Volume 122, Issue 20, 22 May 2005
 ARTICLES

 Theoretical Methods and Algorithms

Densitymatrix renormalizationgroup algorithms with nonorthogonal orbitals and nonHermitian operators, and applications to polyenes
View Description Hide DescriptionWe describe the theory and implementation of two extensions to the densitymatrix renormalizationgroup (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal oneparticle basis (using a biorthogonal formulation) and (ii) to use nonHermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out groundstate calculations on ethene, butadiene, and hexatriene, in a polarized atomicorbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecularorbital DMRG calculations, and comparable to or better than coupledcluster calculations, although we encountered numerical problems associated with nonHermiticity. We believe that the nonHermitian DMRG algorithm may further become useful in conjunction with other nonHermitian Hamiltonians, for example, similaritytransformed coupledcluster Hamiltonians.

An improved density matrix functional by physically motivated repulsive corrections
View Description Hide DescriptionAn improved density matrix functional [correction to Buijse and Baerends functional (BBC)] is proposed, in which a hierarchy of physically motivated repulsive corrections is employed to the strongly overbinding functional of Buijse and Baerends (BB). The first correction C1 restores the repulsive exchangecorrelation (xc) interaction between electrons in weakly occupied natural orbitals (NOs) as it appears in the exact electron pair density for the limiting twoelectron case. The second correction C2 reduces the xc interaction of the BB functional between electrons in strongly occupied NOs to an exchangetype interaction. The third correction C3 employs a similar reduction for the interaction of the antibonding orbital of a dissociating molecular bond. In addition, C3 applies a selective cancellation of diagonal terms in the Coulomb and xc energies (not for the frontier orbitals). With these corrections, BBC still retains a correct description of strong nondynamical correlation for the dissociating electron pair bond. BBC greatly improves the quality of the BB potential energy curves for the prototype fewelectron molecules and in several cases BBC reproduces very well the benchmark ab initio potential curves. The average error of the selfconsistent correlation energies obtained with BBC3 for prototype atomic systems and molecular systems at the equilibrium geometry is only ca. 6%.

The calculation of excitation energies based on the relativistic twocomponent zerothorder regular approximation and timedependent densityfunctional with full use of symmetry
View Description Hide DescriptionIn the present work, we propose a relativistic timedependent densityfunctional theory (TDDFT) based on the twocomponent zerothorder regular approximation and a noncollinear exchangecorrelation (XC) functional. This twocomponent TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closedshell systems with full use of doublegroup symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closedshell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.

Rosenbluthsampled nonequilibrium work method for calculation of free energies in molecular simulation
View Description Hide DescriptionWe present methods that introduce concepts from Rosenbluth sampling [M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys.23, 356 (1955)] into the Jarzynski nonequilibrium work (NEW) freeenergy calculation technique [C. Jarzynski, Phys. Rev. Lett.78, 2690 (1997)]. The proposed hybrid modifies the way steps are taken in the NEW process. With it, each step is selected from a range of alternatives, with bias given to steps that contribute the least work. The definition of the work average is modified to account for the bias. We introduce two variants of this method, bias sampling and configurationbias sampling, respectively; a combined  and configurationbias method is also considered. By reducing the likelihood that large nonequilibrated work values enter the ensemble average, the Rosenbluth sampling aids in remedying problems of inaccuracy of the calculation. We demonstrate the performance of the proposed methods through a model system of independent harmonic oscillators. This model captures the difficulties involved in calculating free energies in real systems while retaining many tractable features that are helpful to the study. We examine four variants of this model that differ qualitatively in the nature of their phasespace overlap. Results indicate that the bias sampling method is most useful for systems with entropic sampling barriers, while the configurationbias methods are best for systems with energetic sampling barriers. The Rosenbluthsampling schemes yield much more accurate results than the unbiased nonequilibrium work method. Typically the accuracy can be improved by about an order of magnitude for a given amount of sampling; this improvement translates into two or more orders of magnitude less sampling required to obtain a given level of accuracy, owing to the generally slow convergence of the NEW calculation when the inaccuracy is large.

NonFickian interdiffusion of dynamically asymmetric species: A moleculardynamics study
View Description Hide DescriptionWe use molecular dynamics combined with dissipative particle dynamics to construct a model of a binary mixture where the two species differ only in their dynamicproperties(friction coefficients). For an asymmetric mixture of slow and fast particles we study the interdiffusion process. The relaxation of the composition profile is investigated in terms of its Fourier coefficients. While for weak asymmetry we observe Fickian behavior, a strongly asymmetric system exhibits clear indications of anomalous diffusion, which occurs in a crossover region between cases I (Fickian) and II (sharp front moving with constant velocity), and is close to the case II limit.

Improved importance sampling distribution for rate constant calculation
View Description Hide DescriptionAn efficient method to compute the thermal rate constant for rare events within the correlation function approach is presented. This method, which is based on a modification of the sampling function used to evaluate the dynamical correlation function, can be applied to highdimensional systems having a rough energy landscape without previous knowledge on the transition states location. In this work, the sampling of a Boltzmannlike distribution for the linear momenta with a lower inverse temperature than the correct one is proposed as a way to increase the number of reactive trajectories. The mismatch between the and distributions is then corrected by a reweighting procedure which allows one to obtain the exact correlation function. The efficiency of this scheme in computing the rate of a particle jumping across the barrier of a simple 2D double well potential is improved by a factor 4–25 depending on the relative value of the original and modified temperatures. When merged with the “puddle potential” method [S. A. Corcelli, J. A. Rohman, and J. C. Tully, J. Chem. Phys., 118, 1085 (2003)], the new importance sampling function improves the efficiency of the correlation function approach by a factor 16–800 with respect to the unbiased sampling. To test the method in a more challenging case, the previous model system was extended by adding six harmonically restrained particles, each one interacting with the diffusing particle. This model introduces both the possibility of energy exchange and a rougher energy landscape. The new sampling function alone is found to produce an improvement in efficiency of, at least, an order of magnitude when compared with the unbiased case; when merged with the puddle potential method, a 400fold saving in computer time is found.

Calculation of electricfield gradients based on higherorder generalized Douglas–Kroll transformations
View Description Hide DescriptionIn this paper, the calculation of electricfieldlike properties based on higherorder Douglas–Kroll–Hess (DKH) transformations is discussed. The electricfield gradient calculated within the Hartree–Fock selfconsistent field framework is used as a representative property. The properties are expressed as an analytic first derivative of the fourcomponent Dirac energy and the order DKH energy, respectively. The differences between a “forward” transformation of the relativistic energy or the “back transformation” of the wave function is discussed in some detail. Detailed test calculations were carried out on the electricfield gradient at the halogen nucleus in the series for which extensive reference data are available. The DKH method is shown to reproduce (spinfree) fourcomponent Dirac–Fock results to an accuracy of better than 99% which is significantly closer than previous DKH studies. The calculations of both the Hamiltonian and the property operator are shown to be essentially converged after the secondorder transformation, even for elements as heavy as At. In addition, we have obtained results within the densityfunctional framework using the and zerothorder regular approximation (ZORA) methods. The latter results included picturechange effects at the scalar relativistic variant of the ZORA4 level and were shown to be in quantitative agreement with earlier results obtained by van Lenthe and Baerends. The picturechange effects are somewhat smaller for the ZORA method compared to DKH. For heavier elements significant differences in the field gradients predicted by the two methods were found. Based on comparison with fourcomponent Dirac–Kohn–Sham calculations, the DKH results are more accurate. Compared to the spinfree Dirac–Kohn–Sham reference values, the ZORA4 formalism did not improve the results of the ZORA calculations.

Variational calculation of vibrational linear and nonlinear optical properties
View Description Hide DescriptionA variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a selfconsistent solution of the vibrational Schrödinger equation for the complete fielddependent potentialenergy surface and, then, adds higherlevel vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowestlevel vibrational correlation treatment (i.e., vibrational Møller–Plesset perturbation theory). Our results indicate when the conventional Bishop–Kirtman perturbation method can be expected to break down and when highlevel vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.

Ab initio calculation of bowl, cage, and ring isomers of and
View Description Hide DescriptionHighlevel ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of and . The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid densityfunctional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybridmetaDF method TPSSKCIS, only the PBE1PBE method (with ccpVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/ccpVDZ [CCSD(T)—coupledcluster method including singles, doubles, and noniterative perturbative triples; ccpVDZ—correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/ccpVTZ [MP4—fourthorder Moller–Plesset; ccpVTZ—correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/ccpVTZ calculation, both predicting that the bowl is still the lowestenergy structure of at , followed by the ring and the cage. In contrast, both B3LYP/ccpVTZ and B3PW91/ccpVTZ calculations predict that the ring is the lowestenergy structure of . Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among largesized carbon clusters and other carbon nanostructures (e.g., finitesize carbon nanotubes, nanoonions, or nanohorns). The relative stabilities derived from total energy with Gibbs freeenergy corrections demonstrate a changing ordering in which ring becomes more favorable for both and at high temperatures. Finally, photoelectron spectra (PES) for the anionic isomers have been computed. With binding energies up to , the simulated PES show ample spectral features to distinguish the three competitive isomers.

Momentumspace properties from coordinatespace electron density
View Description Hide DescriptionElectron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the manyelectron wave function. However, invoking a variant of the constrainedsearch formulation of densityfunctional theory, we develop a general scheme (valid for arbitrary external potentials) yielding decent momentumspace properties, starting exclusively from the coordinatespace electron density. A numerical illustration of the scheme is provided for the closedshell atomic systems He, Be, and Ne in their ground state and for singlet electronic excited state for helium by calculating the Compton profiles and the expectation values derived from given coordinatespace electron densities.

Relativistic effective valence shell Hamiltonian method: Excitation and ionization energies of heavy metal atoms
View Description Hide DescriptionThe relativistic effective valence shell Hamiltonian 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 ionizationenergies are in favorable agreement with experimental data and with other theoretical calculations. The nuclear magnetic hyperfine constants and lifetimes of excited states are evaluated and they are also in accord with experiment. Some of the calculated quantities have not previously been computed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

UV photodissociation of the van der Waals dimer revisited: Pathways giving rise to ionic features
View Description Hide DescriptionThe stateassisted photofragmentation of the van der Waals dimer at and nearby wavelengths has been revisited experimentally using the timeofflight mass spectrometry with supersonic and effusive molecular beams and the “velocity map imaging” technique. The processes underlying the appearance of two main clusterspecific features in the mass spectra, namely, and translationally “hot” ions, have been studied. Translationally hot ions with an average kinetic energy of appear in the onequantum photodissociation of vibrationally excited ions via a “parallel” photodissociation process with an anisotropy parameter . Comparison of the images of arising from the photoexcitation of clusters versus those from neutral shows that “concerted” photodissociation of the ionized dimer appears to be the most likely mechanism for the formation of molecular iodine ion , instead of photoionization of neutral molecular iodine.

Calculation of accurate permanent dipole moments of the lowest states of heteronuclear alkali dimers using extended basis sets
View Description Hide DescriptionObtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of corecore interaction.

Pseudorotation motion in tetrahydrofuran: An ab initio study
View Description Hide DescriptionThe use of different models based on experimental information about the observed level splitings, rotational constants, and farinfrared transition frequencies leads to different predictions on the equilibrium geometry for tetrahydrofuran. Highlevel ab initio calculations [coupled cluster singles, doubles (triples)/complete basis set (second order Moller–Plesset triple, quadrupole, quintuple)+zeropoint energy(anharmonic)] suggest that the equilibrium conformation of tetrahydrofuran is an envelope structure. The theoretical geometrical parameters might be helpful to plan further microwave spectroscopic studies in order to get a physical interpretation of the measurements.

Anion of the formic acid dimer as a model for intermolecular proton transfer induced by a excess electron
View Description Hide DescriptionThe neutral and anionic formic acid dimers have been studied at the secondorder Møller–Plesset and coupledcluster level of theory with single, double, and perturbative triple excitations with augmented, correlationconsistent basis sets of double and triplezeta quality. Scans of the potentialenergysurface for the anion were performed at the densityfunctional level of theory with a hybrid B3LYP functional and a highquality basis set. Our main finding is that the formic acid dimer is susceptible to intermolecular proton transfer upon an excess electron attachment. The unpaired electron occupies a orbital, the molecular moiety that accommodates an excess electron “buckles,” and a proton is transferred to the unit where the excess electron is localized. As a consequence of these geometrical transformations, the electron vertical detachment energy becomes substantial, 2.35 eV. The anion is barely adiabatically unstable with respect to the neutral at 0 K. However, at standard conditions and in terms of Gibbs free energy, the anion is more stable than the neutral by . The neutral and anionic dimers display different IR characteristics. In summary, the formic acid dimer can exist in two quasidegenerate states (neutral and anionic), which can be viewed as “zero” and “one” in the binary system. These two states are switchable and distinguishable.

Theoretical study on germanium cyanide radical GeCN and its ions
View Description Hide DescriptionA detailed theoretical study is performed on the hitherto unknown germanium cyanide radical and its ions. The state GeCN lies 5.0 kcal/mol lower than the state GeNC at the coupledcluster theory including single and double excitations and perturbative inclusion of triple excitations [CCSD(T)]///quadratic configuration interaction with single and double excitations (QCISD)/+zeropoint vibrational energy (ZPVE) level. For interconversion between them, two electronic state pathways and are located, with the latter being 0.7 kcal/mol more favorable than the former. On the path, the GeCN→GeNC and GeNC→GeCN conversion barriers are 14.5 and 9.5 kcal/mol, respectively. The detailed singlet and triplet potentialenergysurfaces of both the cationic and anionic GeCN species are also investigated. On the groundstate electronic hypersurface, singlet is 4.6 kcal/mol more stable than singlet , whereas triplet is 10.0 kcal/mol less stable than triplet . The relative energy difference between the and can be well correlated with the number of vacant orbitals on the Ge atom. The stability of the neutral and ionic CGeN and cyclic is also discussed. The predicted structures, spectroscopies, ionization, and affinity energies as well as the Renner–Teller properties are expected to provide reliable estimates for future characterization of the potential GeCN and GeNC radicals as well as their ionic counterparts both in the laboratory and in the interstellar space.

Calculation of the dependence of the vibration–internal rotation–overall rotation interactions in from molecular structure and molecular dynamics
View Description Hide DescriptionThe Guan and Quade theory for vibration–largeamplitude internalmotionrotation interactions has been applied to the internal rotation problem in . Through the molecular dynamics, the and dependence of the torsional–rotational coefficients in the effective Hamiltonian have been calculated from molecular structure. The internal rotation coordinate for the vibrationally distorted molecule is shown to have the necessary threefold symmetry for all values of . For the methyl deformation modes, the vibrational dependence of the internal rotation potential energy is shown to have a threefold symmetry. The and dependence of the inertia tensor and Coriolis coupling coefficients has been developed in terms of curvilinear internal coordinates. The transformation separating rotation from vibrations in zeroth order is then applied, the kineticenergy tensor inverted to momentum space, and finally the effective torsion–rotation coefficients are calculated by Van Vleck perturbation theory. When compared to the empirical results, the kineticenergy contributions to the and dependence of the coefficients are as follows: 54% of is accounted for, 28% of , 16% of , and 91% of the asymmetry. The calculation is inadequate to account for the , and coefficients, ranging from factors of 20–70, even with the incorrect sign for some of the terms. Anharmonic force contributions from the vibrations have not been used in the calculation since these forces are not known at this time.

Ab initio potentialenergy surface for the reaction
View Description Hide DescriptionThe potentialenergysurface of the ground electronic state of CaHCl has been obtained from 6400 ab initio points calculated at the multireference configurationinteraction level and represented by a global analytical fit. The reaction is endothermic by with a barrier of at bent geometry, taking the zero energy in the asymptote. On both sides of this barrier are potential wells at linear geometries, a shallow one due to van der Waals interactions in the entrance channel, and a deep one attributed to the ionic configuration. The accuracy of the van der Waals well depth, , was checked by means of additional calculations at the coupledcluster singles and doubles with perturbative triples level and it was concluded that previous empirical estimates are unrealistic. Also, the electric dipole function was calculated, analytically fitted in the regions of the two wells, and used to analyze the charge shifts along the reaction path. In the insertion well, deep, the electric dipole function confirmed the ionic structure of the HCaCl complex and served to estimate effective atomic charges. Finally, bound rovibrational levels were computed both in the van der Waals well and in the insertion well, and the infraredabsorption spectrum of the insertion complex was simulated in order to facilitate its detection.

Low temperature pressure broadening of OCS by He
View Description Hide DescriptionWe report experimentally measured cross sections for pressure broadening of OCS by He from 4.2 to 23 K. These measurements were made in a quasiequilibrium cell using the collisional cooling technique. Cross sections were obtained for the broadening of the , , and rotational transitions of OCS. Theoretical cross sections were also calculated using a recent He–OCS potential surface. While at the higher temperatures,, there is only modest disagreement between experiment and theory, this disagreement increases steadily with decreasing temperature, with predicted cross sections rising steeply while the experimental data remains constant or decreases slightly. Comparisons to similar recent experimental studies are made and reasons for the observed discrepancy between experiment and theory are considered.

Redshift and blueshift of the Ar–H vibrational stretching frequency in complexes of FArH and acetylene
View Description Hide DescriptionTwo planar hydrogenbonded complexes of FArH and acetylene were found to be stable using secondorder Møller–Plesset perturbation theory (MP2) with basis sets. The more stable complex involves bonding between the F atom of FArH and a H atom of acetylene, while the other isomer is a Tshaped complex with the H atom of FArH bonded to the center of the CC bond of acetylene; the zeropoint energy corrected dissociation energies are 29 and , respectively. Interestingly, the Ar–H harmonic vibrational stretching frequency is blueshifted in the more stable isomer and redshifted in the less stable form. The electron density rearrangement of FArH on complexation was investigated and used to explain these unusual findings.