Volume 122, Issue 23, 15 June 2005
 ARTICLES

 Theoretical Methods and Algorithms

Development of a relaxationinducing cluster expansion formalism for treating strong relaxation and correlation effects
View Description Hide DescriptionWe present in this paper a comprehensive account of an explicitly spinfree coupled clustertheory for treating energy differences of openshell states relative to a closedshell ground state, where the openshell states of interest are dominated by a few simple configuration state functions. We develop a valenceuniversal coupled cluster formalism to achieve this via a novel cluster expansion ansatz for the valence part of the wave operator, where the orbital relaxation and the correlation relaxation accompanying ionization/excitation from the ground state are taken care of to all orders in compact, efficient, and explicitly spinfree manner. The essential difference of our proposed ansatz from the ordinary and the normalordered cluster ansatz in vogue is that (a) we allow the valence cluster operators to be connected among themselves with spectator valence lines only and (b) we use suitable combinatoric factors accompanying powers of cluster operators thus connected, which are equal to the number of ways the operators can be joined, leading to the same excitation (the automorphic factor). We emphasize that such an ansatz does not generate terms (diagrams) with chains of cluster operators joined among themselves via spectator lines only. Barring only a few, almost all the terms in the working equations determining the cluster amplitudes involve contraction of the Hamiltonian with the cluster operators via at least one nonspectator line, leading to what we call a “strongly connected” series. The structure of the working equation is remarkably similar to the singlereference closedshell equation, with a few additional terms. The presence of contractions among cluster operators via spectator lines introduces the additional physical effects of orbital and correlation relaxation using lowbody cluster operators. As an illustrative application of the new multireference coupled cluster (CC) theory, we consider in this paper computation of ionization potentials (IPs) of onevalence problem with only one active orbital. The numerical applications are made for both the core and the inner and outervalence IPs for several molecular systems. The numerical values demonstrate the superiority of the relaxationinducing CC theory, as compared to the normalordered ansatz.

The Perdew–Burke–Ernzerhof exchangecorrelation functional applied to the G21 test set using a planewave basis set
View Description Hide DescriptionPresent local and semilocal functionals show significant errors, for instance, in the energetics of small molecules and in the description of band gaps. One possible solution to these problems is the introduction of exact exchange and hybrid functionals. A planewavebased algorithm was implemented in VASP (Vienna abinitio simulation package) to allow for the calculation of the exact exchange. To systematically assess the precision of the present implementation, calculations for the 55 molecules of the G21 quantum chemical test set were performed applying the PBE and PBE0 functionals. Excellent agreement for both atomization energies and geometries compared with the results obtained by GAUSSIAN 03 calculations using large basis sets (augmented correlation consistent polarized valence quadruple zeta for the geometry optimization and augmented correlationconsistent polarized valence quintuple zeta for the energy calculations) was found. The mean absolute error for atomization energies between VASP and the experiment is 8.6 and , as calculated with the PBE and PBE0 functionals, respectively. The mean deviations between VASP and GAUSSIAN are 0.46 and for the PBE and PBE0 functionals, respectively.

At the boundary between reduced densitymatrix and densityfunctional theories
View Description Hide DescriptionHere, we revisit the problem of finding the groundstateenergy of an fermion fluid under an external field, with molecular structure as the ultimate target. Densityfunctional methods only have to deal with electron density, but require an empirical functional; reduced densitymatrix methods involve a matrix on pair space and do give exact bounds, but require very complex linear programming to achieve their results. The polydensity representation that we introduce has the advantage of dealing only with densities, requires no empirical information, and also gives exact bounds; the major problem is that of accumulating and utilizing conditions on the densities that iteratively improve their realizability in the class of fermion systems. We indicate several directions along these lines and make some primitive applications.

Undoing static correlation: Longrange charge transfer in timedependent densityfunctional theory
View Description Hide DescriptionLongrange chargetransferexcited states are notoriously badly underestimated in timedependent densityfunctional theory (TDDFT). We discuss how exact TDDFT captures charge transfer between openshell species: in particular, the role of the step in the groundstate potential, and the severe frequency dependence of the exchangecorrelation kernel. An expression for the latter is derived, that becomes exact in the limit that the chargetransfer excitations are well separated from other excitations. The exchangecorrelation kernel has the task of undoing the static correlation in the ground state introduced by the step, in order to accurately recover the physical chargetransfer states.

The reaction path intrinsic reaction coordinate method and the Hamilton–Jacobi theory
View Description Hide DescriptionThe definition and location of an intrinsic reaction coordinate path is of crucial importance in many areas of theoretical chemistry. Differential equations used to define the path hitherto are complemented in this study with a variational principle of Fermat type, as Fukui [Int. J. Quantum Chem., Quantum Chem. Symp.15, 633 (1981)] reported in a more general form some time ago. This definition is more suitable for problems where initial and final points are given. The variational definition can naturally be recast into a Hamilton–Jacobi equation. The character of the variational solution is studied via the Weierstrass necessary and sufficient conditions. The characterization of the local minima character of the intrinsic reaction coordinate is proved. Such result leads to a numerical algorithm to find intrinsic reaction coordinate paths based on the successive minimizations of the Weierstrass function evaluated on a guess curve connecting the initial and final points of the desired path.

Accounting for correlations with core electrons by means of the generalized relativistic effective core potentials: Atoms Hg and Pb and their compounds
View Description Hide DescriptionA way to account for correlations between the chemically active (valence) and innermore (core) electrons in the framework of the generalized relativistic effective core potential (GRECP) method is suggested. The “correlated” GRECP’s (CGRECP’s) are generated for the Hg and Pb atoms. Only correlations for the external 12 and 4 electrons of them, correspondingly, should be treated explicitly in the subsequent calculations with these CGRECP’s whereas the innermore electrons are excluded from the calculations. Results of atomic calculations with the correlated and earlier GRECP versions are compared with the corresponding allelectron Dirac–Coulomb values. Calculations with the above GRECP’s and CGRECP’s are also carried out for the lowestlying states of the HgH molecule and its cation and for the ground state of the PbO molecule, as compared to earlier calculations and experimental data. The accuracy for the vibrational frequencies is increased up to an order of magnitude and the errors for the bond lengths (rotational constants) are decreased in about two times when the correlated GRECP’s are applied instead of earlier GRECP versions employing the same innercoreoutercorevalence partitioning.

Comparing polarizable force fields to ab initio calculations reveals nonclassical effects in condensed phases
View Description Hide DescriptionIn a recent work [Giese and York J. Chem. Phys.120, 9903 (2004)] showed that manybody force field models based solely on pairwise Coulomb screening cannot simultaneously reproduce both gasphase and condensedphase polarizability limits. In particular, polarizable force fields applied to bifurcated water chains have been demonstrated to be overpolarized with respect to ab initio methods. This behavior was ascribed to the neglect of coupling between manybody exchange and polarization. In the present article we reproduce those results using different ab initio levels of theory and a polarizable model based on the chemicalpotential equalization principle. Moreover we show that, when hydrogenbond (Hbond) forming systems are considered, an additional nonclassical effect, i.e., intermolecular charge transfer, must be taken into account. Such effect, contrarily to that of coupling between manybody exchange and polarization, makes classical polarizable force fields underpolarized. In the case of water at standard conditions, being Hbonded geometries much more probable than the bifurcated ones, intermolecular charge transfer is the dominant effect.

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems
View Description Hide DescriptionWe present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of LennardJones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.

Secondorder quantized Hamilton dynamics coupled to classical heat bath
View Description Hide DescriptionStarting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the secondorder quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zeropoint energy and moderate tunneling effects. The random force and friction as well as the systembath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPCflexible water model.

Hybrid correlation models based on activespace partitioning: Correcting secondorder Møller–Plesset perturbation theory for bondbreaking reactions
View Description Hide DescriptionMøller–Plesset secondorder (MP2) perturbation theory breaks down at molecular geometries which are far away from equilibrium. We decompose the MP2 energy into contributions from different orbital subspaces and show that the divergent behavior of the MP2 energy comes from the excitations located within a small (or sometimes even the minimal) active space. The divergent behavior of the MP2 energy at large interfragment distances may be corrected by replacing a small number of terms by their more robust counterparts from coupledcluster (CCSD) theory. We investigated several schemes of such a substitution, and we find that a coupling between the activespace CCSD and the remaining MP2 amplitudes is necessary to obtain the best results. This naturally leads us to an approach which has previously been examined in the context of costsaving approximations to CCSD for equilibrium properties by Nooijen [J. Chem. Phys.111, 10815 (1999)]. The hybrid MP2–CCSD approach, which has the same formal scaling as conventional MP2 theory, provides potential curves with a correct shape for bondbreaking reactions of BH, , and HF. The error of the MP2–CCSD method (measured against full configurationinteraction data) is smaller than that of MP2 at all interfragment separations and is qualitatively similar to that of full CCSD.

Nonlinear optical property calculations by the longrangecorrected coupledperturbed Kohn–Sham method
View Description Hide DescriptionThe longrange correction (LC) scheme for the exchange functional of densityfunctional theory(DFT) was combined with the coupledperturbed Kohn–Sham (CPKS) method to calculate nonlinear optical response properties. By using this LCCPKS method, we calculated the hyperpolarizabilities of typical molecules and the dipole moments,polarizabilities, and hyperpolarizabilities of push–pull conjugated systems: nitroaniline, 4aminonitrostilbene, and nitroaminopolyenes. It was found that the LC scheme clearly improved the calculation of these optical properties for all of these systems, which have been significantly overestimated by conventional DFTs. We therefore concluded that the longrange exchange interaction played an important role in calculating the optical properties using the DFT formalism.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Timedependent densityfunctional theory for molecular photoionization with noniterative algorithm and multicenter spline basis set: and case studies
View Description Hide DescriptionIn this work a new direct (noniterative) algorithm to solve the timedependent densityfunctional theory equations for molecular photoionization has been proposed and implemented, using a multicentric basis set expansion of spline functions and complete exploiting of the molecular pointgroup symmetry. The method has been applied to study the photoionization dynamics of and : the results confirmed the expectation of large screening effects in . For the screening effects have been found to play a minor role than in , however, also in this case the quality of the final results is definitely improved. The method has proven suitable to study with confidence molecules of medium size, and there is still room for further improvement working on more elaborate treatment of the exchangecorrelation functional.

Mapping rotational coherences onto timeresolved photoelectron imaging observables
View Description Hide DescriptionWe explore the information content of timeresolved photoelectron imaging, a potentially powerful pumpprobe technique whose popularity has been rapidly growing in recent years. To that end, we identify a mapping of the alignment properties of timeevolving wave packets onto the moments of the photoelectron images and investigate its origin and consequences theoretically and numerically.

Photoionization of vibrationally hot and
View Description Hide DescriptionVibrationally hot and were produced by the photodissociation of and , respectively, and probed by singlephoton ionization at . Comparison of the ion images of the and fragments with those of the complementary I atoms, and with previous measurements of the product branching fractions, allowed the determination of the relative photoion yields as a function of the vibrational energy of the molecular radical. Some general ideas about the internalenergy dependence of photoionization cross sections are also discussed.

Elastic electron scattering by
View Description Hide DescriptionRecent measurements [R. Panajotovic, M. Jelisavcic, R. Kajita, T. Tanaka, M. Kitajima, H. Cho, H. Tanaka, and S. J. Buckman, J. Chem. Phys.121, 4559 (2004)] and calculations [C. Trevisan, A. E. Orel, and T. N. Rescigno, Phys. Rev. A70, 012704 (2004)] of the elastic electron cross section for differ materially from our earlier calculations [C. Winstead and V. McKoy, J. Chem. Phys.116, 1380 (2002)]. Some of the differences are readily attributed to approximations made in our computations, but an overall difference in cross section magnitude above ca. 10 eV was surprising. Here we report a reexamination of the electronelastic cross section. After eliminating or minimizing various possible sources of error, we continue to predict a substantially larger cross section at higher energies.

Importance of vibronic effects on the circular dichroism spectrum of dimethyloxirane
View Description Hide DescriptionWe present a theoretical study on the vibrational structure of a circular dichroism (CD) spectrum using timedependent densityfunctional theory in combination with a Franck–Condontype approach. This method is applied to analyze the complex CD spectrum of dimethyloxirane, which involves delicate cancellations of positive and negative CD bands. Our approach reveals that these cancellations are strongly affected by the shapes of the CD bands, and that it is vital for an accurate simulation of the spectrum to take the different envelopes of these bands into account. One crucial point in some former theoretical studies on this compound, which were restricted to vertical excitations, was the appearance of a strong negative CD band in the energy range of , which is not present in the experimental spectrum. We can explain the disappearance of this band by a strong vibrational progression along normal modes with C–O stretching character, so that the band extends over an energy range of almost . Thus, it overlaps with many other (mostly positive) CD bands, leading to a cancellation of its intensity. The dominant vibrational features in the experimental spectrum can be assigned to the , , and bands, which show several clear vibrational peaks and a total bandwidth of only . In order to obtain close agreement between the simulated and the experimental spectrum we have to apply small shifts to the vertical excitation energies that enter the calculation. These shifts account both for possible errors in the timedependent densityfunctional theory calculations and for the neglect of differential zeropoint energy between ground and excited states in our gradientbased vertical Franck–Condon approach.

Fourmode quantum calculations of resonance states in complexforming bimolecular reactions:
View Description Hide DescriptionThe vibrational resonance states of the complexes formed in the nucleophilic bimolecular substitution reaction were calculated by means of the filter diagonalization method employing a coupledcluster potentialenergy surface and a Hamiltonian that incorporates an optical potential and is formulated in Radau coordinates for the carbonhalogen stretching modes. The fourdimensional model also includes the totally symmetric vibrations of the methyl group (C–H stretch and umbrella bend). The vast majority of bound states and many resonance states up to the first overtone of the symmetric stretching vibration in the exit channel complex have been calculated, analyzed, and assigned four quantum numbers. The resonances are classified into entrance channel, exit channel, and delocalized states. The resonance widths fluctuate over six orders of magnitude. In addition to a majority of Feshbachtype resonances there are also exceedingly longlived shape resonances, which are associated with the entrance channel and can only decay by tunneling. The stateselective decay of the resonances was studied in detail. The linewidths of the resonances, and thus the coupling to the energetic continuum, increase with excitation in any mode. Due to the strong mixing of the many progressions in the intermolecular stretching modes of the intermediate complexes, this increase as a function of the corresponding quantum numbers is not monotonic, but exhibits pronounced fluctuations.

Fourdimensional quantum study on exothermic complexforming reactions:
View Description Hide DescriptionThe exothermic gasphase bimolecular nucleophilic substitution reaction and the corresponding endothermic reverse reaction have been studied by timeindependent quantum scattering calculations in hyperspherical coordinates on a coupledcluster potentialenergy surface. The dimensionalityreduced model takes four degrees of freedom into account [Cl–C and C–Br stretching modes (quantum numbers and ); totally symmetric modes of the methyl group, i.e., C–H stretching ( and ) and umbrella bending vibrations ( and )]. Diagonalization of the Hamiltonian was performed employing the Lanczos algorithm with a variation of partial reorthogonalization. A narrow grid in the total energy was employed so that longliving resonance states could be resolved and extracted. While excitation of the reactant umbrella bending mode already leads to a considerable enhancement of the reaction probability, its combination with vibrational excitation of the broken C–Br bond, (0, 1, 1), results in a strong synergic effect that can be rationalized by the similarity with the classical transitional normal mode. Exciting the C–H stretch has a nonnegligible effect on the reaction probability, while for larger translational energies this mode follows the expected spectatorlike behavior. Combination of C–Br stretch and symmetric C–H, (1,0,1), stretch does not show a cooperative effect. Contrary to the spectator mode concept, energy originally stored in the C–H stretching mode is by no means conserved, but almost completely released in other modes of the reaction products. Products are most likely formed in states with a high degree of excitation in the new C–Cl bond, while the internal modes of the methyl group are less important. Reactants with combined umbrella/C–Br stretch excitation, (0, 1, 1), may yield products with two quanta in the umbrella mode.

Ab initio kinetics of the reaction of HCO with NO: Abstraction versus association/elimination mechanism
View Description Hide DescriptionThe kinetics and mechanism for the reaction of HCO with NO occurring by both singlet and triplet electronic state potentialenergysurfaces (PESs) have been studied at the modified Gaussian2 level of theory based on the geometric parameters optimized by the Becke3 Lee–Yang–Parr/ method. There are two major reaction channels on both singlet and triplet PESs studied: one is direct H abstraction producing and the other is association forming a stable HC(O)NO (nitrosoformaldehyde) molecule. The dominant reaction is predicted to be the direct H abstraction occurring primarily by the lowestenergy path via a loose hydrogenbonding singlet molecular complex, ON⋯HCO, with a 2.9kcal/mol binding energy and a small decomposition barrier (1.9 kcal/mol). The commonly assumed HC(O)NO intermediate, predicted to lie below the reactants by 27.7 kcal/mol, has a high HNOelimination barrier (34.5 kcal/mol). Bimolecular rate constants for the formation of the singlet products and their branching ratios have been calculated in the temperature range of 200–3000 K. The rate constant for the disproportionation process producing , found to be affected strongly by multiple reflections above the well of the complex at low temperature, is predicted to be for 200–500 K, and for 500–3000 K in units of . The high and lowpressure rate constants for the association process forming HC(O)NO can be represented by (200–3000 K) and (200–1000 K) and (1000–3000 K) for buffer gas. The absolute values of total rate constant, predicted to be weakly dependent negatively on temperature but positively on pressure, are in close agreement with most experimental data within their reported errors.

Dynamics of the reaction: A comparison of crossed molecularbeam experiments with quasiclassical trajectory and accurate statistical calculations
View Description Hide DescriptionIn this paper we report a combined experimental and theoretical study on the dynamics of the insertion reaction at collision energy. Product angular and velocity distributions have been obtained in crossed beam experiments and quasiclassical trajectory(QCT) and rigorous statistical calculations have been performed on the recent and accurate ab initio potential energy surface of BusseryHonvault, Honvault, and Launay at the energy of the experiment. The molecularbeam results have been simulated using the theoretical calculations. Good agreement between experiment and both QCT and statistical predictions is found.