Applicability of quasi-degenerate many-body perturbation theory to quasi-degenerate electronic states: The H4 model revisited

The performance of the quasi-degenerate many-body perturbation theory up to the third order is investigated for the ground state, five excited states, and the first quintet of a simple four-electron H₄ model system consisting of two stretched hydrogen molecules, in which the degree of quasi-degeneracy can be continuously varied from a nondegenerate to a full degenerate situation. We employ a DZP basis set. The effect of intruder states is considered and a comparison with other multireference correlation techniques is also provided. Finally, a criterion for the model space to be quasi-degenerate will be reformulated and generalized. © 1995 John Wiley & Sons, Inc.     

Analytical energy gradient of high-spin multiplet state calculated by the SAC-CI method

A method of calculating analytical energy gradient of high-spin multiplet state by the SAC-CI (symmetry-adapted-cluster configuration-interaction) method is developed and implemented. This method is expected to be a powerful tool in studying the dynamics and properties of molecules having high spin-multiplicities. Good performance of this method is shown for the quartet states of BH⁺ and C₂⁺ and for the quintet states of C₂. The SAC-CI general-R method is also extended to the high-spin states, and proved to be useful especially for calculating accurate adiabatic excitation energies of the systems having quasi-degenerate orbital structure.     

Ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate excited states in molecules: Population and vibrational coherence transfers

Results of a theoretical study of ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate π-electronic excited states of molecules were presented. Analytical expressions for temporal behaviors of population and vibrational coherence were derived using a simplified model to clarify the quantum mechanical interferences between the two coherently excited electronic states, which appeared in the nuclear wavepacket simulations [M. Kanno, H. Kono, Y. Fujimura, S.H. Lin, Phys. Rev. Lett 104 (2010) 108302]. The photon-polarization direction of the linearly polarized laser, which controls the populations of the two quasi-degenerate electronic states, determines constructive or destructive interference. Features of the vibrational coherence transfer between the two coupled quasi-electronic states through nonadiabatic couplings are also presented. Information on both the transition frequency and nonadiabatic coupling matrix element between the two states can be obtained by analyzing signals of two kinds of quantum beats before and after transfer through nonadiabatic coupling.     

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. I. Single-reference-state formulation

The impact of the choice of molecular orbital sets on the results of single-reference-state coupled-cluster (CC) methods was studied for the H4 model. This model offers a straightforward way of taking into account all possible symmetry-adapted orbitals. Moreover, the degree of quasi-degeneracy of its ground state can be varied over a wide range by changing its geometry. The CCD, CCSD, and CCSDT approaches are considered. Surfaces representing the dependence of the energy on the parameters defining the orbitals are obtained. It is documented that for every method there exist alternative orbital sets which allow one to obtain more accurate energies than the standard (HF, BO, and NO) ones. However, for many of the former orbital sets, one obtains relatively large one-body amplitudes or one may encounter problems with solving the CC equations by conventional methods. An interesting variety of orbitals which might be useful for studies of quasi-degenerate states by the CCD method was found. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 205–219, 1998     

Application of quasi-degenerate perturbation theory to the description of potential curves and electronic excitation of molecules

The potential energy functions of the electronic states and the dipole moments of the electronic transitions of the A10 and AlC molecules have been calculated by second-order quasi-degenerate perturbation theory, using the intermediate Hamiltonian technique. Various means are considered for selecting the zero order approximation for the Hamiltonians of the model and intermediate sub-spaces. The results are compared with those obtained by the configuration interaction method. It is shown that this approach is an effective method for analyzing electronic transitions between states of the same symmetry type in the presence of pseudo-crossing of the electronic terms.Moscow University. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 1, pp. 11–16, January – February, 1991. Original article submitted July 21,1988.     

A Simple Approximate Perturbation Approach to Quasi-degenerate Systems

In this paper a simple approximate approach for the study of quasi-degenerate systems is presented in the frame of multireference perturbation theory. The formulation can be considered as an approximation of the quasi-degenerate perturbation theory (QDPT) with the simplification that only the state specific (diagonal) perturbation corrections to the energy have to be computed. The new approach is discussed and compared with previous QDPT formulations using the weakly avoided crossing model (for which new properties are here presented) and applied to the case of the neutral/ionic energy crossing in the LiF molecule.     

Vibronic coupling and line broadening in polyatomic molecules

The vibronic coupling between quasi-degenerate adiabatic Born-Oppenheimer states is calculated without using the Herzberg-Teller perturbation expansion, and is shown to be strongly dependent on the model chosen.     

Method of moments approach and coupled cluster theory

Summary The single reference coupled cluster (CC) approach to the many-electron correlation problem is examined from the viewpoint of the method of moments (MM). This yields generally an inconsistent (overcomplete) set of equations for cluster amplitudes, which can be solved either in the least squares sense or by selective projection process restricting the number of equations to that of the unknowns. These resulting generalized MM-CC equations always contain the standard CC equations as a special case. Since, in the MM-CC formalism, the Schrödinger equation will be approximately satisfied on a subspace spanned by non-canonical configurations, this procedure may be helpful in extending the standard single reference CC theory to quasi-degenerate situations. To examine the potential usefulness of this idea, we explore the linear version of the CC approach for systems with a quasi-degenerate reference, in which case the standard linear theory is plagued with singularities due to the intruder states. Implications of this analysis for the structure of the wavefunction are also briefly discussed.Killam Research Fellow 1987–89     

A computational study of the excited states of bilirubin IX

We have determined the lowest excited states of bilirubin IX by TD-DFT calculations. The lowest pair of excited states, S(1) and S(2), turn out to be of charge-transfer (CT) nature. Although DFT based methods tend to underestimate the energy of CT states, the small oscillator strengths we have computed indicate that such states may actually exist in this spectral region, but would have escaped spectroscopic detection. The next pair of excited states, S(3) and S(4), account for the most prominent spectral feature of bilirubin. They can be accurately described by the exciton coupling model, as we show by a thorough analysis of wavefunctions and properties. This finding therefore supports the interpretation of bilirubin photoisomerization behaviour, based on the exciton coupling model.     

Application of perturbation theory to the description of the lowest excited states of porphyrin molecules

Consideration has been given to the effect of one-electron perturbation on the energy of the lowest excited singlet and triplet states of high symmetry (D_4h) of porphyrins, corresponding to the transfer of an electron from the pair of quasi-degenerate highest occupied MO a_1u and a_2u to the pair of degenerate unoccupied MO e_g. It is assumed that the MO considered satisfy the SCF equation. With the help of orthogonal transformations of the highest occupied and lowest unoccupied MO it is shown that the secular fourth-order problems for the S- and T-states have exact solutions. By comparing with experimental data and with the results of quantum-chemical calculations for the S₁, S₂ and T₁-levels the accuracy of the results obtained has been analyzed for two series of compounds (metal complexes of the azaporphyrins, and compounds with different numbers and positions of the central hydrogen atoms).Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 3, pp. 257–267, May–June, 1990.     

Superconductivity and the effective electron–electron interaction mechanism in the light of the configuration interaction study

The effect of electron–phonon interactions, described by the effective electron–electron interaction mechanism, on the electronic structure of molecular systems has been investigated by the configuration interaction method. For systems with strongly quasi-degenerate electronic states near to the Fermi surface, this interaction mechanism, according to the BCS theory, results in the electronic ground-state energy lowering and in the gap formation. A more rigorous treatment of the configuration interaction method as applied in this paper confirms the electronic ground-state energy lowering, but the obtained results indicate that the effective electron–electron interaction term does not yield the experimentally detected temperature dependence of the gap. Accordingly, the two-particle mechanism seems not to be the key factor for the gap formation and for the microscopic mechanism of superconductivity, which agrees with the results of the molecular nonadiabatic theory of electron–vibrational interactions.     

Calculation of electric dipole transition moments using quasi-degenerate variational perturbation theory and averaged coupled-pair functional theory

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH₂, and A1H using multireference singles and doubles configuration interaction, quasi-degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi-degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH₂, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled-pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.     

Ab initio molecular calculations including spin-orbit coupling. II. Molecular test on the InH molecule and application to the g states of the Ar2* excimer

Ab initio CI relativistic calculations with non-empirical core pseudopotentials are achieved for the valence states of InH and the gerade Rydberg states of the Ar₂^* excimer using the quasi-degenerate perturbation theory in the Λ · Σ coupling scheme.     

Nucleation of water vapor on Na<Superscript>+</Superscript>Cl<Superscript>−</Superscript> ion pairs: Computer simulation

The Monte Carlo method is used to calculate the free energy, entropy, and work of water cluster formation in the field of Na⁺Cl⁻ ion pairs. A detailed model is used that allows for polarization and covalent many-particle interactions, as well as the effects of ion charge reversal. The model is matched to the experimental data on the free energy of ion hydration and the results of the quantum-chemical calculations of stable configurations. The hydration leads to the cleavage of an ion pair in a molecular cluster after approximately ten water molecules are captured. As vapor molecules are added, the stable interion distance monotonically elongates. The low free energy barrier separating the dissociated and nondissociated states of the ion pair in an equilibrium cluster does not hinders the reversible spontaneous transitions between the states, which are responsible for strong fluctuations and the instability of the system. Unlike hydroxonium-containing ion pairs, the formation of long-lived metastable states of hydrated Na⁺Cl⁻ pairs is impossible.     

Efficient and accurate calculations on the electronic structure of B-type poly(dG).poly(dC) DNA by elongation method: first step toward the understanding of the biological properties of aperiodic DNA

Elongation method was applied to determine the electronic structures of B-type poly(dG).poly(dC) DNA at the ab initio molecular orbital level as a first step toward the calculation of aperiodic DNA. The discrepancy in total energy between the elongation method and a conventional calculation was negligibly small in the order of 10(-8) hartreeat. for 14 G-C base pair model. The local density of states for 10 G-C base pair model estimated by the elongation method well reproduced the results by the conventional calculation. It was found that the band gap of the whole system is mainly due to the energy difference between the valence band of guanine and the conduction band of cytosine. Moreover, the electron transfer path through stacking G-C base pairs rather than sugar-phosphate backbones has been confirmed by the authors' calculations.     

Electronic states at the water/air interface

Using combined path integral-molecular dynamics simulation techniques, we analyze electronic solvation at the water/air interface. Superficial electrons present a considerable extent of spatial confinement, somewhat less marked but still comparable to that found in bulk. The characteristics of the interfacial polarization promote an overall structure for the solvated electron-polymer which looks flatter along the direction perpendicular to the interface. Spatial and orientational responses of different slabs in the close vicinity of the interface were also investigated. Solvent configurations obtained from the simulations have been used to analyze electronic excited states and the optical absorption spectrum of superficial electrons. Compared to bulk results, the distribution of bound electronic states at the surface presents similar characteristics, that is, a ground s-state and three, quasi-degenerate, p-like excited states. The reduction of the energy gap between the ground state and the rest of excited states leads to a approximately 0.52 eV red-shift in the position of the absorption maximum.     

Electronic to vibrational energy transfer assisted by interacting transition dipole moments: a quantum model for the nonadiabatic I2(E) + CF4 collisions

We report a theoretical study of nonadiabatic transitions within the first-tier ion-pair states of molecular iodine induced by collisions with CF(4). We propose a model that treats the partner as a spherical particle with internal vibrational structure. Potential energy surfaces and nonadiabatic matrix elements for the I(2)-CF(4) system are evaluated using the diatomics-in-molecule perturbation theory. A special form of the intermolecular perturbation theory for quasi-degenerate electronic states is implemented to evaluate the corrections to the long-range interaction of transition dipole moments of colliding molecules. The collision dynamics is studied by using an approximate quantum scattering approach that takes into account the coupling of electronic and vibrational degrees of freedom. Comparison with available experimental data on the rate constants and product state distributions demonstrates a good performance of the model. The interaction of the transition dipole moments is shown to induce very efficient excitation of the dipole-allowed upsilon(3) and upsilon(4) modes of the CF(4) partner. These transitions proceed predominantly through the near-resonant E-V energy transfer. The resonant character of the partner's excitation and the large mismatch in vibrational frequencies allow one to deduce the partner's vibrational product state distributions from the distributions measured for the molecule. The perspectives of the proposed theoretical model for treating a broad range of molecular collisions involving the spherical top partners are discussed.     

Multiconfigurational second-order perturbative methods: Overview and comparison of basic properties

Summary The multiconfigurational second-order perturbative treatments of molecular electronic calculations can be classified into four groups: i) quasi-degenerate perturbation theory (QDPT) in the basis of determinants, ii) non-degenerate perturbation theory applied to eigenvectors resulting from a truncated CI, ii) QDPT in a model space of non-interacting multiconfigurational functions, iv) intermediate Hamiltonians theory, and examined according to three criteria: i) risk of numerical instability due to intruder states, ii) ability to treat the effect of the outer-space on the model space component of the wavefunction, especially important for the treatment of weakly avoided crossings, iii) separability for (A* ... B) problems. None of the existing methods satisfies these three criteria, as shown both by model analysis and real ab initio calculations on LiF and CuF.     

Mechanisms for ion retention in molecular water clusters in a planar nanopore against the background of thermal fluctuations

The Monte Carlo method has been used to calculate the potential of mean force for Na⁺ and Cl^? ions interacting in model planar nanopores with structureless walls under the conditions of the material contact with water vapor at room temperature and above water boiling point. The interactions have been described using a detailed many-body model calibrated with respect to experimental data on the free energy of attachment reactions and the results of quantum-chemical calculations. Dissociation becomes possible when the vapor density increases as a sufficient number of molecules are pulled into the field of the ions. The dissociation proceeds sooner under the conditions of the nanopore than in bulk water vapor. Hydration decreases the energy of the dissociated state; however, the entropy component of the free energy partly compensates for the decrease in the internal energy, thereby increasing the stability of a contact ion pair. After the dissociation of a contact ion pair (CIP), ions are retained within a cluster in the state of a solvent-separated ion pair (SSIP). Fluctuations in the number of pulled-in vapor molecules, which are correlated with fluctuations in the interionic distance, stabilize the SSIP states with respect to recombination, while a decrease in the screening of the field of ions under the conditions of the nanopore stabilize the SSIP states with respect to cluster decay. The conditions of the nanopore stimulate the passage of an ion pair from the CIP to the SSIP state due to the rearrangement of the statistical weights in favor of molecules being located in the interionic gap. Thus, under the conditions of the nanopore, the stability of the SSIP states increases with respect to both the recombination of the ions and the decay of the ion-molecular associate.