The connected moments expansion for the zero-point energy of coupled anharmonic oscillators

The connected moment expansion (CMX) technique is used to calculate the zero-point energy of an arbitrary system of coupled anharmonic oscillators. When the anharmonic term has the form of a polynomial with respect to the normal coordinates, it is possible to calculate the zero-point energy in a completely automated way. A numerical example is presented, demonstrating the power of the new method.     

Analytic properties of connected moments expansions

The derivation of the connected moments expansion (CMX ) is examined as well as the singularities that arise in the series expansion for the ground-state energy. Explicit analytic results are presented that show a canceling of these singularities. Also, an alternate moments expansion (AMX ) is derived that closely models the CMX but displays a varied computational range. © 1994 John Wiley & Sons, Inc.     

Connected moments expansion calculations of the correlation energy in small molecules

The second-order connected moments expansion (CMX(2)) approach to calculation of the correlation energy is tested numerically on several closed-shell di- and tri-atomic molecules. Benchmark computations performed within 6–31G⁷ basis set reveal that CMX(2) usually recovers more than 50% of the MP3 correlation energy and improves the SCF molecular geometries at a cost comparable to the MP3 calculations.     

On a resonance energy model based on expansion in terms of acyclic moments: Exact results

Summary The new concept of the resonance energy in conjugated hydrocarbons introduced by Jiang Y, Zhang H (1989) Theor Chim Acta 75:279 is further developed. This model is based on expansion of the -electron energy in terms of moments which are also equal to numbers of closed walks in a molecular graph. The reference system is established by counting only acyclic walks, i.e. those tracing only on acyclic subgraphs. Because acyclic walks could be counted only up to some finite length, the energy of the reference system has been evaluated by truncating higher terms in the expansion. In this paper a finite expression for the energy of the same reference system is derived, thus allowing its exact evaluation. The exact values differ significantly from the truncated ones. This difference, as well as the discrepancy between exact results and chemical experience, are discussed.     

On the representation of molecular quadrupole moments in terms of atomic moments

The magnitude and algebraic sign of the molecular quadrupole moments of the homonuclear diatomic molecules N2, O2, F2, P2, S2 and Cl2 are analyzed by expressing them as a sum of the quadrupole moments of the free atoms and an induced molecular quadrupole due to bond formation. This induced molecular quadrupole is further analyzed in terms of in situ atomic dipole and quadrupole moments constructed following the electron partitioning method suggested by Hirshfeld. These in situ moments are interpreted in terms of the sigma and pi character of the chemical bonds and are compared with those predicted by the DMA method of Stone (The Theory of Intermolecular Forces; Clarendon: Oxford, 1996).     

On the calculation of molecular dipole moments

The approximation made in the calculation of molecular dipole moments by including only the point charges and the atomic dipoles is evaluated in different all-valence (or all)-electrons MO procedures. In the CNDO method, the use of the exact formula after retransformation of the atomic basis into Slater orbitals gives poorer values than the Pople-Segal's procedure.     

On the accuracy of computed excited-state dipole moments

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.     

On the validity of the BEBO method

The use of tha BEBO method proposed by Johnston and Parr is considered, taking into account the observations of Jordan and Kuafman. It is found that the original formulation is applicable even when the new values for noble gas pairs are employed,if an appropriate choice of the constant in Pauling's relation is made.     

On the validity of single atom chemistry

This study is intended to apply to the many experiments in which small numbers of radioactive isotopes are artificially produced whose half lives are approximately the same time as that required for chemical identification. Conventional chemical kinetics combined with radioactive decay yields equations that were analyzed for their applicability to regimes containing much less than a statistical ensemble of atoms. Deviations from the predicted most-probable value for the concentration of a given chemical species are calculated using standard probability functions. It was found that a surprisingly small number of atoms is required to establish chemical identity under the usual conditions of experimentation.     

On establishing the validity of enthalpy-entropy relationships

All the methods so far proposed for deriving enthalpy-entropy relations fail to take into consideration the physical reasons for implied functional dependence between the activation parameters. In order to avoid spurious results it is essential to establish first the physical basis upon which the variation in the specific reaction rate itself depends, and then to carry that information through to the enthalpy-entropy plane.The proposals made here are of general application for establishing valid functional enthalpy-entropy relations, whatever their form, and in this context linear correlations are merely a subset.     

On the thermal expansion of molecules

Experimental results for a variety of molecules have shown that their bond lengths expand appreciably when the molecules are heated, as expected from the asymmetric Morse-like potentials characterizing the bonds. However, in a series of papers on structures determined by gas-phase electron diffraction, Giricheva et al. claimed that, for very hot MX₃ molecules, effects of out-of-plane vibrations cancel the thermal expansion of the M–X bonds. This is incorrect. Although the computations to support their claim were correct as far as they went, the authors neglected the effects of asymmetric vibrational modes and centrifugal stretches of the bonds. In the present report, we show that quantum chemical computations for LaI₃ reveal the crucial roles played by the terms neglected by Giricheva et al., which terms are responsible for thermal bond stretches of approximately 0.023 Å at 1142 K. In addition, because the iodine atoms in LaI₃ are further apart in the mean structure than the sum of their Pauling van der Waals radii, the geminal nonbonded interactions are attractive. This accounts for the fact that the Morse asymmetry constant for the symmetric stretch mode is smaller than that for the asymmetric stretch. It also helps to explain the very large amplitude of the out-of-plane puckering mode, which tends to decrease the La–I bond length during the puckering trajectory.     

On the applicability of the first-order equation for the reactions of solids

It is suggested that besides its traditional application to describe random nucleation, the first-order equation F1 can be used for the diffusion kinetics of gas-solid small particles reactions.

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, F1 - - .

     

On the calculation of induced electric and magnetic moments of atoms and molecules

We present a many-electron method for calculating first and second order perturbed wavefunctions due to external electric and magnetic fields, which identifies the important correlation effects for the response function a priori and calculates them variationally. It is accurate, economical and applicable to ground and excited states with the same ease. Thus, it presents a useful alternative to the well-known coupled Hartree-Fock methods. As an application of this method, we calculate the static electric dipole polarizability of the Be ground state. We find α_d = 5.49 ų in agreement with recent extensive calculations.     

On the use of moments for describing the molecular orientation distribution

The posibilities of drawing conclusions about angular distribution functions F(ω) from measured moments [cos^lω] = ∫ cos^lω F(ω)d(ω) are discussed. F(ω) is expanded as a sum of Legendre polynomials with the moments in the coefficients. In practice only the first few moments are experimentally available. The limited use of a truncated series is demonstrated for distributions in polymers, electric fields and liquid crystals.     

On the applicability of CNDO indices for the prediction of chemical reactivity

A series of CNDO/2 molecular orbital properties were evaluated to determine their utility in parameterizing chemical reactivities. Some of these indices were used previously for only electron methods and were extended here to include the framework. Theoretical rationales were given for this extension to the semi-empirical all valence electron methods. Four systems, the aromatic hydrocarbons, the benzene derivatives, the substituted benzoic acids, and the substituted phenyl amines, were studied to test how well these indices can parameterize chemical reactivities. This study focused on reactions involving both and electrons where the reactive site is not necessarily on the aromatic framework. For the nonplanar and heteropolar systems, these indices performed as well as the Hückel method did for the classical aromatics. These CNDO indices should perform effectively in multivariable regressions to parameterize the reactivities for more complicated problems such as those encountered in quantitative structure activity relationships of drugs.