orbital transformation based on an efficient expansion of the inverse factorization of the overlap matrix that keeps orbitals orthonormal. The orbital transformation maps the orthogonality constrained energy functional to an approximate unconstrained functional, which is correct to some order in a neighborhood of an orthogonal but approximate solution. A conjugate gradient scheme can then be used to find the ground state orbitals from the minimization of a sequence of transformed unconstrained electronic energy functionals. The technique provides an efficient, robust, and numerically stable approach to direct total energy minimization in first principles electronic structure theory based on tight-binding, Hartree-Fock, or density functional theory. For sparse problems, where both the orbitals and the effective single-particle Hamiltonians have sparse matrix representations, the effort scales linearly with the number of basis functions N in each iteration. For problems where only the overlap and Hamiltonian matrices are sparse the computational cost scales as O(M2N), where M is the number of occupied orbitals. We report a single point density functional energy calculation of a DNA decamer hydrated with 4003 water molecules under periodic boundary conditions. The DNA fragment containing a cis-syn thymine dimer is composed of 634 atoms and the whole system contains a total of 12,661 atoms and 103,333 spherical Gaussian basis functions.     

On the implicit bond-dependency origins of bridge interactions

The indirect (through-bridge) components of chemical interactions between atomic orbitals (AO) are shown to originate from the indirect dependencies between AO due to the orbital intermediaries in the bond system of the molecule. They are expressed in terms of the bridge-coupling elements of the density matrix via the chain rule transformation of the implicit derivatives between the indirectly bonded AO in the molecular bond system. The elements of the charge-and-bond-order (CBO) matrix are interpreted as the canonical derivatives between the AO-projections onto the bond subspace combining the occupied Molecular Orbitals (MO). The chain-rule manipulations are then used to express the scattering amplitudes via AO intermediaries in terms of the relevant elements of the CBO matrix. The squares of such amplitudes are related to the Wiberg-type indirect bond components, which complement the familiar direct Wiberg bond-order contributions. The interference implications of the probability scatterings via the multiple cascades involving all basis functions are examined. These probability propagations are shown to preserve the stationary conditional probabilities of the underlying molecular communication channel in AO resolution.     

Theoretical study on platinabenzene and mono- and difluorinated platinabenzenes: Structure, properties, and aromaticity

The electronic structures and properties of the platinabenzene and mono- and difluorinated platinabenzenes isomers have been investigated using hybrid density functional B3LYP theory. Basic measures of aromatic character were derived from structure, molecular orbital, and nuclear independent chemical shift (NICS). An energetic criterion suggests that ortho isomer of monofluorinated and F15 isomer of difluorinated platinabenzenes enjoy conspicuous stabilization. The polarizability and molecular orbital analysis are compatible with this result. NICS values calculated at several points above the ring center fail to give the result consistent with that based on relative energy, polarizability, and molecular orbital analysis. The atoms in molecules analysis indicates a correlation between NICS (1.0) and the electron density of the ring critical point (ρ_rcp) in monofluorinated platinabenzenes. There is a similar correlation in difluorinated platinabenzenes (except for F12 and F24 isomers) between NICS (0.5) and ρ_rcp.