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We constructed an analytic diabatic potential energy matrix (DPEM) that describes the N–H photodissociation of methylamine; the electronic state space includes the ground and first excited singlet states. The input for the fit was calculated by extended multi-state complete active space second-order perturbation theory. The data were diabatized using the dipole–quadrupole diabatization method in which we incorporated a coordinate-dependent weighting scheme for the contribution of the quadrupole moments. To make the resulting potential energy surfaces semiglobal, we extended the anchor points reactive potential method, a multiscale approach that assigns the internal coordinates to categories with different levels of computational treatment. Key aspects of the adiabatic potential energy surfaces obtained by diagonalizing the DPEM agree with the available experimental and theoretical data at energies relevant for photochemical studies. [ABSTRACT FROM AUTHOR]

An analytic full-dimensional diabatic potential energy matrix (DPEM) for the lowest three singlet states of thiophenol (C6H5SH) at geometries accessible during photodissociation is constructed using the anchor points reactive potential (APRP) scheme. The data set used for modeling is obtained from electronic structure calculations including dynamic correlation via excitations into the virtual space of a three-state multiconfiguration self-consistent field calculation. The resulting DPEM is a function of all the internal coordinates of thiophenol. The DPEM as a function of the S−H bond stretch and C−C−S−H torsion and the diabatic couplings along two in-plane bend modes and nine out-of-plane distortion modes are computed using extended multiconfigurational quasidegenerate perturbation theory followed by the fourfold way determination of diabatic molecular orbitals and model space diabatization by configurational uniformity, and this dependence of the DPEM is represented by general functional forms. Potentials along 31 tertiary internal degrees of freedom are modeled with system-dependent, primary-coordinate-dependent nonreactive molecular mechanics-type force fields that are parameterized by Cartesian Hessians calculated by generalized Kohn-Sham density functional theory. Adiabatic potential energy surfaces (PESs) and nonadiabatic couplings are obtained by a transformation of the DPEM. The topography of the APRP PESs is characterized by vertical excitation energies, equilibrium geometries, vibrational frequencies, and conical intersections, and we find good agreement with available reference data. This analytic DPEM is suitable for full-dimensional electronically nonadiabatic molecular dynamics calculations of the photodissociation of thiophenol with analytic gradients in either the adiabatic or diabatic representation. [ABSTRACT FROM AUTHOR]

The photodissociation of thioanisole is very interesting because the experiments of Lim and Kim provide evidence for mode-specific effects on the product distribution. They showed that, with a specific S-CH3 stretching mode being excited as the reagent is excited to the S1 electronic state, there is a sharp increase in the proportion of the ground-state product to the excited-state product. In the present work, we report 78 011 full-dimensional semiclassical multi-state trajectories of the photodissociation process using the coherent switching with decay of mixing dynamics method. The potential surfaces and couplings are based on electronic structure calculations that include dynamic correlation through second order perturbation theory. We report results for four sets of initial conditions, one corresponding roughly to 0-0 excitation and three corresponding to exciting one vibrational mode, to look for modespecific effects. The simulations show no significant mode-specific effect on the product energy distributions, but they do showan effect on the distribution of minimum-energy gaps in the trajectories and on the lifetime for dissociation. In particular, excitation of the S-CH3 stretching mode leads to trajectories passing closer to the S1-S2 conical intersection and to shorter lifetimes. This provides a possible explanation of why experimental results are different for excitation of this vibration. [ABSTRACT FROM AUTHOR]

Analytic potential energy surfaces (PESs) and state couplings of the ground and two lowest singlet excited states of thioanisole (C6H5SCH3) are constructed in a diabatic representation based on electronic structure calculations including dynamic correlation. They cover all 42 internal degrees of freedom and a wide range of geometries including the Franck-Condon region and the reaction valley along the breaking S-CH3 bond with the full ranges of the torsion angles. The parameters in the PESs and couplings are fitted to the results of smooth diabatic electronic structure calculations including dynamic electron correlation by the extended multi-configurational quasi-degenerate perturbation theory method for the adiabatic state energies followed by diabatization by the fourfold way. The fit is accomplished by the anchor points reactive potential method with two reactive coordinates and 40 nonreactive degrees of freedom, where the anchor-point force fields are obtained with a locally modified version of the QuickFF package. The PESs and couplings are suitable for study of the topography of the trilayer potential energy landscape and for electronically nonadiabatic molecular dynamics simulations of the photodissociation of the S-CH3 bond. [ABSTRACT FROM AUTHOR]

The recently developed multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfiguration wave function theory with a density functional that depends on the on-top pair density of an electronic system. In an MC-PDFT calculation, there are two steps: a conventional multiconfiguration self-consistent-field (MCSCF) calculation and a post-MCSCF evaluation of the energy with an on-top density functional. In this work, we present the details of the MC-PDFT algorithm that avoids steeply scaling steps that are present in other post-self-consistent-field multireference calculations of dynamic correlation energy. We demonstrate the favorable scaling by considering systems of H2 molecules with active spaces of several different sizes. We then apply the MC-PDFT method to calculate the heterolytic dissociation enthalpy of ferrocene. We find that MC-PDFT yields results that are at least as accurate as complete active space second-order perturbation theory and are more stable with respect to basis set, but at a fraction of the cost in both time and memory. [ABSTRACT FROM AUTHOR]

Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function. [ABSTRACT FROM AUTHOR]

Diabatization is a procedure that transforms multiple adiabatic electronic states to a new representation in which the potential energy surfaces and the couplings between states due to the electronic Hamiltonian operator are smooth, and the couplings due to nuclear momentum are negligible. In this work, we propose a simple and general diabatization strategy, called model space diabatization, that is applicable to multi-configuration quasidegenerate perturbation theory (MC-QDPT) or its extended version (XMC-QDPT). An advantage over previous diabatization schemes is that dynamical correlation calculations are based on standard post-multi-configurational self-consistent field (MCSCF) multi-state methods even though the diabatization is based on state-averaged MCSCF results. The strategy is illustrated here by applications to LiH, LiF, and thioanisole, with the fourfold-way diabatization and XMC-QDPT, and the results illustrate its validity. [ABSTRACT FROM AUTHOR]

We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P-6) to O(P-12), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ~1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities. [ABSTRACT FROM AUTHOR]

Kohn-Sham (KS) time-dependent density functional theory (TDDFT) with most exchangecorrelation functionals is well known to systematically underestimate the excitation energies of Rydberg and charge-transfer excited states of atomic and molecular systems. To improve the description of Rydberg states within the KS TDDFT framework, Gaiduk et al. [Phys. Rev. Lett. 108, 253005 (2012)] proposed a scheme that may be called HOMO depopulation. In this study, we tested this scheme on an extensive dataset of valence and Rydberg excitation energies of various atoms, ions, and molecules. It is also tested on a charge-transfer excitation of NH3-F2 and on the potential energy curves of NH3 near a conical intersection. We found that the method can indeed significantly improve the accuracy of predicted Rydberg excitation energies while preserving reasonable accuracy for valence excitation energies. However, it does not appear to improve the description of charge-transfer excitations that are severely underestimated by standard KS TDDFT with conventional exchange-correlation functionals, nor does it perform appreciably better than standard TDDFT for the calculation of potential energy surfaces. [ABSTRACT FROM AUTHOR]

As electronic structure methods are being used to obtain quantitatively accurate reaction energies and barrier heights for increasingly larger systems, the choice of an efficient basis set is becoming more critical. The optimum strategy for achieving basis set convergence can depend on the way that electron correlation is treated and can take advantage of flexibility in the order in which basis functions are added. Here we study several approaches for estimating accurate reaction energies and barrier heights from post-Hartree-Fock electronic structure calculations. First and second, we evaluate methods of estimating the basis set limit of second order Mo\ller-Plesset perturbation theory and of coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations by using explicitly correlated basis functions (in the F12a implementation) along with valence, polarization, and diffuse one-electron basis functions. Third, we test the scheme of adding a higher-order correction to MP2 results (sometimes called MP2/CBS + ΔCCSD(T)). Finally, we evaluate the basis set requirements of these methods in light of comparisons to Weizmann-3.2, Weizmann-4, and CCSDT(2)Q/CBS+CV+R results. [ABSTRACT FROM AUTHOR]

Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the highpressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C2H2→C2H2Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C2H2Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C-H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well.We use these results to calculate the standard-state free energy and equilibrium constant of the reaction. [ABSTRACT FROM AUTHOR]

Electron momentum spectroscopy, scanning tunneling microscopy, and photoelectron spectroscopy provide unique information about electronic structure, but their interpretation has been controversial. This essay discusses a framework for interpretation. Although this interpretation is not new, we believe it is important to present this framework in light of recent publications. The key point is that these experiments provide information about how the electron distribution changes upon ionization, not how electrons behave in the pre‐ionized state. Therefore, these experiments do not lead to a "selection of the correct orbitals" in chemistry and do not overturn the well‐known conclusion that both delocalized molecular orbitals and localized molecular orbitals are useful for interpreting chemical structure and dynamics. The two types of orbitals can produce identical total molecular electron densities and therefore molecular properties. Different types of orbitals are useful for different purposes. [ABSTRACT FROM AUTHOR]

Electron momentum spectroscopy, scanning tunneling microscopy, and photoelectron spectroscopy provide unique information about electronic structure, but their interpretation has been controversial. This essay discusses a framework for interpretation. Although this interpretation is not new, we believe it is important to present this framework in light of recent publications. The key point is that these experiments provide information about how the electron distribution changes upon ionization, not how electrons behave in the pre‐ionized state. Therefore, these experiments do not lead to a "selection of the correct orbitals" in chemistry and do not overturn the well‐known conclusion that both delocalized molecular orbitals and localized molecular orbitals are useful for interpreting chemical structure and dynamics. The two types of orbitals can produce identical total molecular electron densities and therefore molecular properties. Different types of orbitals are useful for different purposes. [ABSTRACT FROM AUTHOR]

We extend our recent SOGGA11 approximation to the exchange-correlation functional to include a percentage of Hartree-Fock exchange. The new functional, called SOGGA11-X, has better overall performance for a broad chemical database than any previously available global hybrid generalized gradient approximation, and in addition it satisfies an extra physical constraint in that it is correct to second order in the density-gradient. [ABSTRACT FROM AUTHOR]

We report a detailed theoretical study of the hydrogen abstraction reaction from methanol by atomic hydrogen. The study includes the analysis of thermal rate constants, branching ratios, and kinetic isotope effects. Specifically, we have performed high-level computations at the MC3BB level together with direct dynamics calculations by canonical variational transition state theory (CVT) with the microcanonically optimized multidimensional tunneling (μOMT) transmission coefficient (CVT/μOMT) to study both the CH3OH + H → CH2OH + H2 (R1) reaction and the CH3OH + H → CH3O + H2 (R2) reaction. The CVT/μOMT calculations show that reaction R1 dominates in the whole range 298≤T(K)≤2500 and that anharmonic effects on the torsional mode about the C-O bond are important, mainly at high temperatures. The activation energy for the total reaction sum of R1 and R2 reactions changes substantially with temperature and, therefore, the use of straight-line Arrhenius plots is not valid. We recommend the use of new expressions for the total R1 + R2 reaction and for the R1 and R2 individual reactions. [ABSTRACT FROM AUTHOR]

This paper describes and illustrates a way to construct multidimensional representations of reactive potential energy surfaces (PESs) by a multiconfiguration Shepard interpolation (MCSI) method based only on gradient information, that is, without using any Hessian information from electronic structure calculations. MCSI, which is called multiconfiguration molecular mechanics (MCMM) in previous articles, is a semiautomated method designed for constructing full-dimensional PESs for subsequent dynamics calculations (classical trajectories, full quantum dynamics, or variational transition state theory with multidimensional tunneling). The MCSI method is based on Shepard interpolation of Taylor series expansions of the coupling term of a 2×2 electronically diabatic Hamiltonian matrix with the diagonal elements representing nonreactive analytical PESs for reactants and products. In contrast to the previously developed method, these expansions are truncated in the present version at the first order, and, therefore, no input of electronic structure Hessians is required. The accuracy of the interpolated energies is evaluated for two test reactions, namely, the reaction OH+H2→H2O+H and the hydrogen atom abstraction from a model of α-tocopherol by methyl radical. The latter reaction involves 38 atoms and a 108-dimensional PES. The mean unsigned errors averaged over a wide range of representative nuclear configurations (corresponding to an energy range of 19.5 kcal/mol in the former case and 32 kcal/mol in the latter) are found to be within 1 kcal/mol for both reactions, based on 13 gradients in one case and 11 in the other. The gradient-based MCMM method can be applied for efficient representations of multidimensional PESs in cases where analytical electronic structure Hessians are too expensive or unavailable, and it provides new opportunities to employ high-level electronic structure calculations for dynamics at an affordable cost. [ABSTRACT FROM AUTHOR]

Multiconfiguration molecular mechanics (MCMM) was previously applied to calculate potential energies, gradients, and Hessians along a reaction path and in the large-curvature tunneling swath, and it was shown that one could calculate variational transition state theory rate constants with optimized multidimensional tunneling without requiring more than a few electronic structure Hessians. It was also used for molecular dynamics simulations of liquid-phase potentials of mean force as functions of a reaction coordinate. In the present article we present some improvements to the formalism and also show that with these improvements we can use the method for the harder problem of trajectory calculations on gas-phase bimolecular reactive collisions. In particular, we apply the MCMM algorithm to the model reaction OH+H2→H2O+H, for which we construct the global full-dimensional interpolated potential energy surfaces with various numbers of electronic structure Hessians and various molecular mechanics force fields, and we assess the quality of these fits by quasiclassical trajectory calculations. We demonstrate that chemical accuracy (1–2 kcal/mol) can be reached for a MCMM potential in dynamically important regions with a fairly small number of electronic structure Hessians. We also discuss the origins of the errors in the interpolated energies and a possible way to improve the accuracy. [ABSTRACT FROM AUTHOR]

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode ν2 with n2=0,...,6 quanta of vibration) in the à electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTU/SD+trajectory projection onto ZPE orbit (TRAPZ) and FSTU/SD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH2 internal energy distributions obtained for n2=0 and n2>1, as observed in experiments. Distributions obtained for n2=1 present an intermediate behavior between distributions obtained for smaller and larger n2 values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH2 internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n2=0 and n2=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching. [ABSTRACT FROM AUTHOR]

Recently, a generalized gradient approximation (GGA) to the density functional, called PBEsol, was optimized (one parameter) against the jellium-surface exchange-correlation energies, and this, in conjunction with changing another parameter to restore the first-principles gradient expansion for exchange, was sufficient to yield accurate lattice constants of solids. Here, we construct a new GGA that has no empirical parameters, that satisfies one more exact constraint than PBEsol, and that performs 20% better for the lattice constants of 18 previously studied solids, although it does not improve on PBEsol for molecular atomization energies (a property that neither functional was designed for). The new GGA is exact through second order, and it is called the second-order generalized gradient approximation (SOGGA). The SOGGA functional also differs from other GGAs in that it enforces a tighter Lieb–Oxford bound. SOGGA and other functionals are compared to a diverse set of lattice constants, bond distances, and energetic quantities for solids and molecules (this includes the first test of the M06-L meta-GGA for solid-state properties). We find that classifying density functionals in terms of the magnitude μ of the second-order coefficient of the density gradient expansion of the exchange functional not only correlates their behavior for predicting lattice constants of solids versus their behavior for predicting small-molecule atomization energies, as pointed out by Perdew and co-workers [Phys. Rev. Lett. 100, 134606 (2008); Perdewibid. 80, 891 (1998)], but also correlates their behavior for cohesive energies of solids, reaction barriers heights, and nonhydrogenic bond distances in small molecules. [ABSTRACT FROM AUTHOR]

The accuracy of non-Born-Oppenheimer (electronically nonadiabatic) semiclassical trajectory methods for simulations of “deep quantum” systems is reevaluated in light of recent quantum mechanical calculations of the photodissociation of the Na...FH van der Waals complex. In contrast to the conclusion arrived at in an earlier study, semiclassical trajectory methods are shown to be qualitatively accurate for this system, thus further validating their use for systems with large electronic energy gaps. Product branching in semiclassical surface hopping and decay-of-mixing calculations is affected by a region of coupling where the excited state is energetically forbidden. Frustrated hops in this region may be attributed to a failure of the treatment of decoherence, and a stochastic model for decoherence is introduced into the surface hopping method and is shown to improve the agreement with the quantum mechanical results. A modification of the decay-of-mixing method resulting in faster decoherence in this region is shown to give similarly improved results. [ABSTRACT FROM AUTHOR]

We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. [ABSTRACT FROM AUTHOR]

Bromoacetyl chloride photodissociation has been interpreted as a paradigmatic example of a process in which nonadiabatic effects play a major role. In molecular beam experiments by Butler and co-workers [J. Chem. Phys. 95, 3848 (1991); J. Chem. Phys. 97, 355 (1992)], BrCH2C(O)Cl was prepared in its ground electronic state (S0) and excited with a laser at 248 nm to its first excited singlet state (S1). The two main ensuing photoreactions are the ruptures of the C–Cl bond and of the C–Br bond. A nonadiabatic model was proposed in which the C–Br scission is strongly suppressed due to nonadiabatic recrossing at the barrier formed by the avoided crossing between the S1 and S2 states. Recent reduced-dimensional dynamical studies lend support to this model. However, another interpretation that has been given for the experimental results is that the reduced probability of C–Br scission is a consequence of incomplete intramolecular energy redistribution. To provide further insight into this problem, we have studied the energetically lowest six singlet electronic states of bromoacetyl chloride by using an ab initio multiconfigurational perturbative electronic structure method. Stationary points (minima and saddle points) and minimum energy paths have been characterized on the S0 and S1 potential energy surfaces. The fourfold way diabatization method has been applied to transform five adiabatic excited electronic states to a diabatic representation. The diabatic potential energy matrix of the first five excited singlet states has been constructed along several cuts of the potential energy hypersurfaces. The thermochemistry of the photodissociation reactions and a comparison with experimental translational energy distributions strongly suggest that nonadiabatic effects dominate the C–Br scission, but that the reaction proceeds along the energetically allowed diabatic pathway to excited-state products instead of being nonadiabatically suppressed. This conclusion is also supported by the low values of the diabatic couplings on the C–Br scission reaction path. The methodology established in the present study will be used for the construction of global potential energy surfaces suitable for multidimensional dynamics simulations to test these preliminary interpretations. [ABSTRACT FROM AUTHOR]

In the present study, we comparatively assessed the newly developed M05 functional against a data set of reaction energies for transition-metal chemistry. The functionals to which we compare are BLYP, B3LYP, B97-2, MPWLYP1M, TPSS, and TPSSh. We draw the following conclusions: (1) TPSS gives the best performance for calculating the binding energies of three transition-metal dimers (Sc2, Ni2, and V2) that have severe multireference character, (2) B97-2 gives the best performance for calculating the binding energies of the nine metal-ligand diatomics (three monohydrides, three monoxide, and three monofluorides), and (3) M05 gives the overall best performance for all 18 data in the assessment, and it has a mean unsigned error 55% lower than the popular B3LYP functional. Since the M05 functional also gives good performance for main-group thermochemistry, for noncovalent chemistry, and for calculating barrier heights, M05 can be applied to a wide range of problems where nonhybrid functionals or functionals designed for kinetics fail. [ABSTRACT FROM AUTHOR]

The vibrational partition function of ethane is calculated in the temperature range of 200–600 K using well-converged energy levels that were calculated by vibrational configuration interaction, and the results are compared to the harmonic oscillator partition function. This provides the first test of the harmonic oscillator approximation for a molecule with more than five atoms. The absolute free energies computed by the harmonic oscillator approximation are in error by 0.59–0.62 kcal/mol over the 200–600 K temperature range. [ABSTRACT FROM AUTHOR]

We used multiconfiguration quasidegenerate perturbation theory and the fourfold-way direct diabatization scheme to calculate ab initio potential-energy surfaces at 3600 nuclear geometries of NH3. The calculations yield the adiabatic and diabatic potential-energy surfaces for the ground and first electronically excited singlet states and also the diabatic coupling surfaces. The diabatic surfaces and coupling were fitted analytically to functional forms to obtain a permutationally invariant 2×2 diabatic potential-energy matrix. An analytic representation of the adiabatic potential-energy surfaces is then obtained by diagonalizing the diabatic potential-energy matrix. The analytic representation of the surfaces gives an analytic representation of the four-dimensional conical intersection seam which is discussed in detail. [ABSTRACT FROM AUTHOR]

[Display omitted] • Two different basis set series, both labeled cc-pV x Z, for calculation on Li compounds are different. • Different levels of theory including DFT, MP, CCSD and CCSD(T) were tested. • The deviations among the basis sets are as large as 22 millihartrees (57 kJ/mol) We have found that two different basis set series, both labeled cc-pV x Z, are widely available and widely used for calculation on Li compounds such that calculations that should be the same are different, causing a reproducibility problem. Here we study the magnitude of the disagreement of these nominally-the-same basis sets for wave function and density functional calculations of Li clusters. We find deviations among the basis sets of as large as 22 millihartrees. In most cases one obtains lower energies with the noncanonical choices. Therefore, it is important to specify which version of the basis set is used for calculations. [ABSTRACT FROM AUTHOR]

An expression is obtained for the electronic decoherence time of the reduced density electronic matrix in mixed quantum-classical molecular-dynamics simulations. The result is obtained by assuming that decoherence is dominated by the time dependence of the overlap of minimum-uncertainty packets and then maximizing the rate with respect to the parameters of the wave packets. The expression for the decay time involves quantities readily available in non-Born-Oppenheimer molecular-dynamics simulations, and it is shown to have a reasonable form when compared with two other formulas for the decay time that have been previously proposed. [ABSTRACT FROM AUTHOR]

Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%–60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of ∼32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The rovibration partition function of CH4 was calculated in the temperature range of 100–1000 K using well-converged energy levels that were calculated by vibrational–rotational configuration interaction using the Watson Hamiltonian for total angular momenta J=0–50 and the MULTIMODE computer program. The configuration state functions are products of ground-state occupied and virtual modals obtained using the vibrational self-consistent field method. The Gilbert and Jordan potential energy surface was used for the calculations. The resulting partition function was used to test the harmonic oscillator approximation and the separable-rotation approximation. The harmonic oscillator, rigid-rotator approximation is in error by a factor of 2.3 at 300 K, but we also propose a separable-rotation approximation that is accurate within 2% from 100 to 1000 K. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The fourfold way is a general algorithm for generating diabatic electronic wave functions that span the same space as a small set of variationally optimized adiabatic electronic wave functions and for using the resulting diabatic wave functions to generate diabatic potential energy surfaces and their couplings. In this paper we extend the fourfold way so it is applicable to more complex polyatomic systems and in particular to the calculation of global potential energy surfaces for such systems. The extension involves partitioning the active space into three blocks, introducing restricted orbital rotation within two of the blocks, introducing a specific resolution of the subspace containing molecular orbitals that are doubly occupied in all dominant configuration state functions, and introducing specific orientations of the coordinate systems for reference molecular orbitals and resolution molecular orbitals. The major strength of the improved method presented in this paper is that it allows the diabatic molecular orbitals to exhibit a gradual change of chemical character with smooth deformation along the reaction coordinate for a change of chemical arrangement while preserving the orbital character required for a physical ordering of the orbitals. This feature is required for the convenient construction of global potential energy surfaces for non-BornOppenheimer rearrangements. The resulting extended algorithm is illustrated by calculating diabatic potential energy surfaces and couplings for the two lowest singlet potential energy surfaces of HNCO. [ABSTRACT FROM AUTHOR]

In previous work, three implicit potential energy surfaces with specific reaction parameters (SRP), namely MPW60, MC-QCISD-SRP, and MCG3-SRP, were developed for the reaction CH[sub 4]+H → CH[sub 3] + H[sub 2]. Forward reaction rate constants obtained by variational transition state theory with multidimensional tunneling (VTST/MT) dynamics calculations on these surfaces give good agreement with recently re-analyzed experimental results. In the present work, again employing VTST/MT, kinetic isotope effects (KIEs) for isotopic variants of the title reaction in both the forward and reverse directions are examined on these SRP surfaces. Various primary and secondary deuterium (D) kinetic isotope reactions are studied; we also calculated the KIE for the reaction between methane and muonium (Mu), which is an ultralight isotope of protium with the Mu/H mass ratio being 0.113. The results are compared with several sets of experimental studies. With the VTST/MT dynamical method and harmonic vibrations, the proposed surfaces predict the KIE quite well, probably within experimental error, for seven different isotopic combinations involving substitution of one to five deuteriums for protium. The calculations also reproduce quite well the high Arrhenius activation energy for Mu+CH[sub 4], and the KIE for muonium atom attack is correctly predicted to be inverse, but the predicted values of the Mu KIE over the experimental temperature range are 0.012-0.06 (without scaling force constants) or 0.021-0.09 (when the force constant of the making bond is scaled), whereas the experimental values in the same temperature range are 0.05-0.3. Several possible reasons for this are discussed. [ABSTRACT FROM AUTHOR]

Diabatic representation of coupled potential energy surfaces and their scalar couplings provides a compact and convenient starting point for dynamics calculations carried out in either the adiabatic or diabatic representation. In a previous paper we presented a general, path-independent scheme, called the fourfold way, for calculating diabatic surfaces and their scalar couplings from adiabatic surfaces and electronic density matrices such that the manifold of diabatic states spans the variationally optimized space of a finite number of adiabatic states. In the present paper we extend that scheme in these ways: (1) We show how to include dynamical electronic correlation energy by multireference perturbation theory or configuration interaction based on a complete active reference space. (2) We present a more general strategy for treating rearrangements. (3) We present consistency criteria for testing the validity of the assumptions for a particular choice of reference geometries, diabatic molecular orbital (DMO) ordering, dominant configuration-state-function lists, and choice(s) for reference DMO(s) for systems involving rearrangements. The first extension is illustrated by multiconfiguration quasidegenerate perturbation theory (MC-QDPT) calculations on LiF, and all three extensions are illustrated by MC-QDPT calculations on the reaction Li(2 ²S,2²p)+HF→LiF+H. [ABSTRACT FROM AUTHOR]

Four implicit potential energy surfaces (PESs) with specific-reaction-parameters (SRP) are developed and tested for the reaction CH[sub 4]+H→CH[sub 3]+H[sub 2]. The first is called MPW60 and is based on the modified Perdew–Wang hybrid density-functional method with the percentage of the Hartree–Fock exchange equal to 60%. The other three PESs are constructed with multi-coefficient correlation methods (MCCMs). The second is called MCOMP2-SRP, and the third is called MC-QCISD-SRP. Both of them are parametrized for this specific reaction by starting with their corresponding global parameters. The fourth is called MCG3-SRP and is based on the MCG3-CHO semiglobal parametrization with further refinement for this specific reaction. All four SRP surfaces have a classical forward barrier height of 14.8 kcal/mol, and all three MCCM SRP surfaces have a classical endoergicity of 3.3 kcal/mol. The stationary point geometries, vibrational frequencies, and zero-point-energies are reported for several standard single-level methods and MCCMs with global parameters as well as for the four new SRP surfaces. Direct dynamics calculations are carried out using variational transition state theory with multidimensional tunneling contributions on the proposed SRP surfaces. We calculate forward reaction rate constants for the title reaction from 250 to 2400 K and compare them with the latest re-analyzed experimental results over the temperature range from 348 to 1950 K. The calculated rate constants using canonical variational theory with the small-curvature tunneling approximation carried out on the MPW60, MC-QCISD-SRP, and MCG3-SRP surfaces show good agreement with the experimental results. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In order to provide a practical framework for the calculation of diabatic (technically quasidiabatic) states, we generalize the diabatization procedures of Atchity and Ruedenberg to include more general types of crossings and avoided crossings of potential energy surfaces. The resulting diabatization procedure involves two steps: (i) the construction of diabatic orbitals and (ii) the construction of many-electron diabatic state functions in terms of the diabatic orbitals. The procedure for step (i) is more general than the previously proposed occupation number and natural orbital method, and the procedure for step (ii) remains valid even for chemical reactions that require multiple diabatic prototypes. The method is illustrated by applications to LiH, ozone, H[sub 2] dimer, and the reaction Li([sup 2]S,[sup 2]P)+HF→LiF+H. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents high-level ab initio electronic structure calculations for the ground and first excited state of the NaH[sub 2] system. Inclusion of full configuration interaction theory and second-order Moller-Plesset perturbation theory; Comparison of the matrix potential and its eigenvalues to previous literature.

Proposes an algorithm used for solving a reaction path and a set of vibrational frequencies along a reaction path for dynamics calculations. Introduction of the reorientation of the dividing surface (RODS) algorithm; Comparison of the variational reaction path (VRP) algorithm with the Euler method; Accuracy and efficiency of both the RODS and VRP algorithm.

Abstract Electronically nonadiabatic photodissociation can be investigated in detail by experiments. This provides an opportunity to validate the current theory of electronically nonadiabatic processes, but is great challenge because the time scale of photodissociation processes can be long compared to the current capability for accurate direct dynamics simulations. To circumvent this difficulty, we have been using analytic diabatic potential energy matrices, such that the simulation time scale can be extended to the nanosecond region without neglecting the effects of external electron correlation. In previous work, we have developed full-dimensional three-state potential energy matrices for thioanisole photodissociation. In the current work, we extend this work in two main ways: (i) we improve the treatment of the initial torsional potential, and (ii) we shift the potential energy surfaces to investigate the quantitative effect on the dissociation lifetimes and product branching ratios of changing the energy and location of the S 1 –S 2 conical intersection. [ABSTRACT FROM AUTHOR]

Presents a simulation of the photoabsorption spectrum of Na***FH van der Waals molecule. Use of analytic representation of potential NaFH surfaces in the simulation; Importance of photodissociation in determining the branching probability between the harpooning reaction to form NaF; Implementation of the Franck-Condon analysis.

Presents high-level ab initio calculations of the ground and several excited-state adiabatic potential surfaces of NaFH systems. Derivation of an analytic 2x2 matrix fit for ground and first excited states; Determination of off-diagonal coupling; Use of full fit in locating the barrier and the van der Waals well on the ground-state potential surface.

Presents a statistical model for the decay of an exciplex that is strongly coupled to repulsive ground-state potential energy surface. Assumption that the motion of the exciplex is governed by the excited electronic state adiabatic potential surface; Diabatic representation for the Hamiltonian matrix for the system.

Presents a general method for treating doubly generate bending vibration frequencies of curvilinear internal coordinates. Treatment improving the generalized normal mode frequencies; Need for constant rate calculations with variational transition state theory.

This paper presents a way of improving second-order perturbation theory calculations by summing contributions of uncoupled excitations to infinite order. For problems involving molecular vibrations, the new theory is shown to give similar results to conventional second-order perturbation theory when the system treated has no near resonances but also to give accurate and stable results even very close to resonance. The new theory is tested by comparison to converged variational calculations for vibrational energy levels of formaldehyde, formaldehyde-d2, and two two-dimensional model subsystems based on formaldehyde. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The centrifugal-dominant small-curvature semiclassical adiabatic tunneling approximation is used with variational transition state theory to calculate diffusion coefficients for hydrogen, deuterium, and tritium atoms on the (100) face of copper for temperatures in the range 80–1000 K. The system is modeled by the embedded cluster method, and the copper lattice is constructed with a lattice constant optimized for the assumed potential energy function. Calculations are presented with up to 171 nonfixed degrees of freedom. The results are well converged with respect to the number of lattice atoms whose motion is allowed to couple to the adatom. The difference between the diffusion coefficients calculated with rigid and nonrigid lattices at 300 K are 3.7, 3.3, and 3.1 for H, D, and T, respectively, increasing to factors of 24.1, 19.4, and 17.2 at 120 K. The effect levels off for lower temperatures, e.g., the ratio for H is 27.3 at 100 K and 24.4 at 80 K. The convergence with respect to the number of moving copper atoms is nonmonotonic; detailed examination of the intermediate results shows that such nonmonotonicities result from the nonsmooth cancellation of a large number of competing effects attributable to many surface phonon modes. We compare the present results to those predicted by path integral transition state theory and to those predicted by transition state theory with quantum effective potentials, and we find them to be in reasonably good agreement. This is very encouraging since tests of multidimensional semiclassical tunneling approximations have been limited to systems with only a few degrees of freedom in the past. [ABSTRACT FROM AUTHOR]

Interpolated variational transition state theory calculations with centrifugal-dominant, small-curvature tunneling coefficients have been carried out for the case of the deuterium kinetic isotope effect (KIE) in the reaction OH+12CD4→HDO+12CD3 and for the 13C KIE for the reaction OH+13CH4→H2O+13CH3. The interpolated variationally optimized generalized transition states predict notably different nontunneling KIEs than the conventional ones, and factorization analyses of the KIEs are presented to illustrate the origin of the differences. The zero-point energies at the variational transition states differ from those at the saddle point by up to 0.19 kcal/mol for the OH+12CD4 reaction and by up to 0.34 kcal/mol for the OH+13CH4 reaction. The incorporation of multidimensional tunneling effects partly cancels the effect of variational optimization of the transition state. [ABSTRACT FROM AUTHOR]

Projection operator techniques for enforcing bond-distance and bond-angle constraints in reaction-path dynamics calculations are presented. These techniques provide a systematic method for carrying out reduced-dimensionality calculations in generalized normal mode coordinates with constrained values for selected internal coordinates. The methods are illustrated with generalized transition-state theory and multidimensional semiclassical tunneling calculations for the reactions OH+H2→H2O+H and CH3+H2→CH4+H in which one or more bond lengths and/or bond angles is held fixed. [ABSTRACT FROM AUTHOR]

We have carried out ab initio calculations for the reaction OH+CH4→H2O+CH3 using second-order Mo\ller–Plesset perturbation theory, employing a very large basis set and scaling all correlation energy for the final energy calculation, but optimizing the equilibrium and transition state structures without scaling (MP-SAC2//MP2). We found that inclusion of correlation energy has an important effect on the geometry, barrier height, and vibrational frequencies of the transition state. The final calculated values for the forward and reverse classical barrier heights are 7.4 and 20.6 kcal/mol, respectively. We have used these with interpolated canonical variational transition state theory and the centrifugal-dominant small-curvature tunneling approximation, including information at the reactants, products, transition state, and two other points along the minimum energy path, to predict the rate constants for the above reaction in the temperature range from 223 to 2400 K. The calculated rate constants agree well with experiment over a wide temperature range. [ABSTRACT FROM AUTHOR]

We define a general set of effective solvent coordinates for reactions in solution that should be especially well suited for polar solvents. No specific functional form is assumed for the variation of charges with motions along or orthogonal to the reaction coordinate, and as a consequence the formalism allows the treatment of arbitrary reaction types using electronic structure calculations for the solute charge distribution. A critical assumption of the theory is that the nonequilibrium polarization field may be represented in terms of the adiabatic polarization fields that arise for linear geometric displacements. The results are combined with the Cartesian-coordinate canonical variational transition state theory presented previously to provide a general method for including both equilibrium and nonequilibrium solvation effects of a nondissipative, continuum-dielectric solvent in practical calculations of rate constants. [ABSTRACT FROM AUTHOR]

The Fourier coefficient path-integral representation of the quantum density matrix is used to carry out direct, accurate calculations of coupled vibrational partition functions. The present implementation of the Fourier path-integral method incorporates two noteworthy features. First, we use a Gaussian in Fourier space as a probability density function, which is sampled using the Box–Muller algorithm. Second, we introduce an adaptively optimized stratified sampling scheme in Cartesian coordinates to sample the nuclear configurations. We illustrate these strategies by applying them to a coupled stretch–bend model which resembles two of the vibrational modes of H2O. We also apply a simple, yet accurate method for estimating the statistical error of a Metropolis integration, and we compare the Box–Muller and Metropolis sampling algorithms in detail. The numerical tests of the new method are very encouraging, and the approach is promising for accurate calculations of quantum free energies for polyatomic molecules. [ABSTRACT FROM AUTHOR]

In this paper we optimize several algorithms for the computation of reaction rates based on information calculated along minimum energy reaction paths and we evaluate the efficiencies of the optimized algorithms. The investigations are based on the calculation of chemical reaction rate constants using variational transition state theory and multidimensional semiclassical transmission coefficients including reaction path curvature. Several methods are evaluated and compared by a systematic set of applications to test cases involving the hydrogen-atom transfer reactions CH3+H2→CH4+H and OH+H2→H2O+H. For each method we present general recommendations for all algorithmic choices other than gradient step size so that future calculations may be carried out reasonably efficiently by varying only one parameter. In the process of these optimizations we have found that the accuracy of the Euler stabilization method can be significantly increased by choosing the auxiliary parameters differently than in previous work; the optimized algorithm is called ES1*. Our final recommendations for future work are (i) when the Hessian/gradient computational cost ratio is low (<=3): the Page–McIver algorithm with the Hessian recalculated at every step, with a cubic starting step, and with curvature calculated from the derivative of the gradient, and (ii) when the Hessian/gradient computational cost ratio is moderate or large: the ES1* algorithm with a Hessian step size three times larger than the gradient step size, with a quadratic starting step, and with curvature calculated from the derivative of the gradient. [ABSTRACT FROM AUTHOR]

State-to-state reaction probabilities are found to be highly final-state specific at state-selected threshold energies for the reactions O+H2→OH+H and H+H2→H2+H. The study includes initial rotational states with quantum numbers 0–15, and the specificity is especially dramatic for the more highly rotationally excited reactants. The analysis is based on accurate quantum mechanical reactive scattering calculations. Final-state specificity is shown in general to increase with the rotational quantum number of the reactant diatom, and the trends are confirmed for both zero and nonzero values of the total angular momentum. [ABSTRACT FROM AUTHOR]