Nonstationary perturbation theory for open-shell molecules

Nonstationary perturbation theory equations have been obtained for open-shell molecules. The equations were formulated in terms of a density matrix in the MO-LCAO method. The first variant is coupled perturbation theory in the framework of the restricted Hartree-Fock method for open shells, and the second variant is variational perturbation theory for ground and excited electronic states of molecules, in which the perturbed wave function of the system is constructed in the form of a superposition of the ground and singly excited configurations composed of the Hartree-Fock orbitals of the open shell. A calculation of the Cauchy moments of the dynamic dipole polarizability of several molecules of conjugated open-shell hydrocarbons, viz., doublet states of odd alternant hydrocarbons, as well as triplet excited states and doublet states of radical ions of even alternant hydrocarbons, has been carried out in the framework of both methods.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 18–27, January–February, 1985.     

Convergence radii of the perturbation expansions for the ground-state energies of finite Hubbard models

The ground state energies of finite Hubbard molecules are calculated by numerically solving the Lieb–Wu equations for a complex Hubbard repulsion parameter U. From the positions of the singular points located in the complex plane, the radii of convergence of the perturbation expansions for the ground state energies are determined.     

Interpreting ultrafast molecular fragmentation dynamics with ab initio electronic structure calculations

High-level ab initio electronic structure calculations are used to interpret the fragmentation dynamics of CHBr(2)COCF(3), following excitation with an intense ultrafast laser pulse. The potential energy surfaces of the ground and excited cationic states along the dissociative C-CF(3) bond have been calculated using multireference second order perturbation theory methods. The calculations confirm the existence of a charge transfer resonance during the evolution of a dissociative wave packet on the ground state potential energy surface of the molecular cation and yield a detailed picture of the dissociation dynamics observed in earlier work. Comparisons of the ionic spectrum for two similar molecules support a general picture in which molecules are influenced by dynamic resonances in the cation during dissociation.     

Probing the spin multiplicity of gas-phase polycyclic aromatic hydrocarbons through their infrared emission spectrum: A theoretical study

The anharmonic infrared emission spectrum following an optical excitation has been calculated for a variety of polycyclic aromatic hydrocarbon molecules in their ground singlet electronic state or in their triplet state. The computational protocol relies on second-order perturbation theory and involves a quartic vibrational Hamiltonian, the vibrational quantum numbers being sampled according to a Monte Carlo procedure. In the case of neutral naphthalene, the IR spectrum obtained in the (ground) singlet state differs significantly from the spectrum in the triplet state, especially for out-of-plane CH bending modes. Although not as prominent, spectral differences in larger molecules are still observable.     

Connections between perturbation theory and the Van Vleck transformation: Illustrative calculations on the perturbed harmonic oscillator

We continue to examine the connection between perturbation theory and the Van Vleck unitary transformation. Here we illustrate the formalism derived earlier by applying it to compute the stationary states of the perturbed harmonic oscillator. We find that each solution of the traditional Brillouin-Wigner perturbation theory equations gives rise to a different unitary transformation which, when operating on the unperturbed ground state, produces one or the other of the perturbed eigenstates. With any of the perturbed states able to be reached by a unitary transformation on the unperturbed ground state, we advise caution in using approximate solutions of the perturbation equations in general cases, lest an unexpected stationary state be obtained.     

Application of fragment molecular orbital scheme to silicon-containing systems

The fragment molecular orbital (FMO) scheme has been successfully used for a variety of large-scale molecules such as proteins and nucleic acids so far. We have applied the FMO calculations to the silicon-containing systems like polysilanes. The error caused by the fragmentation was examined by the Hartree–Fock method and the second-order Møller-Plesset (MP2) perturbation method for the ground state energy. The dynamic polarizability as a linear response property was also evaluated with and without the fragmentation. A series of numerical comparisons showed that the FMO scheme is applicable to silicon-based molecules with reasonable accuracy. This implied a potential availability of FMO calculations for the issues relevant to nanoscience and nanotechnology.     

Molecular association in dimethyl sulfoxide-nitromethane mixtures: Raman spectroscopy and quantum-chemical calculations

Dimethyl sulfoxide-nitromethane (DMSO-NM) binary mixtures have been studied. Intermolecular associates are formed in these mixtures via the interaction between DMSO and NM molecular dipoles and hydrogen bonding. Ab initio calculations have been carried out at the MP2 perturbation theory level using the 6-31G(d, p) basis set to determine the optimal ground state geometry for DMSO complexes with NM and correctly assign new vibrational bands of molecules in various types of mixed intermolecular associates.     

The calculation of ground and excited state molecular polarizabilities: A simple perturbation treatment

Second order perturbation theory has been coupled with the CNDO/S CI method of Del Bene and Jaffé to calculate the ground and excited state polarizabilities of various molecules. It is found that this treatment produces reasonably good polarizabilities with great computational ease.     

Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory

The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.     

CNDO calculation of polarizabilities including polarization functions in the basis set

Electric polarizabilities are calculated by solving the first- and second-order perturbation equations through a variational procedure. Satisfactory numerical results are obtained for a number of molecules using the CNDO approximation with an extended basis set.     

Recent developments in the theory of one- and two-electron molecules

Recent theoretical work dealing with one- and two-electron molecules is reviewed. Results obtained using both the variational method and the perturbation theory are discussed for the ground states as well as for excited states of the molecules. Emphasis is placed on those results which are sufficiently accurate to yield definite conclusions with regard to either the system or the method.     

A modified PCILO method

The perturbative configuration interaction using strictly localized molecular orbitals, called the modified PCILO method, for which the use of the Rayleigh-Schrödinger many-body perturbation theory with the Moller-Plesset Hamiltonian partitioning is characteristic, has been proposed in this communication. On the CNDO/2 and INDO levels of Hamiltonian approximations strictly localized molecular orbitals have been constructed by solving modified Roothaan equations. From the zero and second order energy interatomic distances and harmonic force constants for some diatomic molecules have been calculated. The linear dependence of the correlation energy on the number of valence electrons in the series of the molecules CH₄, CH₃F, CH₂F₂, CHF₃ and CF₄ is perfect.     

Anharmonic Force Fields and Perturbation Theory in the Interpretation of Vibrational Spectra of Polyatomic Molecules

The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotational-vibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.     

Random-phase-approximation calculations on triplet spectra of conjugated molecules

Random-phase approximations (RPA) have been applied to the calculation of the triplet π-π* transition spectra of 18 conjugated molecules in the framework of Pariser-Parr-Pople approximations. It is found that the normal RPA (n-RPA) shows the triplet instability for most molecules in the Nishimoto-Mataga approximation of electron-repulsion integrals. However, it is shown that this instability can be circumvented by the use of the renormalized RPA (r-RPA) in which the correlated ground states are calculated by the second-order perturbation theory. It is also shown that even in the n-RPA the suitable parametrization of electron-repulsion integrals removes this instability. It is ascertained that such an increasing order of energies as ω(n-RPA)<ω(Tamm-Dancoff approximation)<ω(r-RPA) holds for most of energy levels.     

Electronic ground state and the d-d transitions in bis(biuretato)cobaltate(III) ions

The electronic structure of a class of compounds based on the bis(biuretato)cobaltate(III) ion has been investigated by spectroscopic methods (UV-vis, CD, MCD), magnetic susceptibility, and ligand field theory. The concept of molecules in molecules has been introduced to account for the conjugated pi system of the whole ligand entity and its perturbation of the metal ion 3d orbitals. The Slater-Condon-Racah scheme was fully exploited; in particular, differences in occupation numbers of the spin orbitals have been used in the spectral assignments of the d-d transitions. The energy calculations used one sigma parameter, two pi parameters, and two Racah parameters. The pi parameters, which were derived from Orgel orbitals of chi and psi type, were found to be positive. The observed charge-transfer transitions are metal <-- ligand. The results of our calculations are in agreement with available experimental data, including the spin triplet ground state and the position of the lower d-d transitions. The approach is general and, for example, applicable to heme iron(II).     

Perturbation theory for excited states of molecules. III

The configuration interaction perturbation theory and the single configuration perturbation theory developed in Paper I is applied to the problem of chemical reactivity for conjugated hydrocarbon molecules. Various related hetromolecules are also considered. It is found that the pattern of reactivity for excited states is much the same as for the ground state.I wish to express my appreciation to Dr. A. T. Amos for constant encouragement during the preparation of this paper and to the S.R.C. for the provision of a maintenance grant.     

Excited state radiationless decay process with Duschinsky rotation effect: formalism and implementation

Duschinsky rotation effect is a simple and effective way to characterize the difference between the ground state and excited state potential energy surfaces. For complex molecules, harmonic oscillator model is still the practical way to describe the dynamics of excited states. Based on the first-order perturbation theory a la Fermi golden rule, the authors have applied the path integral of Gaussian type for the correlation function to derive an analytic formalism to calculate the internal conversion rate process with Duschinsky rotation effect being taken into account. The validity of their formalism is verified through comparison with previous work, both analytically for the case of neglecting Duschinsky rotation and numerically for the ethylene molecules with two-mode mixing. Their expression is derived for multimode mixing.     

Thermodynamics of the polarizable stockmayer fluid

Pressure and internal energy of a fluid composed of polarizable Stockmayer molecules have been calculated by a molecular dynamics computation as well as by thermodynamic perturbation theory. It is found that the effect of molecular polarizability is underestimated by perturbation theory.     

GVVPT2 multireference perturbation theory description of diatomic scandium, chromium, and manganese

With relatively simple model spaces derived from valence bond models, a straightforward zero-order Hamiltonian, and the use of moderate-sized Dunning-type correlation consistent basis sets (cc-pVTZ, aug-cc-pVTZ, and cc-pVQZ), the second order generalized Van Vleck perturbation theory (GVVPT2) method is shown to produce potential energy curves (PECs) and spectroscopic constants close to experimental results for both ground and low-lying excited electronic states of Sc(2), Cr(2) and Mn(2). In spite of multiple quasidegeneracies (particularly for the cases of Sc(2) and Mn(2)), the GVVPT2 PECs are smooth with no discontinuities. Since these molecules have been identified as ones that widely used perturbative methods are inadequate for describing well, due to intruder state problems, unless shift parameters are introduced that can obfuscate the physics, this study suggests that the conclusion about the inadequacy of multireference perturbation theory be re-evaluated. The ground state of Sc(2) is predicted to be X(5)∑(u)(-), and its spectroscopic constants are close to the ones at the MRCISD level. Near equilibrium geometries, the 1(3)∑(u)(-) electronic state of Sc(2) is found to be less stable than the quintet ground state by 0.23 eV. The Cr(2) PEC has several features of the Rydberg-Klein-Rees (RKR) experimental curve (e.g., the pronounced shelf at elongated bond lengths), although the predicted bond length is slightly long (R(e) = 1.80 ? with cc-pVQZ compared to the experimental value of 1.68 ?). The X(1)∑(g)(+) ground state of Mn(2) is predicted to be a van der Waals molecule with a long bond length, R(e), of 3.83 ? using a cc-pVQZ basis set (experimental value = 3.40 ?) and a binding energy, D(e), of only 0.05 eV (experimental value = 0.1 eV). We obtained R(e) = 3.40 ? and D(e) = 0.09 eV at the complete basis set (CBS) limit for ground state Mn(2). Low lying excited state curves have also been characterized for all three cases (Cr(2), Mn(2), and Sc(2)) and show similar mathematical robustness as the ground states. These results suggest that the GVVPT2 multireference perturbation theory method is more broadly applicable than previously documented.