Self-consistent perturbation theory for conjugated molecules

The first order changes in the orbital energies of a number of hydrocarbons due to perturbations at particular atoms are given. These are useful for discussing ionization potentials, polarographic reduction and oxidation potentials, and electron affinities of heteromolecules.

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Zusammenfassung Die Änderungen erster Ordnung von Einelektronenenergien bei Störung an bestimmten Atomen werden für eine Reihe von Kohlenwasserstoffen angegeben. Sie erweisen sich als brauchbar für die Diskussion von Ionisationspotentialen, polarographischen Oxydations- und Reduktionspotentialen und Elektronenaffinitäten von Heteromolekülen.

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Résumé Les variations au premier ordre des énergies des orbitales, sous l'influence de perturbations sur des atomes déterminés, sont données pour un certain numbre d'hydrocarbures. Elles sont utiles pour la discussion des potentiels d'ionisation, des potentiels d'oxydation et de réduction polarographiques et des affinités électroniques des molécules hétéroatomiques.

     

Self-consistent perturbation theory for conjugated molecules

Since an external field produces a drift of the mobile -electrons in the plane of a conjugated molecule the electric polarizability of these molecules is anisotropic. The S.C.F. perturbation theory is used to calculate the -electron contribution to the polarizability tensor for a number of conjugated molecules. Using previous theoretical and semi-empirical values for the polarizabilities of C-C and C-H bonds the contribution is estimated and total polarizabilities for the molecules obtained as the sum of the and contributions. There is reasonable agreement between these theoretical values and the available experimental ones.

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Zusammenfassung Ein äußeres elektrisches Feld verschiebt die -Elektronen in der Molekülebene, so daß die elektrische Polarisierbarkeit von Molekülen mit konjugierten Bindungen anisotrop ist. Mittels SCF-Störungsrechnung wurde der Beitrag der -Elektronen zum Tensor der Polarisierbarkeit für eine Anzahl von Molekülen berechnet und der Beitrag des -Bindungsgerüstes aus semiempirischen Größen ermittelt. Die Übereinstimmung mit gemessenen Werten ist zufriedenstellend.

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Résumé La polarisabilité électrique des molécules conjuguées est anisotrope car un champ extérieur provoque un déplacement des électrons mobiles dans le plan moléculaire. La théorie des perturbations SCF est utilisée pour le calcul de la contribution des électrons au tenseur de polarisabilité d'un certain nombre de molécules conjuguées. En utilisant des valeurs théoriques et semi-empiriques antérieures concernant les polarisabilités des liaisons C-C et C-H on peut évaluer la contribution des électrons . Les polarisabilités totales sont obtenues comme la somme des contributions et . L'accord avec les données expérimentales disponibles est raisonnable.

     

Self-consistent perturbation theory for conjugated molecules

Using self-consistent perturbation theory the first order changes in the spin densities of positive and negative ions of substituted hydrocarbons are calculated. By comparison with ESR hyperfine splitting constants the values of the inductive parameters for aza and methyl substitution are obtained. For aza substitution the most reliable estimate is –1.73 eV in agreement with the best theoretical estimate of –1.85 eV. For methyl substitution in anthracene the data can best be explained by using different values for the positive and negative ions so as to allow for hyperconjugation. The values obtained are –0.3 for the positive ion and –0.15 for the negative ion. The theoretical values are –0.33 and –0.11 .

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Zusammenfassung Mittels selbstkonsistenter Störungsrechnung wurden die Spindichteänderungen erster Ordnung von substituierten Kohlenwasserstoffen berechnet. Durch Vergleich mit ESR-Hyperfeinstrukturkonstanten erhält man dann die induktiven Parameter für Aza- und Methylsubstitution. Für Azasubstitution ist der wahrscheinlichste Wert –1,73 eV, in guter Übereinstimmung mit dem als dem besten geltenden Wert von –1,85 eV. Bei Methylsubstitution im Anthrazen benötigt man für positive und negative Ionen verschiedene Werte, um die Hyperkonjugation zu berücksichtigen, und zwar –0,3 für das positive Ion und –0,15 für das negative. Theoretische Werte sind –0,33 bzw. –0,11 .

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Résumé La théorie des perturbations self-consistantes est utilisée pour le calcul de la variation du premier ordre des densités de spin des ions positifs et négatifs des hydrocarbures substitués. Les valeurs des paramètres inductifs pour les dérivés aza ou méthylés sont obtenues par comparaison avec les constantes de séparation hyperfine en R.P.E. Pour une substitution aza l'estimation la plus sûre donne –1,73 eV en accord avec la meilleure valeur théorique de –1,85 eV. Pour la substitution du méthyle dans l'anthracène les données expérimentales sont le mieux expliquées en utilisant des valeurs différentes pour les ions positifs et négatifs afin de tenir compte de l'hyperconjugaison. Les valeurs obtenues sont –0,3 pour l'ion positif et –0,15 pour l'ion négatif. Les valeurs théoriques sont –0,33 et –0,11 .

     

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.     

Self-consistent perturbation theory calculations of nuclear spin coupling constants in thiophenes

The ring proton-proton coupling constants of thiophene and 14 monosubstituted derivatives have been calculated using the perturbated SCF INDO method. The results reproduce satisfactorily signs, magnitudes and some trends of the experimental values, but the internal order of long-range constants in the 3-substituted thiophenes is not reflected.     

Möller-plesset perturbation theory for excited states of molecules

We consider the criteria that should be met by the perturbation theory for excited states to preserve the advantages of the Möller-Plesset version for the ground state. A few zero-approximation Hamiltonians are proposed and discussed. Expressions for the first-order corrections to the wave function and for the second-order corrections to the energy of excited states are obtained. The expressions are consistent with the conditions of orthogonality of states with the same symmetry. It is shown that the perturbation theory for excited states proposed in this work is identical to the Möller-Plesset perturbation theory for the ground state.     

Generalized Jansen's perturbation theory for exchange interactions between aroms or molecules

The theory for treating exchange interactions between atoms or molecules as a perturbation, which was first propoed by Jansen, is extended to general cases by the use of the group algebraic technique and a nonorthogonal basis set. As a result, a new expresion for the perturbation ket and energy of each order is obtained. A comparion of the expression with those presented by other investigators is made.     

Møller-Plesset (MP2) perturbation theory for large molecules

Summary A novel formulation of MP2 theory is presented which starts from the Laplace transform MP2 ansatz, and subsequently moves from a molecular orbital (MO) representation to an atomic orbital (AO) representation. Consequently, the new formulation is denoted AO-MP2. As in traditional MP2 approaches electron repulsion integrals still need to be transformed. Strict bounds on the individual MP2 energy contribution of each intermediate four-index quantity allow to screen off numerically insignificant integrals with a single threshold parameter. Implicit in our formulation is a bound to two-particle density matrix elements. For small molecules the computational cost for AO-MP2 calculations is about a factor of 100 higher than for traditional MO-based approaches, but due to screening the computational effort in larger systems will only grow with the fourth power of the size of the system (or less) as is demonstrated both in theory and in application. MP2 calculations on (non-metallic) crystalline systems seem to be a feasible extension of the Laplace transform approach. In large molecules the AO-MP2 ansatz allows massively parallel MP2 calculations without input/output of four-index quantities provided that each processor has in-core memory for a limited number of two-index quantities. Energy gradient formulas for the AO-MP2 approach are derived.Dedicated to Prof. W. Kutzelnigg whose books on theoretical chemistry aroused my interest in this field     

Monte carlo simulation and thermodynamic perturbation theory for mixtures of diatomic molecules

The thermodynamic properties and site—site distribution functions of mixtures of non-spherical molecules are obtained by Monte Carlo simulation. A non-spherical reference-system perturbation theory based on the RISM equation is developed to predict these results. The agreement between theory and simulation for the thermodynamic properties is encouraging. Important differences in the relative peak heights of the site—site distribution functions from theory and simulation are attributed to the role of attractive forces in determining local structure in the fluid mixtures, where the volumes of the components are similar but the well depths differ.     

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.     

One-electron properties of molecules calculated using second-order multireference perturbation theory

A new form of second-order multireference perturbation theory coupled with finite-field perturbation theory is applied to evaluate some one-electron molecular properties. Several possible definitions of the zeroth-order Hamiltonian are considered and results tested against bench-mark full CI calculations. © 1995 John Wiley & Sons, Inc.     

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction.     

An application of mean-field perturbation theory for the adsorption of polar molecules in nanoslit-pores

In the present research study, we present the development of a model for characterizing and predicting the adsorption of polar molecules between two parallel plates based on mean-field perturbation theory. The electrostatic forces between fluid–fluid molecules in the slit shaped pore are modeled by considering permanent dipole–dipole interactions and permanent dipole-induced dipole moment interactions. The intermolecular potential for the electrostatic interactions was obtained by considering statistical averages over all possible orientations of the molecules. The proposed model is then used to study the sorption of water molecules in the slit shaped pore and an explicit equation for the Helmholtz free energy of the pore phase fluid is derived. Adsorption isotherms for different pore sizes are simulated and the relative contributions of fluid–wall and fluid–fluid interactions to the Helmholtz free energy are calculated as an illustration and compared with the results of existing models in the literature.AMS subject classification: 82B03, 82B05, 82B26, 82B30, 82D15, 31B10, 41A25     

Bounds for Hartree-Fock perturbation theory

Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.     

Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements

Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of ${\gamma = 1.4 a_{0}^{-1}}$ can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated.     

Accounting for translational invariance in analyzing contributions of perturbation theory to force-constant tensors of molecules

It has been shown that there are an infinite number of modes of representation of force constants in the form of a sum of the contributions of first-order and second-order perturbation theory, depending on the selection of the admixture of translation of the nuclear skeleton as a whole to the displacement of the nuclei. In particular, any force constant can be reprsented in the form of a specially constructed second-order relaxation term (or first-order with zero contribution); a representation has been found in which the first-order contributions for the displacements of all nuclei in the molecule are identical; rules of the sums for the relaxation terms have been derived, relating the changes in the Gel-Mann-Feynman forces on the nuclei in the molecule with displacements of various nuclei. For the electronic ground state of the molecule, the optimal representation of the force constants has been found, in which the minimum in the first-order contribution is combined with the minimum in the absolute magnitude of the second-order relaxation contribution. It has been proven that in the case of an unperturbed electronic state, the first-order contribution to any diagonal force constant is positive.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 3, pp. 280–287, May–June, 1985.     

Self-consistent wave functions of conjugated molecules by the one-dimensional electron gas model: Application to geometries and absorption spectra

A model based on one-dimensional electron gas theory has been developed which improves the π-electron wave functions of conjugated molecules by taking changes of bond length differences into account. Experimental bond lengths are reproduced with an average deviation of 0·005 Å; excitation energies are markedly improved over the simple model. The reliability of the model with respect to geometries is comparable to the PPP-SCF method.     

Self-consistent second-order screening in many-body theory

Self-consistent screening arises in all many-body problems where one-particle equations containing functionals of the solutions are considered. In the theory of simple metals, e.g., these one-particle equations are usually solved to second-order perturbation in the crystal pseudopotential and to first order in the screening. However, higher-order screening terms have a sizable effect on the form factors, the electron charge density, and the screened pseudopotential. The effects of second order are presented for the bcc simple metals Na and Ba. A nonlocal exchange-correlation potential has been used since local density approximations such as ρ^1/3 cause difficulties in the electron–electron dielectric function. © 1994 John Wiley & Sons, Inc.