Volume 123, Issue 20, 22 November 2005
 ARTICLES

 Theoretical Methods and Algorithms

On the connectivity of seams of conical intersection: Seam curvature
View Description Hide DescriptionThe seam of conical intersection of two electronic states is said to be curved when the span of the basis vectors describing the branching plane varies along the seam. In this work degenerate perturbation theory is used to determine an approximately diabatic Hamiltonian that can reliably reproduce the potentialenergysurfaces in the vicinity of a point of conical intersection. This Hamiltonian provides a rigorous description of seam curvature, and a means for obtaining the full dimensional seam of conical intersection connected to a point of conical intersection.

Stochastic transition states: Reaction geometry amidst noise
View Description Hide DescriptionClassical transition state theory(TST) is the cornerstone of reactionrate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This norecrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. Highaccuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact norecrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a timedependent dividing surface that is stochastically moving in phase space, such that it is crossed once and only once by each transition path.

The electrostatic potential generated by topological atoms. II. Inverse multipole moments
View Description Hide DescriptionQuantum chemical topology defines finite atoms, whose bounded electron density generates a welldefined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on “inverse” multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in , oxygen in , and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.

Gaugeoriginindependent magnetizabilities of solvated molecules using the polarizable continuum model
View Description Hide DescriptionWe present an implementation of the polarizable continuum model in its integral equation formulation for the calculation of the magnetizabilities of solvated molecules. The gaugeorigin independence of the calculated magnetizabilities and the fast basis set convergence are ensured through the use of London atomic orbitals. Our implementation can use HartreeFock and multiconfigurational selfconsistentfield (MCSCF) wave functions as well as densityfunctional theory including hybrid functionals such as B3LYP. We present the results of dielectric continuum effects on water and pyridine using MCSCF wave functions, as well as dielectric medium effects on the magnetizability of the aromatic amino acids as a model for how a surrounding protein environment affects the magnetizability of these molecules. It is demonstrated that the dielectric medium effects on the magnetizability anisotropies of the aromatic amino acids may be substantial, being as large as 25% in the case of tyrosine.

Efficient linearresponse method circumventing the exchangecorrelation kernel: Theory for molecular conductance under finite bias
View Description Hide DescriptionAn iterative approach for calculating the frequency domain linear response of molecular systems within timedependent densityfunctional theory is presented. The method completely avoids computing the exchangecorrelation kernel which is typically the most expensive step for large systems. In particular, virtual orbitals are not needed. This approach may be useful for treating the response of large systems. We give an outline of the theory and a demonstration on a jellium model of an elliptic gold cluster. A detailed theory is appended discussing the computation of conductance and ac impedance of molecular junctions under bias.

A combinatorial approach to the electron correlation problem
View Description Hide DescriptionStarting from a pathintegral formulation of quantum statistical mechanics expressed in a space of Slater determinants, we develop a method for the Monte Carlo evaluation of the energy of a correlated electronic system. The pathintegral expression for the partition function is written as a contracted sum over graphs. A graph is a set of distinct connected determinants on which paths can be represented. The weight of a graph is given by the sum over exponentially large numbers of paths which visit the vertices of the graph. We show that these weights are analytically computable using combinatorial techniques, and they turn out to be sufficiently well behaved to allow stable Monte Carlo simulations in which graphs are stochastically sampled according to a Metropolis algorithm. In the present formulation, graphs of up to four vertices have been included. In a HartreeFock basis, this allows for paths which include up to sixfold excitations relative to the HartreeFock determinant. As an illustration, we have studied the dissociation curve of the molecule in a VDZ basis, which allows comparison with full configurationinteraction calculations.

Ab initio calculation of interatomic decay rates by a combination of the Fano ansatz, Green’sfunction methods, and the Stieltjes imaging technique
View Description Hide DescriptionA new computational technique is introduced for the ab initio calculation of the rates of interatomic and intermolecular nonradiative decay processes occurring due to electronic correlation. These recently discovered phenomena are described theoretically using the configurationinteraction formalism first introduced by Fano [Phys. Rev.124, 1866 (1961)] and later adapted to an Auger decay by Howat et al. [J. Phys. B11, 1575 (1978)]. The boundlike and the continuumlike components of the wave function of the decaying state are constructed using a Green’sfunction method known as algebraic diagrammatic construction. A combination of atomic and distributed Gaussian basis sets is shown to provide an adequate description of both boundlike and continuumlike wavefunction components. The problem of the normalization of the continuum (final state) wave function is addressed using the Stieltjes imaging technique. The new method is applied to the calculation of the rates of interatomic decay in alkalineearth–raregas clusters. The obtained results help to verify our earlier conclusions [Phys. Rev. Lett.93, 263002 (2004)] regarding the validity of the virtualphoton transfer model for the interatomic Coulombic decay. In addition, we demonstrate that the process of electrontransfermediated decay is responsible for the finite lifetimes of the outer valence vacancies in alkalineearth–raregas clusters.

Molecular theory of irreversibility
View Description Hide DescriptionA generalization of the Gibbs entropy postulate is proposed based on the BogolyubovBornGreenKirkwoodYvon hierarchy of equations as the nonequilibrium entropy for a system of interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that it reaches its maximum at equilibrium and is coherent with the second law. By using a generalization of the Liouville equation describing the evolution of the distribution vector, it is demonstrated that the entropy production is a nonnegative quantity. Moreover, following the procedure of nonequilibrium thermodynamics a transport matrix is introduced and a microscopic expression for this is derived. This framework allows one to perform the thermodynamicanalysis of nonequilibrium steady states with smooth phasespace distribution functions which, as proven here, constitute the states of minimum entropy production when one considers small departures from stationarity.

An investigation of nodal structures and the construction of trial wave functions
View Description Hide DescriptionThe factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the singleparticle orbitals, and the configurations included in the wavefunction expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than HartreeFock orbitals, multiconfiguration expansions perform better than singledeterminant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed nodediffusion Monte Carlo energies for a series of dimers of firstrow atoms.

Correlated complex independent particle potential for calculating electronic resonances
View Description Hide DescriptionWe have formulated and applied an analytic continuation method for the recently formulated correlated independent particle potential [A. Beste and R. J. Bartlett J. Chem. Phys.120, 8395 (2004)] derived from Fock space multireference coupled clustertheory. The technique developed is an advanced ab initio tool for calculating the properties of resonances in the lowenergy electronmolecule collision problem. The proposed method quantitatively describes elastic electronmolecule scattering below the first electronically inelastic threshold. A complex absorbing potential is utilized to define the analytic continuation for the potential. A separate treatment of electron correlation and relaxation effects for the projectiletarget system and the analytic continuation using the complex absorbing potential is possible, when an approximated form of the correlated complex independent particle potential is used. The method, which is referred to as complex absorbing potentialbased correlated independent particle (CAPCIP), is tested by application to the wellknown shape resonance of and the shape resonance of (ethylene) with highly satisfactory results.

The nonMarkovian quantum master equation in the collectivemode representation: Application to barrier crossing in the intermediate friction regime
View Description Hide DescriptionThe calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantummechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a nonMarkovian quantum master equation (NMQME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NMQME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the nonMarkovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensedphase rate constants.

Relativistic calculation of indirect NMR spinspin couplings using the DouglasKrollHess approximation
View Description Hide DescriptionWe have employed the DouglasKrollHess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spinspin couplings in molecules containing heavy elements. We have applied this twocomponent quasirelativistic approach using finite perturbation theory in combination with a generalized KohnSham code that includes the spinorbit interaction selfconsistently and works with HartreeFock and both pure and hybrid density functionals. We present numerical results for onebond spinspin couplings in the series of tetrahydrides , , , and . Our twocomponent HartreeFock results are in good agreement with fourcomponent DiracHartreeFock calculations, although a densityfunctional treatment better reproduces the available experimental data.

Accurate and efficient treatment of twoelectron contributions in quasirelativistic highorder DouglasKroll densityfunctional calculations
View Description Hide DescriptionTwocomponent quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the fourcomponent Dirac equation (with fixed particle number). For oneelectron systems, this also holds in practice, but in manyelectron systems one has to transform the twoelectron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a twocomponent method. For oneelectron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the twoelectron picture change problem. The new approach, called the “model potential” approach because it makes use of atomic (four and twocomponent) data to estimate picture change effects in molecules, shares with the nuclearonly approach that the DouglasKroll operator needs to be constructed only once (not in each selfconsistentfield iteration) and that no timeconsuming multicenter relativistic twoelectron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalarrelativistic as well as the spinorbit parts of the Hamiltonian. The approach is tested on atomic and molecularorbital energies as well as spectroscopic constants of the lead dimer.

Calculating initialstateselected reaction probabilities from thermal flux eigenstates: A transitionstatebased approach
View Description Hide DescriptionAn approach for the calculation of initialstateselected reaction probabilities utilizing a transitionstate view and the multiconfigurational timedependent Hartree approach is presented. Using flux correlation functions, wave packets located in the transitionstate region are constructed and propagated into the asymptotic region to obtain initialstateselected reaction probabilities. A complete set of reaction probabilities is obtained from a single set of thermal flux eigenstates. Concepts previously applied with success to the calculation of or are transferred to the calculation of stateselected probabilities. The benchmark reaction on the LSTH potentialenergysurface is used to test the reliability of this approach.

Quantum dynamics driven by continuous laser fields under measurements: Towards measurementassisted quantum dynamics control
View Description Hide DescriptionWe study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to twolevel and type threelevel systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the limit suggests the possibility of the measurementassisted quantum control.

Cooperative versus dispersion effects: What is more important in an associated liquid such as water?
View Description Hide DescriptionWe implemented the quantum cluster equilibrium theory in our postprocessing program PEACEMAKER. This program may be run in conjunction with the very efficient vibrational frequency analysis code SNF and can therefore provide access to all electronic structure programs combined with this program. We applied the quantum cluster equilibrium theory in order to investigate the influence of a wide range of electronic structure models on the description of the liquid state. This investigation revealed much about the relevance of approximations in modern simulations of associated liquids such as water. While it is often claimed that the use of densityfunctional theory in condensed matter is leading to gravely erroneous results, we found that, contrary to these assertions, the exact exchange functional B3LYP and the gradientcorrected functional BP perform very well in combination with sizable basis sets as compared to secondorder MøllerPlesset perturbation theory employing the same basis set. The use of densityfunctional theory with smaller basis sets does, in fact, lead to better results in the liquid state than the use of secondorder MøllerPlesset perturbation theory in combination with these small basis sets. Most importantly, the neglect of cooperative effects disturbs a good description much more evenly if we apply secondorder MøllerPlesset perturbation theory in combination with large basis sets than densityfunctional theory including cooperativity with smaller basis sets or HartreeFock using a very small basis set.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoionization of hot radicals: , and
View Description Hide DescriptionThe combination of ionimaging and vacuumultraviolet (vuv) singlephoton ionization is used to study the internal energy dependence of the relative photoionization yields of the , and radicals following the 266 nm photodissociation of the corresponding alkyl iodides. The comparison of the ion images obtained by vuvphotoionization of the radical with those obtained by twophotonresonant, threephoton ionization of the complementary and atoms allows the extraction of the internal energy dependence of the cross sections. Factors influencing the appearance of the ion images in the different detection channels are discussed, including the secondary fragmentation of the neutral radicals, FranckCondon factors for the photoionization process, and the unimolecular fragmentation of the parent photoions.

An elementary method for calculating orientationaveraged fully differential electronimpact ionization cross sections for molecules
View Description Hide DescriptionCurrently there are no reliable theoretical approaches for calculating fully differential cross sections (FDCS) for lowenergy electronimpact ionization of large molecules. We have recently introduced the distortedwave impulse approximation as a first step in developing improved theoretical approaches. One significant obstacle to evaluating improved theoretical approaches which require significant computer resources lies in the fact that the existing experimental data require taking averages over all molecular orientations. To circumvent this problem, it has been proposed to approximate the orientationaverage by using an orientationaveraged molecular orbital in the calculation of the FDCS. The theoretical justification and expected range of validity for the approximation is given in this paper. Examples are presented for electronimpact ionization of and .

Does exist?
View Description Hide DescriptionThe existence or nonexistence of has been widely discussed [N. M. Mitzel, Angew. Chem. Int. Ed.42, 3856 (2003)]. Seven possible structures for gallium pentahydride have been systematically investigated using ab initio electronic structure theory. Structures and vibrational frequencies have been determined employing selfconsistent field, coupled cluster including all single and double excitations (CCSD), and CCSD with perturbative triples levels of theory, with at least three correlationconsistent polarizedvalence( and ) type basis sets. The state for is predicted to be weakly bound complex 1 between gallane and molecular hydrogen, with symmetry. The dissociation energy corresponding to is predicted to be . The H–H stretching fundamental is predicted to be , compared to the tentatively assigned experimental feature of Wang and Andrews [J. Phys. Chem. A107, 11371 (2003)] at . A second structure 2 with nearly equal energy is predicted to be a transition state, corresponding to a 90° rotation of the bond. Thus the rotation of the hydrogen molecule is essentially free. However, hydrogen scrambling through the structure 3 seems unlikely, as the activation barrier for scrambling is at least higher in energy than that for the dissociation of to and . Two additional structures consisting of with a dihydrogen bond perpendicular to gallane ( structure 4) and an inplane dihydrogen bond [ structure 5] were also examined. A symmetry secondorder saddle point has nearly the same energy as the dissociation limit, while the structure 5 is a transition structure to the structure. The structure 6 and the structure 7 are much higher in energy than by 88 and , respectively.

Directpotentialfit analysis of new infrared and UV/visible emission spectra of AgH and AgD
View Description Hide DescriptionNew highresolution infrared and UV/visible spectra of , , , and have been recorded with a Fourier transform spectrometer. The new line positions are combined with published microwave and older electronic data and used, first in a decoupled analysis of the state alone, and then in a global multiisotopologue analysis which yields comprehensive descriptions of both the and states of all four isotopologues of AgH. While the state was long believed to be heavily perturbed, it is shown that its irregular spectrum merely reflects an unusual potential function shape. A direct fit of all data to appropriate radial Hamiltonians yields analytic potentialenergy functions and BornOppenheimer breakdown radial functions for the ground and states.