Volume 131, Issue 2, 14 July 2009

The effective fragment potential (EFP) method, a model potential for treating solvent effects and other intermolecular interactions, is interfaced with an electronic structure method, the fragment molecular orbital (FMO) method, that is able to retain high accuracy for ab initio calculations on large molecular systems. The accuracy of the total energies in this novel combined FMO/EFP method is assessed by comparisons with the conventional quantum mechanics (QM)/EFP method. The test cases are water clusters, a peptide, and a dianionic protein (treated with full QM and FMO) combined with water clusters (treated with EFP) at the RHF, B3LYP, and MP2 levels of theory. The basis sets employed range from minimal to augmented double zeta plus polarization. The energy differences between FMO/EFP and the conventional QM/EFP methods are within “chemical accuracy” .
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Virial theorem in the Kohn–Sham densityfunctional theory formalism: Accurate calculation of the atomic quantum theory of atoms in molecules energies
View Description Hide DescriptionA new approach for computing the atominmolecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn–Sham densityfunctional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlationkinetic energy is computed using the densityfunctional theory virial relation. Based on our calculations, it is shown that the conventional approach where atomic energies are computed using only the noninteracting part of the kinetic energy might be in error by hundreds of kJ/mol.

Spin conserving natural orbital functional theory
View Description Hide DescriptionThe natural orbital functionaltheory is considered for spin uncompensated systems, i.e., systems that have one or more unpaired electrons. The wellknown cumulant expansion is used to reconstruct the twoparticle reduced density matrix. A new condition to ensure the conservation of the total spin is obtained for the twoparticle cumulant matrix. An extension of the Piris natural orbital functional 1 (PNOF1), based on an explicit form for the cumulant, to spin uncompensated systems is also considered. The theory is applied to the calculation of energy differences between the ground state and the lowest lying excited state with different spins for firstrow atoms (Li, Be, B, C, N, O, and F) and diatomic oxygen molecule . The values we obtained are very accurate results as compared to the CCSD(T) method and the experimental data.
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 ARTICLES

 Theoretical Methods and Algorithms

A combined effective fragment potential–fragment molecular orbital method. I. The energy expression and initial applications
View Description Hide DescriptionThe effective fragment potential (EFP) method, a model potential for treating solvent effects and other intermolecular interactions, is interfaced with an electronic structure method, the fragment molecular orbital (FMO) method, that is able to retain high accuracy for ab initio calculations on large molecular systems. The accuracy of the total energies in this novel combined FMO/EFP method is assessed by comparisons with the conventional quantum mechanics (QM)/EFP method. The test cases are water clusters, a peptide, and a dianionic protein (treated with full QM and FMO) combined with water clusters (treated with EFP) at the RHF, B3LYP, and MP2 levels of theory. The basis sets employed range from minimal to augmented double zeta plus polarization. The energy differences between FMO/EFP and the conventional QM/EFP methods are within “chemical accuracy” .

First and secondorder electrical properties computed at the FSMRCCSD level for excited states of closedshell molecules using the constrainedvariational approach
View Description Hide DescriptionFock space multireference coupledcluster (FSMRCC) method emerged as an efficient tool to describe the electronic structure of nearly degenerate cases. Development of linear response has been one of the challenging problems in FSMRCC due to the multipleroot nature of the effective Hamiltonian. A response from any of the roots would span the space for getting the properties. Hence, all roots perturbed by the external field would proliferate the excited states. We recently developed the FSMRCC method for the efficient evaluation of analytic response properties using a constrained variation approach. In this paper, we present analytic dipole moments and polarizabilities of , , and molecules in lowlying excited states along with brief discussion of singlet triplet decoupling of (1,1) sector of FSMRCC resulting from spin adaptation.

The multiscale coarsegraining method. IV. Transferring coarsegrained potentials between temperatures
View Description Hide DescriptionThis work develops a method for the construction of multiscale coarsegrained (MSCG) force fields at different temperatures based on available atomistic data at a given reference temperature. The validity of this theory is demonstrated numerically by applying it to construct MSCG models of the LennardJones liquid and simple point charge water modelsystems.

Partial photoionization cross sections of and Rydberg radicals
View Description Hide DescriptionPhotoionization cross sections for various Rydberg series that correspond to ionization channels of ammonium and oxonium Rydberg radicals from the outermost, occupied orbitals of their respective ground states are reported. These properties are known to be relevant in photoelectron dynamics studies. For the present calculations, the molecularadapted quantum defect orbital method has been employed. A Cooper minimum has been found in the Rydberg channel of beyond the ionization threshold, which provides the main contribution to the photoionization of this radical. However, no net minimum is found in the partial cross section of despite the presence of minima in the and Rydberg channels. The complete oscillator strength distributions spanning the discrete and continuous regions of both radicals exhibit the expected continuity across the ionization threshold.

Rovibrational energy levels of with energies above the barrier to linearity
View Description Hide DescriptionThe potential energy surface is sampled at 5900 geometries with the emphasis on the nonequilibrium and asymptotic points. Apart from the Born–Oppenheimer energy converged to the accuracy better than , the adiabatic and the leading relativistic corrections are computed at each geometry. To represent analytically the potential energy surface, the parameters of a power series are determined by fitting to the computed energy points. Possible choice of nuclear masses simulating the nonadiabatic effects in solving the nuclear Schrödinger equation is analyzed. A set of theoretically predicted rovibrational transitions is confronted with the experimental data in the window of the spectra.

Accurate thermochemistry for transition metal complexes from firstprinciples calculations
View Description Hide DescriptionThe “correlation consistent Composite Approach” or ccCA is an ab initio model chemistry based on the single reference MP2 level of theory. By adjusting the basis set and level of theory of the core valence additive correction, ccCA is capable of reliable thermochemical predictions of inorganic and organometallic transition metalcontaining molecules, as well as achieving chemical accuracy on main group species, with a mean absolute deviation of against the 147 enthalpies of formation in the G2/97 test set. For a set of 52 complexes containing elements Sc–Zn, ranging in size from diatomics to and , ccCA on average predicts enthalpies of formation to within of the experimental result with a mean absolute deviation of and a root mean square deviation of . The ccCA methodology is a significant step toward quantitative theoretical modeling of transition metal thermodynamics.

Isotropic periodic sum of electrostatic interactions for polar systems
View Description Hide DescriptionIsotropic periodic sum (IPS) is a method to calculate longrange interactions based on homogeneity of simulation systems. Longrange interactions are represented by interactions with isotropic periodic images of a defined local region and can be reduced to short ranged IPS potentials. The original electrostatic threedimensional (3D)IPS potential was derived based on a nonpolar homogeneous approximation and its application is limited to nonpolar or weak polar systems. This work derived a polar electrostatic 3DIPS potential based on polar interactions. For the convenience of application, polynomial functions with rationalized coefficients are proposed for electrostatic and LennardJones 3DIPS potentials. Model systems of various polarities and several commonly used solvent systems are simulated to evaluate the 3DIPS potentials. It is demonstrated that for polar systems the polar electrostatic 3DIPS potential has much improved accuracy as compared to the nonpolar 3DIPS potential. For homogeneous systems, the polar electrostatic 3DIPS potential with a local region radius or cutoff distance of as small as 10 Å can satisfactorily reproduce energetic, structural, and dynamic properties from the particlemeshedEwald method. For both homogeneous and heterogeneous systems, the 3DIPS/discrete fast Fourier transform method using either the nonpolar or the polar electrostatic 3DIPS potentials results in very similar simulation results.

Solving the eigenvalue equations of correlated vibrational structure methods: Preconditioning and targeting strategies
View Description Hide DescriptionVarious preconditioners and eigenvector targeting strategies in combination with the Davidson and Olsen methods are presented for solving eigenvalue equations encountered in vibrational configuration interaction, its response generalization, and vibrational coupled cluster response theory. The targeting methods allow significant flexibility and robustness in computing selected vibrational states, which are particularly important in the often occurring but nontrivial cases of near degeneracies. We have investigated the effect of a modeexcitation levelbased generally applicable preconditioning scheme aiming to improve the robustness of the more standard diagonal preconditioning method. Although increasing convergence rates may be achieved in general through a hierarchy of these preconditioners, the strategy is not always beneficial in terms of CPU time. Features of the methods are demonstrated in calculations of the overtone vibrational states of formaldehyde and the fundamental states of vinyl fluoride, vinyl chloride, vinyl bromide, and naphthalene.

Effectivemode representation of nonMarkovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics
View Description Hide DescriptionAn approach to nonMarkovian systemenvironment dynamics is described which is based on the construction of a hierarchy of coupled effective environmental modes that is terminated by coupling the final member of the hierarchy to a Markovian bath. For an arbitrary environment, which is linearly coupled to the subsystem, the discretized spectral density is replaced by a series of approximate spectral densities involving an increasing number of effective modes. This series of approximants, which are constructed analytically in this paper, guarantees the accurate representation of the overall systemplusbath dynamics up to increasing times. The hierarchical structure is manifested in the approximate spectral densities in the form of the imaginary part of a continued fraction similar to Mori theory. The results are described for cases where the hierarchy is truncated at the first, second, and thirdorder level. It is demonstrated that the results generated from a reduced density matrix equation of motion and large dimensional systemplusbath wavepacket calculations are in excellent agreement. For the reduced density matrix calculations, the system and hierarchy of effective modes are treated explicitly and the effects of the bath on the final member of the hierarchy are described by the Caldeira–Leggett equation and its generalization to zero temperature.

Kramerslike turnover in loaddependent activated dynamics
View Description Hide DescriptionRecent advancement of experimental techniques at the single molecule level has demonstrated how an external load affects a chemical reaction which controls the transport of biological motor proteins. Majority of these studies are concerned with thermodynamically open systems. We have examined a prototype model reaction in terms of inertial Brownian motion of a particle in a force field subjected to an overdamped motion of a viscous load coupled harmonically to the particle. A general analytical expression for the rate constant has been derived to demonstrate that depending on the strength of harmonic coupling and drag coefficient of the load a Kramerslike turnover can be realized in the spatial diffusionlimited regime. The turnover reduces to a crossover between the two states characterized by zeroload and finite load conditions.

Path integral evaluation of equilibrium isotope effects
View Description Hide DescriptionA general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of at 500 K and more at room temperature. We describe the implementation of the methodology in the molecular dynamics package AMBER 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering et al. , [J. Am. Chem. Soc.128, 9080 (2006); J. Am. Chem. Soc.129, 2488 (2007)] confirming the accuracy of the most recent measurement on 2,4,6,7,9pentamethyl5(5,5 )methylene11,11adihydro naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2methyl10(10,10 )methylenebicyclo[4.4.0]dec1ene.

Electrochemical protoncoupled electron transfer: Beyond the golden rule
View Description Hide DescriptionElectrochemical protoncoupled electron transferrate constant expressions that interpolate between the golden rule and solventcontrolled limits are derived. These expressions include the effects of solvent dynamics and thus are applicable for a wide range of vibronic couplings and solventrelaxation times. The golden rule limit is defined in terms of weak vibronic coupling and fast solvent relaxation, and the solventcontrolled limit is defined in terms of strong vibronic coupling and slow solvent relaxation. In the golden rule limit, the rate constant is proportional to the square of the vibronic coupling and is independent of the solventrelaxation time. In the solventcontrolled limit, the rate constant is independent of the vibronic coupling and increases as the solventrelaxation time decreases. The interconversion between the solventcontrolled and golden rule limits can be induced by altering the proton donoracceptor mode frequency and the overlap between the reactant and product proton vibrational wave functions, as well as the electronic coupling, the solventrelaxation time, and the overpotential. The kinetic isotope effect behaves differently in the solventcontrolled and golden rule limits and thus provides a unique probe for characterizing electrochemical protoncoupled electron transfer processes. The analogous rate constant expressions for electrochemicalelectron transfer and homogeneous protoncoupled electron transfer are also presented. The impact of electrode overpotential, solventrelaxation time, and proton donoracceptor mode frequency on the rate constants are analyzed for model systems.

Dynamics of chemically powered nanodimer motors subject to an external force
View Description Hide DescriptionThe chemically powered selfpropelled directed motions of nanodimer motors confined in a rectangular channel and subject to an applied external conservative force are investigated using hybrid molecular dynamics/multiparticle collision dynamics. The influence of factors, such as dimer sizes, chemical reaction type, and the nature of the interaction potentials between dimer monomers and solvent molecules, on the propulsion force and friction constant are examined. The stall force, for which the nanodimer has zero net velocity, and the thermodynamic efficiency of the motor are calculated. Both irreversible and reversible chemical reactions are considered. The simulation results are compared to theoretical predictions which are able to capture the major features of the selfpropelled motion.

Numerically exact quantum dynamics for indistinguishable particles: The multilayer multiconfiguration timedependent Hartree theory in second quantization representation
View Description Hide DescriptionA new theory is proposed to accurately simulate quantum dynamics in systems of identical particles. It is based on the second quantization formalism of manybody quantum theory, in which the Fock space is represented by occupationnumber states. Within this representation the overall Fock space can be formally decomposed into smaller subspaces, and the wave function can be expressed as a multilayer multiconfiguration Hartree expansion involving subvectors in these subspaces. The theory unifies the multilayer multiconfiguration timedependent Hartree theory for both distinguishable and indistinguishable particles. Specific formulations are given for systems of identical fermions, bosons, and combinations thereof. Practical implementations are discussed, especially for the case of fermions, to include the operator algebra that enforces the symmetry of identical particles. The theory is illustrated by a numerical example on vibrationally coupled electron transport.

Viscoelastic properties of crystals
View Description Hide DescriptionWe examine the question of whether fluids and crystals are differentiated on the basis of their zero frequency shear moduli or their limiting zero frequency shear viscosity. We show that while fluids, in contrast with crystals, do have a zero value for their shear modulus, in contradiction to a widespread presumption, a crystal does not have an infinite or exceedingly large value for its limiting zero frequency shear viscosity. In fact, while the limiting shear viscosity of a crystal is much larger than that of the liquid from which it is formed, its viscosity is much less than that of the corresponding glass that may form assuming the liquid is a good enough glass former.

Quantitative prediction of gasphase nuclear magnetic shielding constants
View Description Hide DescriptionBenchmark calculations of NMRchemical shifts for a series of 19 molecules with 22 chemical shifts are presented. This includes calculations at the HFSCF, DFT (BP86 and B3LYP), MP2, CCSD(T), and for a special case full CCSDT level of theory using basis sets of quadruple zeta quality and better. The effects of the quality of the geometry, electron correlation, basis set, and the inclusion of zeropoint vibrational and temperature corrections are discussed in detail and the results are compared to gasphase experimental values. Mean and standard deviations are 6 and 24 ppm for HFSCF, −20 and 14 ppm for BP86, −20 and 13 ppm for B3LYP, and 26 and 12 ppm for MP2. Results at the CCSD(T)/ level of theory using geometries optimized at the CCSD(T)/ccpVTZ level of theory exhibit a mean deviation of 16 ppm and a standard deviation of 6 ppm. A mean deviation of 6 ppm and a standard deviation of 4 ppm are obtained if these values are corrected for zeropoint vibrational and temperature effects.

Classical Wigner method with an effective quantum force: Application to reaction rates
View Description Hide DescriptionWe construct an effective “quantum force” to be used in the classical molecular dynamics part of the classical Wigner method when determining correlation functions. The quantum force is obtained by estimating the most important short time separation of the Feynman paths that enter into the expression for the correlation function. The evaluation of the force is then as easy as classical potential energy evaluations. The ideas are tested on three reaction rate problems. The resulting transmission coefficients are in much better agreement with accurate results than transmission coefficients from the ordinary classical Wigner method.

Onedimensional slow invariant manifolds for spatially homogenous reactive systems
View Description Hide DescriptionA reactive system’s slow dynamic behavior is approximated well by evolution on manifolds of dimension lower than that of the full composition space. This work addresses the construction of onedimensional slow invariant manifolds for dynamical systems arising from modeling unsteady spatially homogeneous closed reactive systems. Additionally, the relation between the systems’ slow dynamics, described by the constructed manifolds, and thermodynamics is clarified. It is shown that other than identifying the equilibrium state, traditional equilibrium thermodynamic potentials provide no guidance in constructing the systems’ actual slow invariant manifolds. The construction technique is based on analyzing the composition space of the reactive system. The system’s finite and infinite equilibria are calculated using a homotopy continuation method. The slow invariant manifolds are constructed by calculating attractive heteroclinic orbits which connect appropriate equilibria to the unique stable physical equilibrium point. Application of the method to several realistic reactive systems, including a detailed hydrogenair kinetics model, reveals that constructing the actual slow invariant manifolds can be computationally efficient and algorithmically easy.