Local response dispersion method. II. Generalized multicenter interactions

Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C(6) coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jure?ka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three- or four-center interactions is shown to be optimal in the cost-performance balance.     

Origin invariant approaches to the calculation of two-photon circular dichroism

The origin dependence of the expression of two-photon circular dichroism in the length formulation employed by the authors in a recent computational study [B. Jansik et al., Chem. Phys. Lett. 414, 461 (2005)] is discussed in detail, and some inherently origin invariant alternative formulations are introduced. Extensive computational tests on a small reference chiral system, namely, a chiral form of H(2)O(2), are performed at the density functional theory (DFT)/B3LYP level of theory with large diffuse correlation consistent basis sets. The results indicate that the velocity formulation originally proposed by Tinoco, Jr. [J. Chem. Phys. 62, 1006 (1975)] provides the most convenient approach for an origin invariant calculation of two-photon circular dichroism.     

Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique

Summary A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.Also affiliated with the Department of Chemistry, and Guelph-Waterloo Center for Graduate Work in Chemistry, Waterloo Campus, University of Waterloo, Waterloo, Ontario, Canada. Killam Research Fellow 1987–89     

The role of the excited electronic states in the C+ + H2O reaction

The electronic excited states of the [COH2]+ system have been studied in order to establish their role in the dynamics of the C+ + H2O-->[COH]+ +H reaction, which is a prototypical ion-molecule reaction. The most relevant minima and saddle points of the lowest excited state have been determined and energy profiles for the lowest excited doublet and quartet electronic states have been computed along the fragmentation and isomerization coordinates. Also, nonadiabatic coupling strengths between the ground and the first excited state have been computed where they can be large. Our analysis suggests that the first excited state could play an important role in the generation of the formyl isomer, which has been detected in crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], but could not be explained in quasiclassical trajectory computations [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003); J. R. Flores, J. Chem. Phys. 125, 164309 (2006)].     

Symmetry-adapted formulation of the combined G-particle-hole hypervirial equation and Hermitian operator method

High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole hypervirial (GHV) equation method (Alcoba et al. in Int J Quantum Chem 109:3178, 2009) and the Hermitian operator (HO) one (Bouten et al. in Nucl Phys A 202:127, 1973). This work reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, which leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries. The new formulation is used to study the low-lying excited states torsional potentials in the ethylene molecule.     

Two-electron integrations in the quantum theory of atoms in molecules with correlated wave functions

A recent method proposed to compute two-electron integrals over arbitrary regions of space [Martin Pendas, A. et al., J Chem Phys 2004, 120, 4581] is extended to deal with correlated wave functions. To that end, we use a monadic factorization of the second-order reduced density matrix originally proposed by E. R. Davidson [Chem Phys Lett 1995, 246, 209] that achieves a full separation of the interelectronic components into one-electron terms. The final computational effort is equivalent to that found in the integration of a one determinant wave function with as many orbitals as occupied functions in the correlated expansion. Similar strategies to extract the exchange and self-interaction contributions from the two-electron repulsion are also discussed, and several numerical results obtained in a few test systems are summarized.     

Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions

We explore different variants of the random phase approximation to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated density-functional theory, i.e., by combining the long-range random phase approximations with short-range density-functional approximations. We perform tests on the rare-gas dimers He(2), Ne(2), and Ar(2), and on the weakly interacting molecular complexes of the S22 set of Jurec?ka et al. [P. Jurec?ka, J. S?poner, J. C?erny?, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones originally proposed by Szabo and Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)]. With range separation, they reach mean absolute errors on the equilibrium interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to mean absolute percentage errors of about 4%, with the aug-cc-pVDZ basis set.     

Alchemical prediction of hydration free energies for SAMPL

Hydration free energy calculations have become important tests of force fields. Alchemical free energy calculations based on molecular dynamics simulations provide a rigorous way to calculate these free energies for a particular force field, given sufficient sampling. Here, we report results of alchemical hydration free energy calculations for the set of small molecules comprising the 2011 Statistical Assessment of Modeling of Proteins and Ligands challenge. Our calculations are largely based on the Generalized Amber Force Field with several different charge models, and we achieved RMS errors in the 1.4-2.2 kcal/mol range depending on charge model, marginally higher than what we typically observed in previous studies (Mobley et al. in J Phys Chem B 111(9):2242-2254, 2007, J Chem Theory Comput 5(2):350-358, 2009, J Phys Chem B 115:1329-1332, 2011; Nicholls et al. in J Med Chem 51:769-779, 2008; Klimovich and Mobley in J Comput Aided Mol Design 24(4):307-316, 2010). The test set consists of ethane, biphenyl, and a dibenzyl dioxin, as well as a series of chlorinated derivatives of each. We found that, for this set, using high-quality partial charges from MP2/cc-PVTZ SCRF RESP fits provided marginally improved agreement with experiment over using AM1-BCC partial charges as we have more typically done, in keeping with our recent findings (Mobley et al. in J Phys Chem B 115:1329-1332, 2011). Switching to OPLS Lennard-Jones parameters with AM1-BCC charges also improves agreement with experiment. We also find a number of chemical trends within each molecular series which we can explain, but there are also some surprises, including some that are captured by the calculations and some that are not.     

Local hardness equalization: exploiting the ambiguity

In the density-functional theory of chemical reactivity, the local hardness is known to be an ambiguous concept. The mathematical structure associated with this problematic situation is elaborated and three common definitions for the local hardness are critically examined: the frontier local hardness [S. K. Ghosh, Chem. Phys. Lett. 172, 77 (1990)], the total local hardness [S. K. Ghosh and M. Berkowitz, J. Chem. Phys. 83, 2976 (1985)], and the unconstrained local hardness [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000)]. The frontier local hardness has particularly nice properties: (a) it has smaller norm than most, if not all, other choices of the local hardness and (b) it is "unbiased" in an information-theoretic sense. For the ground electronic state of a molecular system, the frontier local hardness is equal to the global hardness. For an electronic system in its ground state, both the chemical potential and the frontier local hardness are equalized. The frontier local hardness equalization principle provides a computational approach for designing reagents with desirable chemical reactivity profiles.     

Hybrid one-electron/many-electron methods for ionized states of molecular clusters

To describe singly-ionized states of molecular clusters we devised an effective Hamiltonian approach that combines (1) accurate monomer ionization potentials from many-electron wave functions with (2) polarization shifts and (3) effective monomer couplings obtained from a simple one-electron approach (the superposition-of-fragment-states (SFS) method [Valeev et al., J. Am. Chem. Soc., 2006, 128, 9882]). The accuracy of the intermolecular coupling parameters evaluated with SFS Hartree-Fock (HF) and Density-Functional-Theory (DFT) variants was evaluated for several weakly-bound dimers and compared against the state-of-the-art equation-of-motion ionization-potential coupled-cluster singles and doubles (EOM-IP-CCSD) data of Krylov and co-workers. The SFS-HF method produces coupling integrals accurate to a few percent, whereas SFS-DFT predictions are substantially worse. A hybrid approach combining SFS-HF couplings and shifts with EOM-IP-CCSD ionization potentials of monomers (denoted as SFS-EOM-IP-CCSD) was applied to ionized states of two conformers of a benzene dimer and ten representative DNA base pairs. The 16 considered SFS-EOM-IP-CCSD ionization potentials of the benzene dimer differed from the reference EOM-IP-CCSD IPs of Krylov and co-workers [Pieniazek et al., J. Chem. Phys. 2007, 127, 044317; Bravaya et al., Phys. Chem. Chem. Phys. 2010, 12, 2261] by less than 0.1 eV on average, and at most by 0.2 eV. For the DNA base pairs the mean absolute (median) deviation of the SFS-EOM-IP-CCSD IPs was 0.27 (0.23) eV; several deviations for non-Koopmans states were as large as 0.9 eV. The SFS-EOM-IP-CCSD method can be readily applied to large molecular clusters with computational effort scaling cubically with the size of the cluster.     

New evaluation of reconstructed spatial distribution function from radial distribution functions

Although three dimensional (3D) solvation structure is much more informative than one dimensional structure, its evaluation is difficult experimentally and theoretically. In our previous Communication [Yokogawa et al., J. Chem. Phys. 123, 211102 (2005)], we proposed a new method to present reconstructed spatial distribution function (RC-SDF) from a set of radial distribution functions (RDFs). In this article, we successfully extended the method more accurately with new basis sets. This new method was applied to two liquid solvation structures, methanol and dimethyl sulfoxide, as examples. Their RC-SDFs evaluated here clearly show that the former solvation structure is well defined while the latter one is broad, which agrees well with the SDFs calculated directly from molecular dynamics simulations. These results indicate that the method can reproduce well these 3D solvation structures in reasonable computational cost.     

Quantum Monte Carlo calculations of the dissociation energy of the water dimer

We report diffusion quantum Monte Carlo (DMC) calculations of the equilibrium dissociation energy D(e) of the water dimer. The dissociation energy measured experimentally, D(0), can be estimated from D(e) by adding a correction for vibrational effects. Using the measured dissociation energy and the modern value of the vibrational energy Mas et al., [J. Chem. Phys. 113, 6687 (2000)] leads to D(e)=5.00+/-0.7 kcal mol(-1), although the result Curtiss et al., [J. Chem. Phys. 71, 2703 (1979)] D(e)=5.44+/-0.7 kcal mol(-1), which uses an earlier estimate of the vibrational energy, has been widely quoted. High-level coupled cluster calculations Klopper et al., [Phys. Chem. Chem. Phys. 2, 2227 (2000)] have yielded D(e)=5.02+/-0.05 kcal mol(-1). In an attempt to shed new light on this old problem, we have performed all-electron DMC calculations on the water monomer and dimer using Slater-Jastrow wave functions with both Hartree-Fock approximation (HF) and B3LYP density functional theory single-particle orbitals. We obtain equilibrium dissociation energies for the dimer of 5.02+/-0.18 kcal mol(-1) (HF orbitals) and 5.21+/-0.18 kcal mol(-1) (B3LYP orbitals), in good agreement with the coupled cluster results.     

Coupling microscopic and mesoscopic scales to simulate chemical equilibrium between a nanometric carbon cluster and detonation products fluid

This paper presents a new method to obtain chemical equilibrium properties of detonation products mixtures including a solid carbon phase. In this work, the solid phase is modelled through a mesoparticle immersed in the fluid, such that the heterogeneous character of the mixture is explicitly taken into account. Inner properties of the clusters are taken from an equation of state obtained in a previous work, and interaction potential between the nanocluster and the fluid particles is derived from all-atoms simulations using the LCBOPII potential (Long range Carbon Bond Order Potential II). It appears that differences in chemical equilibrium results obtained with this method and the "composite ensemble method" (A. Hervouet et al., J. Phys. Chem. B, 2008, 112.), where fluid and solid phases are considered as non-interacting, are not significant, underlining the fact that considering the inhomogeneity of such system is crucial.     

Symmetry-adapted formulation of the G-particle-hole hypervirial equation method

Highly accurate 2-body reduced density matrices of atoms and molecules have been directly determined without calculation of their wave functions with the use of the G-particle-hole hypervirial (GHV) equation method (Alcoba et?al. in Int. J. Quantum Chem. 109:3178, 2009). Very recently, the computational efficiency of the GHV method has been significantly enhanced through the use of sum factorization and matrix-matrix multiplication (Alcoba et?al. in Int. J. Quantum Chem 111:937, 2011). In this paper, a detailed analysis of the matrix contractions involved in GHV calculations is carried out. The analysis leads to a convenient strategy for exploiting point group symmetry, by which the computational efficiency of the GHV method is further improved. Implementation of the symmetry-adapted formulation of the method is reported. Computer timings and hardware requirements are illustrated for several representative chemical systems. Finally, the method is applied to the well-known challenging calculation of the torsional potential in ethylene.     

A consistent integral equation theory for hard spheres

The standard integral equation approach is used to extract the bridge function and other correlation functions of hard spheres fluid. To achieve this, we first use a recent consistent closure relation proposed by Bomont et al. [J. Chem. Phys. 119, 2188 (2003)] that has already proven to be accurate to describe the Lennard-Jones fluid properties. Second, we take advantage of the coherent scheme derived by Bomont [J. Chem. Phys. 119, 11484 (2003)] to calculate the excess chemical potential, the entropy and some relative transport properties. Very good agreement is obtained for structural quantities and thermodynamic properties as compared to exact data at densities ranging from 0.1 to 0.9.     

Rigid-body dynamics in the isothermal-isobaric ensemble: a test on the accuracy and computational efficiency

We have developed a time-reversible rigid-body (rRB) molecular dynamics algorithm in the isothermal-isobaric (NPT) ensemble. The algorithm is an extension of rigid-body dynamics [Matubayasi and Nakahara, J Chem Phys 1999, 110, 3291] to the NPT ensemble on the basis of non-Hamiltonian statistical mechanics [Martyna, G. J. et al., J Chem Phys 1994, 101, 4177]. A series of MD simulations of water as well as fully hydrated lipid bilayer systems have been undertaken to investigate the accuracy and efficiency of the algorithm. The rRB algorithm was shown to be superior to the state-of-the-art constraint-dynamics algorithm SHAKE/RATTLE/ROLL, with respect to computational efficiency. However, it was revealed that both algorithms produced accurate trajectories of molecules in the NPT as well as NVT ensembles, as long as a reasonably short time step was used. A couple of multiple time-step (MTS) integration schemes were also examined. The advantage of the rRB algorithm for computational efficiency increased when the MD simulation was carried out using MTS on parallel processing computer systems; total computer time for MTS-MD of a lipid bilayer using 64 processors was reduced by about 40% using rRB instead of SHAKE/RATTLE/ROLL.     

An augmented effective core potential basis set for the calculation of molecular polarizabilities

Calculations of molecular polarizabilities require basis sets capable of accurately describing the responses of the electrons to an external perturbation. Unfortunately, basis sets that yield suitable quantitative results have traditionally been all-electron sets with large numbers of primitives, making their use computationally intractable even for moderately sized systems. We present a systematic augmentation of the effective core potential basis set of Stevens et al. [J Chem Phys 81, 12 (1984), Can J Chem 70, 612 (1992)] for 39 main group elements based on the procedure used to construct diffuse and polarization functions in the well-known Sadlej basis sets [Collec Czech Chem Comm 53, 1995 (1988)]. Representative calculations have been performed and we have shown that results to within 1% of all-electron calculations using the Sadlej basis set can be obtained for <1-35% of the computational cost using this new basis set.     

Adsorption‐induced changes of intramolecular optical transitions: PTCDA/NaCl and PTCDA/KCl

Structural and optical properties of isolated perylene‐3,4,9,10‐tetracarboxylic acid dianhydride molecules adsorbed on (100) oriented NaCl and KCl surfaces were studied theoretically to analyze the recently observed red‐shift of the optical excitation spectrum after adsorption (Müller et al., Phys. Rev. B, 2011, 83, 241203; Paulheim et al. Phys. Chem. Chem. Phys., 2013, 15, 4906). The ground‐state structures were obtained by periodic dispersion‐corrected density functional theory (DFT) calculations. For the excited‐state calculations, nonperiodic time‐dependent DFT methods were applied for a cluster model embedded in point charges. The range‐separated hybrid functional CAM‐B3LYP was used. Correlation‐consistent basis sets were used and the calculated excitation energies were extrapolated to the complete basis set limit. The shift of the first optical excitation energy was analyzed in terms of electronic and geometric contributions. It was found that both the distortion of the molecule due to the interaction with the surface and the electrostatic potential of the surface play an important role. © 2015 Wiley Periodicals, Inc.