Multi-reference Fock space coupled-cluster method in the intermediate Hamiltonian formulation for potential energy surfaces

The effective and intermediate Hamiltonian multi-reference coupled-cluster (CC) method with singles and doubles for the doubly ionized (0,2) sector of Fock space (FS) is formulated and implemented. The intermediate Hamiltonian realization of the (0,2) FS problem provides a robust computational scheme for solving the FS-CC equations free from the intruder state problem. By introducing an efficient factorization strategy, we obtain a very efficient tool that can be used for computing double ionization potentials but more significantly to describe multi-reference problems in CC theory, illustrated by twisted ethylene and the potential energy curve for F(2). The latter separates smoothly to two F atoms, while the former avoids the cusp behavior at the 90° dihedral. We also explore the double ionization potentials for several small molecules, H(2)O, CO, C(2)H(2), and C(2)H(4).     

Intermediate Hamiltonian Fock-space multireference coupled-cluster method with full triples for calculation of excitation energies

The intermediate Hamiltonian multireference coupled-cluster (CC) method with singles, doubles, and triples within the excited (1,1) sector of Fock space (FS) is implemented and formulated to calculate excitation energies (EEs). Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, coupled to an efficient factorization strategy, relatively large basis sets and model spaces are employed permitting basis set converged comparisons of the calculated vertical EEs, which can be compared to the experimental data for the N(2) and CO molecules. The issue of charge-transfer separability is also addressed.     

Recent computational developments with the self-consistent electron pairs method and application to the stability of glycine conformers

Significant improvements in calculational efficiency and capability with the self-consistent electron pairs (SCEP ) method has resulted from several new computational developments. A new procedure for constructing the important internal Coulomb and exchange operators has substantially reduced the preiteration time. A general scheme for utilizing molecular symmetry has been used to advantage in reducing the number of pair functions and external operators that must be found explicitly at each iteration. A projection operator tool has been implemented and found to be quite effective at minimizing the number of iterations required at some point on a potential energy surface when an SCEP wavefunction exists for some nearby point. These and other improvements in the program construction have yielded sizable reductions in time for some representative test cases, including water and a potential energy curve for formaldehyde. The new SCEP program also performs low-order perturbation theory treatments and coupled electron pair approximation (CEPA ) calculations using the same operator approach. The usefulness of the approach is demonstrated by very large scale calculations on the stability of the two interstellar glycine conformers. These calculations involve the variational treatment of 82,205 symmetry-adapted singly and doubly substituted configurations involving 225 internal electron pairs.     

Laplacian of the Hamiltonian Kinetic Energy Density as an Indicator of Binding and Weak Interactions

The kinetic energy is the center of a controversy between two opposite points of view about its role in the formation of a chemical bond. One school states that a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism of covalent bonding. In contrast, the opposite school holds that a chemical bond is formed by a decrease in the potential energy due to a concentration of electron density within the binding region. In this work, a topographic analysis of the Hamiltonian Kinetic Energy Density (KED) and its laplacian is presented to gain more insight into the role of the kinetic energy within chemical interactions. This study is focused on atoms, diatomic and organic molecules, along with their dimers. In addition, it is shown that the laplacian of the Hamiltonian KED exhibits a shell structure in atoms and that their outermost shell merge when a molecule is formed. A covalent bond is characterized by a concentration of kinetic energy, potential energy and electron densities along the internuclear axis, whereas a charge-shift bond is characterized by a fusion of external concentration shells and a depletion in the bonding region. In the case of weak intermolecular interactions, the external shell of the molecules merge into each other resulting in an intermolecular surface comparable to that obtained by the Non-covalent interaction (NCI) analysis.     

Independent particle theory with electron correlation

We formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equation-of-motion coupled-cluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupled-cluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.     

细菌光合反应中心Q~A和Q~B间电子转移反应的量子化学研究

用量子化学半经验的AM1和密度泛函DFT(BELYP/6-31G(d))方法分别优化了质体醌MQ1(Q~A)、泛醌UQ1(Q~B)及其阳离子自由基的结构。用Nelsen方法计算了电子转移反应MQ1-UQ1→MQ1UQ^-~1的内重组能λi。用线性反应坐标方法构造了该电子转移反应的双势阱,两透热势能面在反应坐标R≈0.30处相交。对该电子转移体系进行闭壳层的单点计算,并用Koopmans定理计算了体系的分裂能△,得到△随线性反应坐标R的变化关系。结果表明,在R=0.342处△有一极小值,从而得到该电子转移反应的电子转移矩阵元Vrp,并由此确定了反应的过渡态。在此基础上,用两球模型计算了反应的溶剂重组能λ0。本文还计算了该电子转移反应的活化自由能△G。最后,根据Marcus电子转移理论计算了该反应的速率常数ket为5.93×10^4s^-^1,由此得到该反应的半衰期与文献报道的结果一致。     

Ab initio investigation of the autoionization process Ar*(4s3P2, 3P0)+Hg --> (Ar-Hg)+ + e-: potential energy curves and autoionization widths, ionization cross sections, and electron energy spectra

Multireference configuration interaction (MRCI) calculations have been performed for the Ar*(4s3P2,0) + Hg collision complex. Feshbach projection based on orbital occupancy defines the entrance channel resonance states and provides their potential energy curves as well as resonance-continuum coupling matrix elements, which are turned into an autoionization width function by Stieltjes imaging. Coupled cluster calculations with singles, doubles, and pertubative triples [CCSD(T)] give the exit channel potential of ArHg+. The Hg20+ core is treated by a scalar-relativistic effective core potential, reparametrized to reproduce experimental excitation and ionization energies. Spin-orbit interaction is included for the Ar* open 3p shell. The nuclear motion is treated within the local complex potential approximation. Ionization occurs for 85% (3P0) and 98% (3P2) of the symmetry allowed close collisions. Calculated ionization cross sections show good agreement with experimental data. The difference potential of the collision complex is remarkably flat down to internuclear separations of 8a0 and leads to very sharp peaks in theoretical electron energy spectra for single collision energies. After accounting for the experimental energy distribution and the resolution function of the spectrometer, a very satisfying agreement with experimental electron energy spectra is found, including subtle differences due to spin-orbit coupling. Theoretical input appears indispensable for an analysis of the measured data in terms of potential energy curves and autoionization width functions.     

Artefacts in computed potential energy surfaces

We examine critically the adequacy of different LCAO molecular orbital methods, especially the restricted (closed shell) LCAO Hartree-Fock method, for the construction of reliable potential energy surfaces for processes that are accompanied by a change in electron configuration.     

Correlated one-particle method: numerical results

In a previous paper a correlated one-particle method was formulated, where the effective Hamiltonian was composed of the Fock operator and a correlation potential. The objective was to define a correlated one-particle theory that would give all properties that can be obtained from a one-particle theory. The Fock-space coupled-cluster method was used to construct the infinite-order correlation potential, which yields correct ionization potentials (IP's) and electron affinities (EA's) as the negative of the eigenvalues. The model, however, was largely independent of orbital choice. To exploit the degree of freedom of improving the orbitals, the Brillouin-Brueckner condition is imposed, which leads to an effective Brueckner Hamiltonian. To assess its numerical properties, the effective Brueckner Hamiltonian is approximated through second order in perturbation. Its eigenvalues are the negative of IP's and EA's correct through second order, and its eigenfunctions are second-order Brueckner orbitals. We also give expressions for its energy and density matrix. Different partitioning schemes of the Hamiltonian are used and the intruder state problem is discussed. The results for ionization potentials, electron affinities, dipole moments, energies, and potential curves are given for some sample molecules.     

On an application of the intermediate Hamiltonian method for molecular systems

An application of the intermediate Hamiltonian method is reported in estimation of the lower bounds to the potential energy curve of the hydrogen molecule ion. An improvement of the method and its limitation are also discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 101–107, 1999     

A variationally stable quasi-relativistic method: low-order approximation to the normalized elimination of the small component using an effective potential

A simple and variationally stable quasi-relativistic method based on a modified low-order (LO) approximation to the normalized elimination of the small component (NESC) method is presented. The modification of the original LO-NESC scheme implies the use of an energy-independent factor in the relativistic correction to the potential energy. This factor cuts off the potential energy at short distances from the nucleus and in this way restores the variational stability of LO-NESC. The new method, dubbed LO-NESC-effective potential (EP) was tested in calculations on one-, two- and many-electron atoms. The LO-NESC-EP can be easily implemented into the existing nonrelativistic quantum-chemical program codes because its Hamiltonian matrix can be expressed entirely in terms of the integrals appearing in a nonrelativistic calculation. Received: 1 April 2002 / Accepted: 23 June 2002 / Published online: 30 August 2002     

Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H(2)O, potential energy curves of LiF, and valence excitation energies of H(2)CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H(2)O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H(2)CO, the maximum deviation from available experimental values is 0.28 eV.     

A general efficient implementation of the BSSE-free SCF and MP2 methods based on the chemical Hamiltonian approach

We describe some details related to a new, general, and efficient implementation of the BSSE‐free SCF and second‐order Møller–Plesset perturbation theories of intermolecular interactions, based on the “Chemical Hamiltonian Approach” (CHA). The program is applicable for both open‐shell and closed‐shell systems and for an arbitrary number of interacting subsystems. With the new program the CHA method is faster than the usual “counterpoise correction” scheme for single point calculations, especially for clusters consisting of several molecules. The numerical results provided by these conceptually different schemes, however, have again found to be very close to each other. The CHA scheme is particularly good for providing truly BSSE‐free MP2 data for intermolecular potentials. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1505–1516, 2006     

Electron-induced chemistry of alcohols

We studied dissociative electron attachment to a series of compounds with one or two hydroxyl groups. For the monoalcohols we found, apart from the known fragmentations in the 6-12 eV range proceeding via Feshbach resonances, also new weaker processes at lower energies, around 3 eV. They have a steep onset at the dissociation threshold and show a dramatic D/H isotope effect. We assigned them as proceeding via shape resonances with temporary occupation of sigma orbitals. These low energy fragmentations become much stronger in the larger molecules and the strongest DEA process in the compounds with two hydroxyl groups, which thus represent an intermediate case between the behavior of small alcohols and the sugar ribose which was discovered to have strong DEA fragmentations near zero electron energy [S. Ptasińska, S. Denifl, P. Scheier and T. D. M?rk, J. Chem. Phys., 2004, 120, 8505]. Above 6 eV, in the Feshbach resonance regime, the dominant process is a fast loss of a hydrogen atom from the hydroxyl group. In some cases the resulting (M- 1)(-) anion (loss of hydrogen atom) is sufficiently energy-rich to further dissociate by loss of stable, closed shell molecules like H(2) or ethene. The fast primary process is state- and site selective in several cases, the negative ion states with a hole in the n(O) orbital losing the OH hydrogen, those with a hole in the sigma(C-H) orbitals the alkyl hydrogen.     

Perturbation–variational methods revisited

We describe a simple expansion of the Krylov type for the estimation of the electronic correlation energy of the ground state of closed-shell systems and show its relationship with Brillouin–Wigner perturbation theory. We demonstrate the Brillouin–Wigner perturbation theory can be quickly solved in a noniterative fashion. Examples are presented using the intermediate neglect of the differential overlap model Hamiltonian (INDO /1), which indicates that this scheme captures well over 95% of the configuration interaction over double excitations method (CID ) in a fraction of the computational effort. © 1993 John Wiley & Sons, Inc.     

Bond dissociation of the dipeptide dialanine and its derivative alanine anhydride induced by low energy electrons

Dissociative electron attachment to dialanine and alanine anhydride has been studied in the gas phase utilizing a double focusing two sector field mass spectrometer. We show that low-energy electrons (i.e., electrons with kinetic energies from near zero up to 13 eV) attach to these molecules and subsequently dissociate to form a number of anionic fragments. Anion efficiency curves are recorded for the most abundant anions by measuring the ion yield as a function of the incident electron energy. The present experiments show that as for single amino acids (M), e.g., glycine, alanine, valine, and proline, the dehydrogenated closed shell anion (M-H)(-) is the most dominant reaction product. The interpretation of the experiments is aided by quantum chemical calculations based on density functional theory, by which the electrostatic potential and molecular orbitals are calculated and the initial electron attachment process prior to dissociation is investigated.     

Relativistic effective valence shell Hamiltonian method: excitation and ionization energies of heavy metal atoms

The relativistic effective valence shell Hamiltonian H(v) method (through second order) is applied to the computation of the low lying excited and ion states of closed shell heavy metal atoms/ions. The resulting excitation and ionization energies are in favorable agreement with experimental data and with other theoretical calculations. The nuclear magnetic hyperfine constants A and lifetimes tau of excited states are evaluated and they are also in accord with experiment. Some of the calculated quantities have not previously been computed.     

An ab initio effective potential for two particles in the field of the core: a reduction of (N + 2)-electron problem to two-electron problem

We have used many-body Green function theory and the two-electron Bethe—Salpeter equation to derive an approximate two-electron position space hamiltonian eigenvalue equation for two electrons in the presence of a closed shell core. The resulting effective hamiltonian is nonlocal, energy independent, hermitian and nonadiabatic. It includes all the core—valence, valence—valence exchange effects, core screening effects and electron—electron correlation effects. If a closed form solution of the equation is difficult because of the need to construct the hamiltonian, a semi-empirical approach can be taken which expresses much of the hamiltonian in terms of known properties of the core. A semi-empirical analysis of this effective hamiltonian is shown to give well-known phenomenological effective hamiltonians and the connections to them. Thus this work can also be viewed as a theoretical justification and extension of the two-electron model potential or pseudopotential theories.     

Combining ab initio techniques with analytical potential functions for structure predictions of large systems: Method and application to crystalline silica polymorphs

A computational scheme is presented which combines quantum mechanical ab initio techniques with methods using analytical potential functions. The scheme is designed for use in structure optimizations and is also applicable to molecular dynamics simulations. The implementation covers both molecular and periodic systems. The problem of the link atoms is solved by a subtraction scheme which is easily implemented for any combination of methods. As a first application dense and microporous silica polymorphs are studied. The Hartree-Fock method is combined with both a force field and an ion pair shell model potential. Comparison is made with lattice energy minimizations which use the force field or the shell model potential alone as well as with free cluster optimizations and optimizations in which the outer part of the cluster is kept fixed. © 1997 by John Wiley & Sons, Inc.     

Relation between electron scattering resonances of isolated NTCDA molecules and maxima in the density of unoccupied states of condensed NTCDA layers

The empty-level structure of the 1,4,5,8-naphthalenetetracarboxylic dianhydride (NTCDA) molecule is characterized by means of dissociative electron attachment (DEA) experiments in the gas phase coupled with DFT calculations. Distinct maxima in the anion currents generated by electron attachment to NTCDA, as a function of incident electron energy, are ascribed to capture of incident electrons into empty orbitals, i.e., the process referred to as shape resonance. The empty orbital energies of gas-phase NTCDA shifted to 1.2 eV lower energy reproduce satisfactorily the maxima of the unoccupied electronic states of a multilayer NTCDA film measured by means of the very low energy electron diffraction method and the total current spectroscopy measurement scheme. The present results indicate that the empty levels of individual NTCDA molecules are stabilized in the solid state, but their relative energies remain nearly unaltered. The stabilization energy in multilayer film of NTCDA molecules is likely due to attractive polarization forces. Fragmentation of the gas-phase NTCDA temporary parent anions via the DEA mechanism, the other issue of the present investigation, leads to the rupture of the bonds between the end carbonyl groups and the naphthalene core, and occurs at incident electron energies above 2 eV. Possible chemical changes in condensed NTCDA molecules initiated by the DEA mechanism under conditions of electron transport through the film are discussed.