Finite-field many-body perturbation theory. X. Electric field gradients and other properties of N2

Finite-field MBPT calculations have been carried out for the electric field gradient and other electric properties of the nitrogen molecule. On the basis of correlation corrections computed through the fourth order in the electron correlation perturbation the infinite order MBPT result for the electric field gradient at the nitrogen nucleus has been estimated. The corresponding result combined with the NQR coupling constant for N₂ leads to the ¹⁴N nuclear quadrupole moment of 0.0205 ± 0.0010 barn in agreement with the experimental atomic measurement and other molecular calculations. The MBPT estimate of the quadrupole moment of N₂ gives −1.107 ± 0.038 au in agreement with the most recent experimental value.     

Near-degeneracy effects and efficiency of MBPT calculations of molecular properties. Polarizability curve of H2

The polarizability curve of H₂ is calculated by using the finite-field perturbation method. All self-consistency effects are accounted for at the HF level and many-body perturbation theory (MBPT) is used to evaluate the correlation contributions. Using a single HF determinant as a reference in MBPT calculations makes the near-degeneracy effects of essential importance on increasing the interatomic distance. Nevertheless, applying the MBPT scheme with appropriate fourth-order terms gives nearly exact values of both components of the polarizability tensor for interatomic distances up to ≈3.6 au.     

Direct versus indirect many-body methods for calculating vertical electron affinities: applications to F−, OH− , NH2−, CN−, Cl−, SH− and PH2−

Electron propagator theory (EPT) is applied to calculating vertical ionization energies of the anions F⁻, Cl⁻, OH⁻,SH⁻, NH₂⁻, PH₂⁻ and CN⁻. Third-order and outer valence approximation (OVA) quasiparticle calculations are compared with ΔMBPT(4) (MBPT, many-body perturbation theory) results using the same basis sets. Agreement with experiment is satisfactory for EPT calculations except for F⁻ and OH⁻, while the ΔMBPT treatments fail for CN⁻. EPT(OVA) estimates are reliable when the discrepancy between second- and third-order results is small. Computational aspects are discussed, showing relative merits of direct and indirect methods for evaluating electron binding energies.     

Counterpoise corrected calculations at the correlated level: A simplified method using LMOs

Ab initio calculations have been performed in order to investigate the counterpoise corrections, especially at the correlated level for molecular interactions. It is pointed out that, when using a localized representation, the calculations using the MBPT/MP2 method can be simplified. The H₂O + H₂O system was studied, with the use of 6-31 G* basis set. The method allows one to determine the intramolecular correlation components in a simplified way. Boys' localization procedure was applied throughout, both in the occupied as well as in the virtual spaces.     

An ab initio calculation of 14n quadrupole coupling constants

Ab initio SCF-MO calculations of ¹⁴N quadrupole coupling constants are reported for HCN, HNC, CH₃CN, CH₃NC, NH₃, NH₂NH₂, FCN, N₂O, (CN)₂, BrCN, pyridine and pyrazine. There is excellent correlation between calculation and experiment yielding Q = 1.503 ± 0.159 × 10^?26 cm² for the ¹⁴N nuclear quadrupole moment. Dunning sp basis sets are more than adequate for such calculations, STO/4G basis sets yielding almost identical results for pyridine and pyrazine. Unsuccessful attempts were made to correlate coupling constants with electronic population analysis indices.     

Is fifth-order MBPT enough?

Fifth- and higher-order MBPT results are reported for a series of examples, BH, Be₂, HF and H₂O, for which higher-order perturbation theory might be important. MBPT(5) differs from MBPT(4) by as much as 4.3 mh, and by constructing the size-extensive [2,1] Padé approximant, which is possible with E⁽⁵⁾, one can get exceptional agreement with the full CI results. Variational perturbation results are also reported.     

Consideration of dipole–quadrupole interactions in molecular based equations of state

The thermodynamic behaviour of a number of real substances is determined by dipolar as well as quadrupolar interactions of the molecules. In equations of state (EOS) like, e.g. BACKONE separate contributions to the Helmholtz energy for the dipolar and the quadrupolar interactions are considered but no cross contributions. Here, the concept of effective dipole and quadrupole contributions is suggested in which the effective dipole strength μ_e is influenced by the quadrupole cross interaction. Similarily, the effective quadrupole strength Q_e takes into account the dipole cross interaction. In order to arrive at these effective dipolar and quadrupolar strengths, molecular simulations are performed. From the simulation results correlation equations are derived which are used in combination with BACKONE for the calculation of vapour–liquid equilibria (VLE) of real mixtures. By using these effective moments, the only required binary mixing rule parameter k_ij tends to small values of about 0.01 and becomes temperature-independent. Moreover, the VLE pressures are predicted now considerably better than without consideration of the cross contributions.     

Application of many-body perturbation theory in the localized representation for the all-trans conjugated polyenes

Ab initio self-consistent field (SCF ) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C_2n+2H_2n+4. The canonical occupied and virtual molecular orbitals (MO s) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT , the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.     

Vibrational deactivation of CO(v = 1) by p-H2. The importance of the higher-order multipole moments

Detailed calculations show that the agreement with the experimental rate constant for the vibrational deactivation of CO by p-H₂ is improved by including the octopole moment and the hexadecapole moment of CO. Previous calculations included only the dipole and the quadrupole moments. The present theoretical rates are 10–30 percent lower than the experimental values.     

A fast CI method for closed shells

A variational method for closed shells derived from MBPT is proposed. The method consists in the diagonalization of the hamiltonian in the subspace generated by the HF ground state |φ_HF) and f_i(H_o) V_res|φ_HF) (i = 1,2,… m) where H_o is the HF hamiltonian, V_res is the residual potential and the f_iti are arbitrary functions. Test calculations performed on H₂O give 97% of the double excitations CI limit with very short computer time.     

Information theoretic indices for characterization of chemical structures. By Danail Bonchev Wiley,New York, 1983

Wilson, Jankowski, and Paldus have recently applied nondegenerate many-body perturbation theory (MBPT ) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H₄). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low-order sum of the perturbation series is not very meaningful, depends strongly on details of the zero-order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.     

Hydrogen bond studies : 79. Correlation curves for properties of hydrogen bonded water molecules based on ab initio calculations

Correlation curves have been derived from previous ab initio MO-LCAO-SCF calculations made on water molecules in hydrates. The OH-stretching frequency shifts have been correlated with: (a) ratios of the intensity of v?v_OH for bonded water to that for free water, (b) shifts in the OH-distances and (c) quadrupole coupling constants for deuterium in D₂O. Shifts in quadrupole coupling constants are also correlated with shifts in OH-distances. Comparisons have been made with experimental data and the agreement is found to be satisfactory.     

Direction-dependent circular dichroism spectra of single crystals of cubic sodium uranyl acetate

The contribution of the electric quadrupole mechanism to the chirality of optically active cubic sodium uranyl acetate single crystals has been established by measurements of the direction dependence of circular dichroism spectra. The CD bands for Σ_g⁺→Δ_g transitions are found to be direction dependent while those for Σ_g⁺→Π_g are direction-independent for light propagation k parallel to the (100) and (111) directions of the cubic cell. The contribution of the electric quadrupole mechanism to the chirality relative to that of the magnetic dipole mechanism is estimated to be about 20%.     

Methods for the calculation of Voh in OH?O hydrogen bonds

Ab initio calculations are reported for dimerization-induced changes, Δk, in the harmonic force constant k of the H-bonded OH in water dimer. Two dimer geometries are considered. Δk is obtained by considering the perturbation of a given monomer OH potential by the interaction energy in the dimer in question. The interaction energy is partitioned to identify the role of the various contributions to Δk. The sensitivity of Δk to the choice of the one-electron basis set is studied by using five different basis sets, some of which have a set of bond functions in the H? O bond. At the correlated level, correction for basis set superposition error is found to be essential. A comparison is made of the correlation contribution to Δk as given by the CEPA1, MP2, MP3, and MP4 methods. Of these, MP2 gives exaggerated results. Nevertheless, for economical and reasonably accurate calculations on large systems the MP2 approach in the ESPB basis set is advocated. The most accurate calculations yield a shift Δv_0-;1 of – 121 cm^?1 for the uncoupled donor O-H vibrational frequency in water dimer.     

On the quadrupole splitting of a low-spin Iron(III)-Dithio Chelate

The magnetically perturbed Mössbauer spectra of iron(III) (dithioacetylacetonate)₃ show V_zz<0 corresponding to a d_xy hole and a²A ground term. These results support a recent study of the temperature dependence of the quadrupole splitting and suggest that the origin of the quadrupole splitting is primarily in the distribution of non-bonding electrons.     

A comparison of different many-body perturbation theory calculations of the ground state of SiS

A comparison of different many-body perturbation theory (MBPT ) calculations of the ground state rotational and vibrational constants of SiS is made. The calculations are performed up to the complete fourth-order MBPT level, and in all cases two basis sets are utilized. The results of the third-order and some incomplete fourth-order calculations are in good agreement, but the complete fourth-order is among the worst as compared with the experimental data. Analysis of the different contributions to the calculated correlation eneriges points towards the necessity of including even higher-order terms of the(MBPT ) expansion.     

Concentration fluctuations in binary mixtures of model polar fluids

We present calculations of the mean square concentration fluctuations, S_α(0), for binary mixtures of model polar fluids. The assumed pair interactions are taken to be of the forms of a hard core plus either dipole-dipole, quadrupole-quadrupole or dipole- quadrupole terms. The calculations are carried out within a mean field approximation. We have considered in some detail the interplay between size differences and the difference in the strength and range of the potentials in deciding how S_α(0) deviates from the ideal behaviour.     

Applicability of multi-reference many-body perturbation theory to the determination of potential energy surfaces: A model study

The recently written CI -based multi-reference many-body perturbation theory (MR-MBPT ) program package is exploited to study a simple ab initio minimum basis set model involving four hydrogen atoms in a rectangular configuration. This model was examined earlier by several authors using both coupled cluster (CC ) and finite-order MBPT approaches. Here we present the MR-MBPT results up to the 50th order and examine the effect of various shifting techniques on the convergence behavior of this approach. It is shown that in contrast with CC methods, both single and MR finite-order MBPT potential energy calculations are plagued with convergency and intruder state problems, which can be particularly severe when the latter approach is employed for non-degenerate situations.     

Coupled‐perturbed Hartree–Fock theory for quasi–one‐dimensional periodic systems: Calculation of static and dynamic nonlinear optical properties of model systems

An alternative method to solve the coupled‐perturbed Hartree–Fock (CPHF) equations for infinite quasi–one‐dimensional systems is presented. The new procedure follows a proposal made by Langhoff, Epstein, and Karplus to obtain perturbed wavefunctions free from arbitrary phase factors in each order of perturbation. It is based on the intermediate orthonormalization of the perturbed wavefunctions (which is different from the usual one) and a corresponding selection of the Lagrangian multipliers. In this way it is possible to incorporate the orthonormalization conditions into the set of CPHF equations. Moreover, a new, advantageous procedure to determine the derivatives of the wavefunction with respect to the quasimomentum k is presented. We report calculations of the dipole moment, the polarizability α, and the first hyperpolarizability β for different polymers (poly‐HF, poly‐H₂O, trans‐polyacetylene, polyyne, and polycarbonitrile) for different frequencies. These results are extensively compared with oligomer calculations. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 251–268, 2003     

Electric field gradients in the ionic crystals NaNO2, NaBF4, NaNO3, and Ba(NO3)2

The electric field gradients (EFG) at the sites of the cations and the “central” atoms of the anions in the ionic crystals NaNO₂, NaBF₄, NaNO₃ and Ba(NO₃)₂ are calculated by a method based on a combination of the semi-empirical INDO method for the charge distribution and the intramolecular EFG with a lattice summation in the framework of the extended multipole model. At some lattice sites the contribution of the induced dipole and quadrupole moments to the EFG is comparable with the contribution of the point charges. The charge distribution within the molecular ions is found by adjusting either the calculated asymmetry parameter η or the z-component of the EFG to the experimental value deduced from nuclear quadrupole coupling constants. These charge distributions are in good agreement with those gained from INDO calculations. The calculated and experimental quadrupole coupling constants of nuclei in anions and cations are compared.