Role of the configuration interaction in the CNDO/S calculation of optical rotatory strengths

The rotatory strengths calculated directly by the CNDO/S method exhibit a pronounced dependence on the size of configuration interaction (CI). In order to elucidate the role of highly excited configurations in such calculations the perturbation theory is employed. It is shown that the restriction of the CI size to 20–40 may be quite inadequate in some cases. The calculations of rotatory strengths of several optically active molecules containing carbonyl and amide chromophores has shown that the best results can be obtained for half of full CI but sometimes it is possible to restrict the CI size to 100 configurations. The agreement with experiment for all molecules considered is satisfactory.     

The internal rotational barrier of biphenyl studied with multiconfigurational second-order perturbation theory (CASPT2)

Summary A detailedab initio study of the molecular structure and rotational barriers of biphenyl has been performed. First, non-dynamical correlation effects involving the system are taken into account at the CASSCF level. These wave functions are subsequently employed as reference functions in a multiconfigurational second-order perturbation treatment (CASPT2). The performance single-reference approaches is in addition analysed. The molecular geometries of biphenyl in twisted, coplanar, and perpendicular conformations have been optimized at the CASSCF level. A rotational angle of 44.3° is predicted for the minimum energy conformer in agreement with gas-phase electron diffraction data (44.4±1.2°). The highest level of theory employed yields the values 12.93 (6.0±2.1) and 6.40 (6.5±2.5) kJ/mol for the barrier heights at 0° and 90°, respectively (electron diffraction data within parentheses). In the light of the present findings, the reliability of the available experimental data is discussed.     

An application of RPA theory to conjugated systems in the excited states

In order to obtain a relationship between the molecular dimension and the correlation effect, RPA method has been applied to the calculation of electronic transition energies of linear polyenes. It has been found that the effect of electron correlation on the excitation energy decreases with increasing the size of molecule. The calculated oscillator strengths are remarkably improved by RPA calculation.     

Perturbative calculation of intermolecular interactions in orthogonalized or biorthogonal basis sets

Two versions of a many-body perturbation theory for the computation of molecular interaction energies are investigated. The methods are based on the partitioning of the second-quantized form of the dimer Hamiltonian written either in the orthogonalized basis of the monomer MOs, or, alternatively, in the original non-orthogonal dimer basis set handling the overlap by the biorthogonal formalism. The zeroth-order Hamiltonian H ⁰ is the sum of effective monomer Fockians and the zeroth-order wave functions are exact eigenfunctions of H ⁰. Full antisymmetry is ensured by the second-quantized formalism. Basis set superposition error is accounted for by the counterpoise correction recipe. Results for He₂, (H₂)₂ and (H₂O)₂ indicate the reliability of the biorthogonal technique.     

Complete TDA and RPA Calculations on the Electronic Transitions of Fullerene‐C60 in the CNDO/S and INDO/S Approximations*

Complete single‐excitation mixing calculations on the electronic transitions of the icosahedral C₆₀ molecule have been carried out with the Tamm–Dancoff approximation (TDA) and random‐phase approximation (RPA) schemes in the CNDO/S and INDO/S approximations. The complete space of 14,400 (1p–1h) pairs is partitioned into subspaces classified according to the irreducible representations of the Ih group. For this purpose, matrix representations of the group generators are obtained on a fixed set of basis functions and are used to construct the projection operators. Degenerate molecular orbitals in each energy level are symmetry‐adapted to these projection operators. Degenerate (1p–1h) pairs or singly excited configuration wave functions are similarly symmetrized. In addition, the Clebsch–Gordan coefficients are obtained and listed in an Appendix. The TDA and RPA equations are then solved for each irreducible representation separately. Both schemes with the projection operators and with the Clebsch–Gordan coefficients gave the same results as expected, indicating that the calculations were correctly done. The transition energies from the ground state 1¹A_g to low‐lying singlet and triplet excited states and the oscillator strengths for the allowed transitions (n¹T_1u–1¹A_g) are given in tables. A proper way to normalize is discussed for the eigenvectors of the RPA‐type matrix equation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Ab Initio studies on the rotational equilibria of 2-substituted furan and thiophene carbonyl derivatives

Summary The relative stabilities of syn- and anti-isomers of 2-substituted furan and thiophene carbonyl derivatives are investigated by theab initio MO method. The energy differences between the rotamers are 1–3 kcal mol^–1 but the barriers to rotation are ca. 10 kcal mol^–1 so that free rotational mode is predicted to be a rather difficult process. Application of the self-consistent reaction field (SCRF) method to account for the solvent effect indicates that the isomer with a higher dipole moment (syn) is favored in solution. An electron withdrawing 2-substituent favors syn-isomers for furan carbonyls in contrast to thiophene carbonyls for which anti-isomers are favored. These trends are ascribable to a decrease in electrostatic repulsive and attractive interactions, respectively, in the syn forms of furan and thiophene carbonyls. Contribution of non-bonded repulsive interaction in the anti-isomer is important for the relative stability of the syn-isomer of furan carbonyl derivative. Solvent effects due to higher dielectric continuum are small on the absolute values of energy differences but can reverse the order of stability of the two isomers due to a greater stability acquired by an isomer (syn) with higher dipole moment in solution. The major factor determining stability, or instability, of syn-isomer is a repulsive electrostatic interaction between the two oxygen atoms for furan carbonyls and an attractive electrostatic interaction between the sulfur and oxygen atoms for thiophene carbonyls.     

An application of second-order n-electron valence state perturbation theory to the calculation of excited states

n–electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory where all the zero-order wave functions are of multireference nature, being generated as eigenfunctions of a two–electron model Hamiltonian. The absence of intruder states makes NEVPT an interesting choice for the calculation of electronically excited states. Test calculations have been performed on several valence and Rydberg transitions for the formaldehyde and acetone molecules; the results are in good accordance with the best calculations and with the existing experimental data.Contribution to the Jacopo Tomasi Honorary Issue     

Further studies on the rotational barriers of Carbamates. An NMR and DFT analysis of the solvent effect for Cyclohexyl N,N-dimethylcarbamate

The solvent effect on the Gibbs energy of activation for rotation around the (C=O)–N bond in cyclohexyl N,N-dimethylcarbamate was investigated by dynamic NMR spectroscopy and density-functional theory at the B3LYP/6-311+G^** level. The experimental barriers were about 15 kcal mol⁻¹ with no appreciable variation when the solvent polarity was changed. A reaction field model was applied to theoretically mediate the solvent effect and the results were comparable to the experimental data. An analysis, based on the Onsager solvation theory, showed that the solvent effect on rotational barriers can be understood employing the total molecular dipole moment, the difference between the dipole moments of the ground and the transition state structures, or both, as appropriate.     

An ab initio CI study on the rotational barrier of the allyl anion

All-electron and pseudopotential non-empirical calculations have been performed on C _2v and C _s (syn, anti) allyl anion conformations. Using a double-zeta valence-shell basis set within the Epstein-Nesbet definition of the unperturbed Hamiltonian, a value about 19 kcal/mol is found for the barrier to rotation of the allyl anion. This value is the theoretical value obtained with greater accuracy, and the lowest one for the rotational barrier.     

An application of RPA theory to conjugated systems in the excited states

RPA theory has been applied to the calculations of the electronic spectra of some conjugated systems, considering only -electrons explicitly. Electron repulsion integrals have been calculated using Slater AO's with appropriate orbital exponents. The present calculation shows that the correlation effect between -electrons is rather small for the lowest — ^* transitions. Good results have been obtained, when we calculate the electron repulsion integrals using orbital exponents evaluated by Slater rule. Effective electron interaction in the excited states has been discussed, using the calculated results. The calculated oscillator strengths were considerably improved by RPA,

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Zusammenfassung Die RPA wurde auf die Berechnung der UV-Spektren des -Elektronensystems konjugierter Moleküle angewendet, wobei die Coulombintegrale für Slaterorbitate mit Exponenten gemäß der Slaterregeln ermittelt wurden. Es zeigt sich, daß die Korrelationseffekte für die tieferen Übergänge ziemlich gering sind und daß sich insbesondere die Oszillatorenstärken sehr gut ergeben. Schließlich wurden eine effektive Elektronenwechselwirkung in angeregten Zuständen diskutiert.

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Résumé La théorie RPA fondée sur l'équation du mouvement a été appliquée à des calculs de la structure électronique et des spectres de systèmes conjugués en ne considérant explicitement que les électrons . Les intégrales de répulsion électronique ont été calculées en utilisant des OA de Slater avec des exposants orbitaux appropriés. Nos calculs montrent que les effets de corrélation entre électrons sont plutôt faibles pour les plus basses transitions — ^*. De bons résultats ont été obtenus en calculant les intégrales de répulsion électronique en utilisant les exposants orbitaux évalués par la règle de Slater. L'interaction électronique effective dans les états excités est discutée sur la base des résultats obtenus.

     

Perturbative calculation of the Hartree–Fock interaction energy using orthogonalized orbitals

A many‐body perturbation theory based on the partitioning of the dimer Hamiltonian, formulated in an orthogonalized basis set, is used for the calculation of interaction energies at the Hartree–Fock (HF) level. Numerical results for the (HF)₂ and (H₂O)₂ systems in selected geometries are presented. The interaction‐energy components are compared with the results obtained from the standard supermolecular approach and the intermolecular perturbation theory based on the biorthogonal basis set. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 81–88, 1999     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Generalized gaussian model for uniaxial rotational motion: application to the calculation of spectroscopic responses

An exact model aimed at describing uniaxial rotational motions, based on a rotational adapted Gaussian statistics, is presented. In its simplest form, it depends on only two parameters, an order parameter which can vary from 1 (perfect order) to 0 (isotropic diffusion) and a time-dependent correlation parameter rho which varies from 1 to 0 between initial and infinite times. This model yields closed form expressions for the correlation functions relevant to the main spectroscopic techniques (dielectric absorption, light and neutron scattering, NMR line shape, spin-lattice relaxation, etc.) for all values of the two parameters. According to the functional form postulated for rho(t), in particular forms decaying as power laws at long times, one obtains shapes for the spectroscopic correlation functions and spectra that are similar to those experimentally observed in a large variety of complex systems (liquid crystals, polymers, gels, and amorphous and glassy materials), especially in confined geometries, which often resemble "stretched" exponentials. A simple way to introduce time coherent effects through a modification of rho(t) is proposed. Examples of theoretical correlation functions and spectra are presented. Important remarks concerning the application of this model to the analysis of real data are made. This model is the rotational analogue of the Gaussian translational model developed recently (Volino et al. J. Phys. Chem B 2006, 110, 11217).     

Perturbation calculation of the interaction energy using orthogonalized orbitals

The diagrammatic Rayleigh-Schr?dinger perturbation theory for the interaction of two closed-shell systems is developed up to the third order of pertur-bation using orthogonalized orbitals. The interaction energy is expressed by the Rayleigh-Schr?dinger perturbation expansion. A simple approach for the estimation of basis set superposition error is introduced. The preliminary calculations of the intermolecular interactions for the He dimer within the augmented cc-pVTZ basis set are compared with the supermolecular approach, perturbation calculation in biorthogonal basis sets and symmetry adapted perturbation theory results. Received: 17 December 1996 / Accepted: 5 November 1997     

On the many-body contributions to the interaction polarisability and hyperpolarisability of Hen

The many-body contributions to the interaction polarisability and hyperpolarisability of He _{n (n}=3,4, 5), for various configurations and distances have been determined and analysed. Several cases have been found where the three-body terms contribute more than 20% to or of He _n . The remarkable dependence of the above interaction properties on the internuclear distances and the shape of the cluster has been demonstrated. The interaction hyperpolarisabilities are shown to be uniquely sensitive probes of the electronic structure changes induced by variation of the cluster configuration. The results were computed by employing a computational procedure which relies on anab initio wave function, McWeeny's et al. coupled Hartree-Fock perturbation theory and an efficient algorithm for the determination of hyperpolarisabilities starting from a non-orthogonal basis set. The function counterpoise method has been used to reduce the basis set superposition error.     

A calculation of the rotatory strengths of the electron-transfer transitions of the Tris-(1,10-phenanthroline)iron(II) ion

The rotatory strengths of the metal-to-ligand transitions observed in the spectrum of the complex ion (–)-Fe(phen) ₃ ⁺² have been calculated theoretically. The excited electronic states were characterized using a coupled chromophore model. The calculated rotatory strengths are higher than the corresponding experimental values by a factor of about four.     

Time‐dependent pair distribution functions based on Smoluchowski equation and application to an electrolyte solution

Time‐dependent pair distribution function characterizes the diffusion of pairs of molecules in liquids. In the diffusion regime, the function is described with three‐dimensional Smoluchowski equation. We propose a scheme to numerically calculate the function between polyatomic and monoatomic species based on the Smoluchowski equation. The present scheme is successfully applied to the diffusion of Ar–Ar pair in liquid Ar and ethylene carbonate (EC)‐Li⁺ pair in 1 M LiPF₆/EC electrolyte solution. © 2018 Wiley Periodicals, Inc.