Third-order many-body perturbation theory for the ground state of the carbon monoxide molecule

Many-body perturbation calculations have been performed for the ground state of the carbon monoxide molecule at its equilibrium internuclear separation. The calculations are complete through third order within the algebraic approximation; i.e., the state functions are parameterized by expansion in a finite basis set. All two-, three-, and four-body terms are rigorously determined, and many-body effects are found to be very important. A detailed comparison is made with a previously reported configuration interaction study. Padé approximants to the energy expansion are constructed. The many-body perturbative wave function is used in the Rayleigh quotient to produce upper bounds to the electronic energy.     

Complex Franck—Condon overlap integral in nonradiative decays

Considering the nuclear coordinate (Q) dependence of the electronic energy denominator appearing in the virbonic coupling matrix element, a complex Franck—Condon overlap integral which is needed in order to evaluate the nonradiative decay rate constant not only in the weak coupling but also in the strong coupling case is derived. The real part of the overlap integral plays an important role in the weak coupling case. The imaginary part is originated from the potential energy surface crossing regions and, consequently, contributes to the nonradiative decay rate constant in the strong coupling case. When the Q-dependence of the electronic energy denominator is neglected, the complex overlap integral leads to the results ontained by using the usual Herzberg—Teller expansion method. It is shown that the complex integral is expressed by the optical Franck—Condon overlap integral multiplied by a correction factor when the nonradiative decay from the vibrationless state is considered.     

Elimination of translational and rotational motions in nuclear orbital plus molecular orbital theory

The nuclear orbital plus molecular orbital (NOMO) theory was developed in order to determine the nonadiabatic nuclear and electronic wave functions. This study presents a formulation to remove the contamination of rotational motion as well as translational motion in the NOMO theory. We have formulated the translation- and rotation-free (TRF)-NOMO theory by introducing the TRF Hamiltonian. The principal moment of inertia, which is the denominator in the rotational Hamiltonian, is expanded in a Taylor series. The zeroth-order of the Taylor expansion corresponds to a rigid-body rotator. The first-order terms contribute the coupling between the vibration and the rotation. Hartree-Fock equations have been derived in the framework of the TRF-NOMO theory. Numerical assessments, which were preformed for H2, D2, T2, mu2 (muon dimmer), and H2O, confirmed the importance of the TRF treatment.     

Many-body perturbation theory applied to hydrogen fluoride

Pair contributions to the electronic correlation energy of the hydrogen fluoride molecule are computed using many-body perturbation theory (MBPT) with a basis set of Slater orbitals on both atomic centers. Summation of all two-body diagrams through third order gives ≈ 93% of the total correlation energy at the equilibrium internuclear separation. However, including certain higher-order effects, by means of denominator shifts, gives a correlation energy of ?0.3691 hartree, or ≈ 97% of the correlation energy.     

The one-particle green's function: The minimal basis set description of the two-electron bond

The ionization potential (IP), electron affinity (EA), one-matrix and correlation energy of a two-electron chemical bond are calculated in a minimal basis set using one-particle, many-body Green's function theory. Results obtained using the second-order self-energy (Σ) and higher-order Σ's proposed by (1) Pickup and Goscinski, (2) Tsui and Freed, (3) Simons and Smith are compared with each other and with the exact values in the basis. The relationship between these methods and with configuration interaction is discussed and the consequences of making approximations in the context of Green's function theory are clarified.     

Transport of excitation energy in a three-dimensional doped molecular crystal. IV. Fourth-order propagation,exciton clothing,and exciton diffusion

The problem of excitons in interaction with phonons in a molecular crystal has been reinvestigated as a continuation of our earlier work. The exciton-phonon interaction has been taken to be linear in lattice displacements. The external medium, the phonon assembly, has been considered to be in thermal equilibrium. Following Simons, we have incorporated the effects of the medium on the exciton dynamics into a time-dependent effective potential that contains the equilibrium average exciton-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlation function that represents the probability of exciton transfer has been given in the interaction picture. The time evolution of this correlation function has been determined by following Kubo's technique of cumulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The second- and fourth-order contributions have been diagrammatically represented. The second-order contribution has been explicitly calculated in different physical limits, namely, the slow exciton and the slow phonon limits at high and low temperatures and for very large and very small time. A few simple formulas for the transfer probability of a bare exciton in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been specifically shown that the sum over phonon modes in the large time dynamics leads to a fully destructive interference in second order at a very low temperature and gives rise to a diffusive transport at a high enough temperature. A natural way of clothing the excitons has been considered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in terms of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of excitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attaches a novel interpretation to the correlation function which was originally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physical limits under the Debye model of phonon dispersion. From these results a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. © 1996 John Wiley & Sons, Inc.     

The calculation of vibrational intensities in forbidden electronic transitions

A method is described for the use of electronic structure and Franck-Condon factor programs in the calculation of the vibrational intensities in forbidden electronic transitions. Using the B 2B2-X 2B1 electronic transition of benzonitrile cation as a test case, transition moments were calculated using the symmetry adapted cluster/configuration interaction method at various points along the normal mode displacements of the molecule, from which transition moment derivatives were obtained. The transition moments were found to vary almost linearly with respect to the normal mode displacements. Using these, along with Franck-Condon factors, an expansion of the transition moment with respect to the normal coordinates provides a measure of vibrational intensities, including the effects of geometry change and Duschinsky rotation [Acta Physicochim. URSS 7, 551 (1937)]. Second order terms in the moment expansion are calculated, and it is determined that they must be included if the intensity of combination bands is to be properly obtained.     

Multiphonon decay of excited states of rare earth ions in crystals

Although the relaxation of excited electronic states through radiationless multiphonon processes has been well established by experiment, there are several serious problems concerning the current theoretical model in which the electron-phonon interaction is treated as a small perturbation, and the multiphonon transitions are attributed to high order expansion terms of perturbation theory. Here, we approach the problem in the framework of the adiabatic approximation. The rate of the multiphonon process is expressed in the form of the linear response time correlation function which is then evaluated by means of the saddle point approximation. The resulting expression predicts an approximately exponential dependence of the rate on the transition gap and a temperature dependence that agrees quantitatively with experiment.     

Fifth-order constant denominator perturbation therory within a localized bond model: Contributions from single and double excitations

A Fifth-order constant denominator perturbation treatment of all single and double excitations occuring in the third-order perturbation wave function is presented for the perturbation configuration interaction using localized orbitals (PCILO ) method. Contributions from triple and quadruple excitations which decay back to singles and doubles at third order are automatically included in this theory. This method is computationally very fast, with an execution speed proportional to N³, Where N is the number of orbitals present. A [2,1] Padé approximate involving only singles and doubles contributions through to fifth order is shown to be remarkably accurate.     

Accurate ab initio based multisheeted double many-body expansion potential energy surface for the three lowest electronic singlet states of H3+

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.     

两种哈密顿量划分的单参考态微扰展开式的大小一致性研究

利用一个含N个氢分子的超分子模型, 从解析的角度仔细地分析了相应于两种哈密顿量划分方式的单参考态微扰展开式前四级能量的大小一致性. 对于Epstein-Nesbet划分, 微扰展开式是大小一致的. 而对于另一种划分(Chen, F; Davidson, E. R.; Iwata, S. Int. J. Quantum Chem., 2002, 86: 256, 见公式(24)的讨论), 其展开式大小不一致. 但将它的分母作泰勒展开, 经过重新整理, 将那些大小不一致的项消去后, 得到的新微扰展开式是逐项大小一致的.     

On the construction of quasidiabatic state representations of bound adiabatic state potential energy surfaces coupled by accidental conical intersections: incorporation of higher order terms

The quadratic vibronic coupling model is an important computational tool for simulating photoelectron spectra involving strongly coupled electronic states in polyatomic molecules. However, recent work has indicated the need for higher order terms, with most of the initial studies focusing on molecules with symmetry-required degeneracies. In this study we report an extension of our approach for constructing fully quadratic representations of bound electronic states coupled by conical intersections, which allows for the inclusion of higher order terms, demonstrated here employing a quartic expansion. Procedures are developed that eliminate unphysical behavior for large displacements, a problem likely to be an endemic to anharmonic expansions. Following work on representing dissociative electronic states, Lagrange multipliers are used to constrain the constructed representation to reproduce exactly the energy, energy gradients, and∕or derivative couplings at specific points, or nodes, in nuclear coordinate space. The approach is illustrated and systematically studied using the four lowest electronic states of triazolyl, (CH)(2)N(3).     

Decomposition of density matrix renormalization group states into a Slater determinant basis

The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.     

Finite expansion of the inverse matrix in the polarization propagator method

 An alternative theoretical approach to the polarization propagator based on a new finite expansion of a finite-dimensional matrix is presented. The general equations for such an expansion are derived and the validity conditions stated. This method is used to accomplish an approximate scheme for the self-energy of the particle–hole propagator within the superoperator formalism. Within this scheme each contribution includes corrections to infinite order in electronic interaction and so describes collective effects in a natural way. Individual contributions can be interpreted as describing the propagation of the interaction through a particular subset of electronic excitations. Comparison with other known approximation levels, such as the random-phase approximation, is also analyzed. Received: 14 February 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

The coupled perturbed electron propagator in the two-particle-hole and extended two-particle-hole Tamm-Dancoff approximations

The equations satisfied by the first-order perturbed electron propagator in an applied external field are examined at a level equivalent to the two-particle-hole Tamm-Dancoff and extended two-particle-hole Tamm-Dancoff approximations (2ph-TDA). These schemes are derived with the intention of evaluating linear and quadratic response properties through second and third order in correlation. Their derivation is based on a combination of the diagrammatic and algebraic superoperator methods. Both schemes account for the polarization of the 2p-1h and 2h-1p responses and bielectron interactions under an external field. The 2ph-TDA scheme is correct up to second order in electronic correlation and includes infinite geometric series of mixed RPA-ladder-type character. Its extended version is derived consistently through third order and accounts for a first-order screening of the external field and bielectron interaction by the effects of electronic correlation. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 483–509, 1997     

First ultraviolet absorption band of methane: an ab initio study

Quantum mechanical calculations of the cross sections for photodissociation of CH4 and CD4 in the 1t2-->3s band are presented. The potential energy surfaces for the three states correlating with the 1 1T2 state at tetrahedral geometries are calculated. The elements of the (3x3) matrix representing the electronic Hamiltonian in the diabatic basis are expanded in powers of nuclear coordinates, up to the second order. The expansion coefficients are based on accurate multireference configuration interaction calculations. The electronically nonadiabatic dynamics is treated with the multiconfiguration time-dependent Hartree approach. All nine internal degrees of methane are included in the quantum dynamics simulations. The calculated cross section agrees well with experiment. Semiclassical calculations using the reflection principle suggest that the peaks in the spectrum correspond to the three adiabatic electronic states correlating with the 1 1T2 state at Td geometries. However, the non-Born-Oppenheimer terms in the Hamiltonian have a strong effect on the positions of the peaks in the absorption spectrum. The results of semiclassical calculations, which neglect these terms, are therefore quite different from the accurate quantum results and experiment.     

An intermolecular perturbation approach to hydrogen bondings in systems in the ground and excited electronic states

The intermolecular interaction energy for binary systems in the ground and excited electronic states was partitioned into the Coulomb, exchange-repulsion, induction, dispersion and charge-transfer interaction terms by the perturbation expansion method. The various interaction terms were evaluated for the hydrogen bondings in (HF)₂, (H₂O)₂, (CH₃OH)₂, (RCOOH)₂, and HF·H₂O in various geometrical configurations. It has been found that the Coulombic interaction plays a dominant role in the stability of these hydrogen bonded systems. The method was further applied to the HCOOH·H₂O codimer in both the ground and excited singlet electronic states. The results were in accord with the well-known water solvent effects on the shifts of absorption spectral bands.     

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.     

FLAPW方法研究α-铀(001)面的弛豫和电子结构

The full potential linear augmented plane wave method is used to study the relaxation and electronic structure of (001) surface for α U. The current work predicts a contraction of the topmost layer by 2.9% accompanied by an outward expansion of the second and third layers by 1.1% and 0.2%, respectively. The relaxation of topmost and second layers makes up the largest contribution of relaxation energy. Due to the short range screening effect, the atomic interaction is mainly limited to adjacent layers. For the surface atoms, due to the reduced nearest neighbors, the contribution to the bonding from 5f electrons is reduced and 5f electrons appear to be more localized.