High Accuracy Ab Initio Potential Energy Curves and Dipole Moment Functions for the X1Σ+ and a3Π Spin States of the CF+ Diatomic Molecule.

Potential energy curves and dipole moment functions constructed using high-accuracy ab initio methods allow for an in-depth examination of the electronic structure of diatomic molecules. Ab initio computations serve as a valuable complement to experimental data, offering insights into the nature of short-lived molecules such as those encountered within the interstellar medium (ISM). While laboratory experiments provide critical groundwork, the ISM's conditions often permit longer lifetimes for lower stability molecules, enabling unique observations. The CF+ diatomic molecule is one such molecule that has been observed spectroscopically in the ISM. Previous experimental and theoretical work have examined different spectroscopic aspects of the CF+ molecule, but the development of newer, more complete potential energy curves and dipole moment functions allows for even greater insight. We constructed both potential energy curves and dipole moment functions for the ground X1Σ+ and first excited a3Π states of CF+ for both the 12C and 13C isotopologues. The potential energy curves were constructed using coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set limit with corrections from full triple, quadruple, quintuple, and hextuple excitations within a finite-basis coupled cluster wave function as well as corrections from full configuration interaction and relativistic effects. Rovibrational wave functions were calculated using a vibrational Hamiltonian matrix, which moves beyond the harmonic oscillator approximation. The equilibrium bond length, vibrational constant, and rotational constant were reproduced to within 0.00013 Å, 0.28 cm-1, and 0.00045 cm-1, respectively, of experimental values. Experimental transition energies from rovibrational spectra were reproduced with an error of no larger than 0.63 cm-1. The triplet excited state (a3Π) was found to have a longer equilibrium bond length at 1.21069 Å, a vibrational constant of 1611.29 cm-1, and a rotational constant of 1.56376 cm-1. Rovibrational line lists for the 12C and 13C isotopologues for both the X1Σ+ and the excited a3Π states were generated.

High accuracy ab initio potential energy surface for the H2O-H van der Waals dimer.

A representation of the three-dimensional potential energy surface (PES) of the H2O-H van der Waals dimer is presented. The H2O molecule is treated as a rigid body held at its experimentally determined equilibrium geometry, with the OH bond length set to 1.809 650 34 a0 and the HOH bond angle set to 1.824 044 93 radians. Ab initio calculations are carried out at the coupled-cluster single, double, and perturbative triple level, with scalar relativistic effects included using the second-order Douglas-Kroll-Hess approximation. The ab initio calculations employ the aug-cc-pVnZ-DK series of basis sets (n = D, T, Q), which are recontracted versions of the aug-cc-pVnZ basis sets that are appropriate for relativistic calculations. The counterpoise method is used to reduce the basis set superposition error; in addition, results obtained using the aug-cc-pVTZ-DK and aug-cc-pVQZ-DK basis sets were extrapolated to the complete basis set (CBS) limit. The PES is based on calculations carried out at 1054 symmetry-unique H2O-H geometries for which the distance R between the H-atom and the H2O center of mass ranges from R = 2.5-9.0 Å. The reproduction of the PES along the orientational degrees of freedom was performed using Lebedev quadrature and an expansion in spherical harmonics. The mean absolute error of the reproduced PES is <0.02 cm-1 for R ≥ 3.0 Å and <0.21 cm-1 for R between 2.5 and 3.0 Å. The global minimum for the CBS PES is a coplanar H2O-H geometry, with R = 3.41 Å, in which the angle formed between the H2O C2 symmetry axis and the H-atom is 122.25°; the CBS binding energy for this geometry is 61.297 cm-1. In addition, by utilizing the symmetry of the H2O molecule, the spherical harmonic expansion was simplified with no loss in accuracy and a speedup of ∼1.8 was achieved. The reproduced PES can be used in future molecular dynamics simulations.

Selecting Quantum-Chemical Methods for Lanthanide-Containing Molecules: A Balance between Accuracy and Efficiency.

An analysis of how different density functionals, basis sets, and relativistic approximations affect the computed properties of lanthanide-containing molecules allows one to determine which method provides the highest accuracy. Historically, many different density functional methods have been employed to perform calculations on lanthanide complexes and so herein is a detailed analysis of how different methodological combinations change the computed properties of three different families of lanthanide-bearing species: lanthanide diatomic molecules (fluorides and oxides) and their dissociation energies; larger, molecular complexes and their geometries; and lanthanide bis(2-ethylhexyl)phosphate structures and their separation free energies among the lanthanide series. The B3LYP/Sapporo/Douglas-Kroll-Hess (DKH) method was shown to most accurately reproduce dissociation energies calculated at the CCSDT(Q) level of theory with a mean absolute deviation of 1.3 kcal/mol. For the calculations of larger, molecular complexes, the TPSSh/Sapporo/DKH method led to the smallest deviation from experimentally refined crystal structures. Finally, this same method led to calculated separation factors for lanthanide bis(2-ethylhexyl)phosphate structures that matched very closely with experimental values.

Three-body interactions and the elastic constants of hcp solid 4He.

The effect of three-body interactions on the elastic properties of hexagonal close packed solid 4He is investigated using variational path integral (VPI) Monte Carlo simulations. The solid's nonzero elastic constants are calculated, at T = 0 K and for a range of molar volumes from 7.88 cm3/mol to 20.78 cm3/mol, from the bulk modulus and the three pure shear constants C0, C66, and C44. Three-body interactions are accounted for using our recently reported perturbative treatment based on the nonadditive three-body potential of Cencek et al. Previous studies have attempted to account for the effect of three-body interactions on the elastic properties of solid 4He; however, these calculations have treated zero point motions using either the Einstein or Debye approximations, which are insufficient in the molar volume range where solid 4He is characterized as a quantum solid. Our VPI calculations allow for a more accurate treatment of the zero point motions which include atomic correlation. From these calculations, we find that agreement with the experimental bulk modulus is significantly improved when three-body interactions are considered. In addition, three-body interactions result in non-negligible differences in the calculated pure shear constants and nonzero elastic constants, particularly at higher densities, where differences of up to 26.5% are observed when three-body interactions are included. We compare to the available experimental data and find that our results are generally in as good or better agreement with experiment as previous theoretical investigations.

Highly Dynamic Anion-Quadrupole Networks in Proteins.

The dynamics of anion-quadrupole (or anion-π) interactions formed between negatively charged (Asp/Glu) and aromatic (Phe) side chains are for the first time computationally characterized in RmlC (Protein Data Bank entry 1EP0 ), a homodimeric epimerase. Empirical force field-based molecular dynamics simulations predict anion-quadrupole pairs and triplets (anion-anion-π and anion-π-π) are formed by the protein during the simulated trajectory, which suggests that the anion-quadrupole interactions may provide a significant contribution to the overall stability of the protein, with an average of -1.6 kcal/mol per pair. Some anion-π interactions are predicted to form during the trajectory, extending the number of anion-quadrupole interactions beyond those predicted from crystal structure analysis. At the same time, some anion-π pairs observed in the crystal structure exhibit marginal stability. Overall, most anion-π interactions alternate between an "on" state, with significantly stabilizing energies, and an "off" state, with marginal or null stabilizing energies. The way proteins possibly compensate for transient loss of anion-quadrupole interactions is characterized in the RmlC aspartate 84-phenylalanine 112 anion-quadrupole pair observed in the crystal structure. A double-mutant cycle analysis of the thermal stability suggests a possible loss of anion-π interactions compensated by variations of hydration of the residues and formation of compensating electrostatic interactions. These results suggest that near-planar anion-quadrupole pairs can exist, sometimes transiently, which may play a role in maintaining the structural stability and function of the protein, in an otherwise very dynamic interplay of a nonbonded interaction network as well as solvent effects.

Search for anisotropy in the Debye-Waller factor of HCP solid (4)He.

The properties of hexagonal close packed (hcp) solid (4)He are dominated by large atomic zero point motions. An accurate description of these motions is therefore necessary in order to accurately calculate the properties of the system, such as the Debye-Waller (DW) factors. A recent neutron scattering experiment reported significant anisotropy in the in-plane and out-of-plane DW factors for hcp solid (4)He at low temperatures, where thermal effects are negligible and only zero-point motions are expected to contribute. By contrast, no such anisotropy was observed either in earlier experiments or in path integral Monte Carlo (PIMC) simulations of solid hcp (4)He. However, the earlier experiments and the PIMC simulations were both carried out at higher temperatures where thermal effects could be substantial. We seek to understand the cause of this discrepancy through variational quantum Monte Carlo simulations utilizing an accurate pair potential and a modified trial wavefunction which allows for anisotropy. Near the melting density, we find no anisotropy in an ideal hcp (4)He crystal. A theoretical equation of state is derived from the calculated energies of the ideal crystal over a range of molar volumes from 7.88 to 21.3 cm(3), and is found to be in good qualitative agreement with experimental data.

STAAR: statistical analysis of aromatic rings.

The statistical analysis of aromatic rings program allows for an automated search for anion-π interactions between phenylalanine residues and carboxylic acid moieties of neighboring aspartic acid or glutamic acid residues in protein data bank (PDB) structures. The program is written in C++ and is available both as a standalone code and through a web implementation that allows users to upload and analyze biomolecular structures in PDB format. The program outputs lists of Phe/Glu or Phe/Asp pairs involved in potential anion-π interactions, together with geometrical (distance and angle between the Phe's center of mass and Glu or Asp's center of charge) and energetic (quantum mechanical Kitaura-Morokuma interaction energy between the residues) descriptions of each anion-π interaction. Application of the program on the latest content of the PDB shows that anion-π interactions are present in thousands of protein structures and can possess strong energies, as low as -8.72 kcal/mol.

Infrared-active spin-orbit transitions of halogen atom dopants in solid parahydrogen: the role of trapping site geometry.

We present theoretical calculations of the (2)P(1/2) ← (2)P(3/2) spin-orbit transition of Cl dopants embedded as substitutional impurities in solid parahydrogen (pH2) matrices. In the lower-energy (2)P(3/2) spin-orbit level, the Cl atom's electron density distribution is anisotropic, and slightly distorts the geometry of the atom's trapping site. This distortion leads to a blue shift in the spin-orbit transition energy; the blue shift is enhanced when we account for the large-amplitude zero point motions of the pH2 molecules surrounding the Cl dopant. We also show that the intensity of the transition depends on the geometry of the trapping site. In the gas phase, the (2)P(1/2) ← (2)P(3/2) atomic transition is electric dipole forbidden. However, when the Cl atom resides in trapping sites that mimic the hexagonal close packed morphology of pure solid pH2, the transition becomes electric dipole allowed through interaction-induced transition dipole moments. These transition dipole moments originate in the anisotropic electron density distribution of the lower-energy (2)P(3/2) spin-orbit level.

Vibrationally averaged isotropic dispersion energy coefficients of the parahydrogen dimer.

We compare the sum-over-states and coupled cluster linear response formalisms for the determination of imaginary-frequency polarizabilities of H(2). Using both approaches, we compute isotropic dispersion energy coefficients C(n) (n = 6, 8, 10) for H(2)-H(2) molecular pairs over a wide range of H(2) bond lengths. We present vibrationally averaged dispersion energy coefficients for H(2)-H(2), H(2)-D(2), and D(2)-D(2) molecular pairs and examine the coefficients' convergence with respect to basis set.

A survey of aspartate-phenylalanine and glutamate-phenylalanine interactions in the protein data bank: searching for anion-π pairs.

Protein structures are stabilized using noncovalent interactions. In addition to the traditional noncovalent interactions, newer types of interactions are thought to be present in proteins. One such interaction, an anion-π pair, in which the positively charged edge of an aromatic ring interacts with an anion, forming a favorable anion-quadrupole interaction, has been previously proposed [Jackson, M. R., et al. (2007) J. Phys. Chem. B111, 8242-8249]. To study the role of anion-π interactions in stabilizing protein structure, we analyzed pairwise interactions between phenylalanine (Phe) and the anionic amino acids, aspartate (Asp) and glutamate (Glu). Particular emphasis was focused on identification of Phe-Asp or -Glu pairs separated by less than 7 Å in the high-resolution, nonredundant Protein Data Bank. Simplifying Phe to benzene and Asp or Glu to formate molecules facilitated in silico analysis of the pairs. Kitaura-Morokuma energy calculations were performed on roughly 19000 benzene-formate pairs and the resulting energies analyzed as a function of distance and angle. Edgewise interactions typically produced strongly stabilizing interaction energies (-2 to -7.3 kcal/mol), while interactions involving the ring face resulted in weakly stabilizing to repulsive interaction energies. The strongest, most stabilizing interactions were identified as preferentially occurring in buried residues. Anion-π pairs are found throughout protein structures, in helices as well as ß strands. Numerous pairs also had nearby cation-π interactions as well as potential π-π stacking. While more than 1000 structures did not contain an anion-π pair, the 3134 remaining structures contained approximately 2.6 anion-π pairs per protein, suggesting it is a reasonably common motif that could contribute to the overall structural stability of a protein.

Pairwise additive model for the He-MgO(100) interaction.

We develop a model, based on pairwise additive He-Mg and He-O interactions, for the potential energy of He adsorbates above a rigid MgO(100) surface. The attractive long-range He-Mg and He-O interactions are assumed to have the form C(6)/r(6), with the C(6) coefficients determined from atomic data within the context of the Slater-Kirkwood approximation. The repulsive short-range He-Mg and He-O interactions are assumed to have the form C(p)/r(p), with the exponent p and the C(p) coefficients taken as adjustable parameters. We find that for p = 9, the C(p) coefficients can be chosen so that the laterally averaged He-MgO(100) pairwise additive interaction supports low-lying selective adsorption states, some of whose energies agree very well with the states' apparent energies inferred from experimental measurements. However, for realistic values of the adjustable parameters that define our model, the lateral corrugation of the model pairwise additive He-MgO(100) potential energy surface far exceeds the corrugation that has been inferred both from experimental measurements and from density functional calculations of the short-range He-MgO(100) interaction.

A preference for edgewise interactions between aromatic rings and carboxylate anions: the biological relevance of anion-quadrupole interactions.

Noncovalent interactions are quite important in biological structure-function relationships. To study the pairwise interaction of aromatic amino acids (phenylalanine, tyrosine, tryptophan) with anionic amino acids (aspartic and glutamic acids), small molecule mimics (benzene, phenol or indole interacting with formate) were used at the MP2 level of theory. The overall energy associated with an anion-quadrupole interaction is substantial (-9.5 kcal/mol for a benzene-formate planar dimer at van der Waals contact distance), indicating the electropositive ring edge of an aromatic group can interact with an anion. Deconvolution of the long-range coplanar interaction energy into fractional contributions from charge-quadrupole interactions, higher-order electrostatic interactions, and polarization terms was achieved. The charge-quadrupole term contributes between 30 to 45% of the total MP2 benzene-formate interaction; most of the rest of the interaction arises from polarization contributions. Additional studies of the Protein Data Bank (PDB Select) show that nearly planar aromatic-anionic amino acid pairs occur more often than expected from a random angular distribution, while axial aromatic-anionic pairs occur less often than expected; this demonstrates the biological relevance of the anion-quadrupole interaction. While water may mitigate the strength of these interactions, they may be numerous in a typical protein structure, so their cumulative effect could be substantial.

Population size bias in descendant-weighted diffusion quantum Monte Carlo simulations.

We consider the influence of population size on the accuracy of diffusion quantum Monte Carlo simulations that employ descendant weighting or forward walking techniques to compute expectation values of observables that do not commute with the Hamiltonian. We show that for a simple model system, the d-dimensional isotropic harmonic oscillator, the population size must increase rapidly with d in order to ensure that the simulations produce accurate results. When the population size is too small, expectation values computed using descendant-weighted diffusion quantum Monte Carlo simulations exhibit significant systematic biases.

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates.

Estimation of the Ground State Energy of an Atomic Solid by Employing Quantum Trajectory Dynamics with Friction.

Evolution with energy dissipation can be used to obtain the ground state of a quantum-mechanical system. This dissipation is introduced in the quantum trajectory framework by adding an empirical friction force to the equations of motion for the trajectories, which, as an ensemble, represent a wave function. The quantum effects in dynamics are incorporated via the quantum force derived from the properties of this ensemble. For scalability to large systems, the quantum force is computed approximately yet with sufficient accuracy to describe the strongly anharmonic ground state of solid (4)He represented by a simulation cell of 180 atoms.

Accurate Computation of Electric Field Enhancement Factors for Metallic Nanoparticles Using the Discrete Dipole Approximation.

We model the response of nanoscale Ag prolate spheroids to an external uniform static electric field using simulations based on the discrete dipole approximation, in which the spheroid is represented as a collection of polarizable subunits. We compare the results of simulations that employ subunit polarizabilities derived from the Clausius-Mossotti relation with those of simulations that employ polarizabilities that include a local environmental correction for subunits near the spheroid's surface [Rahmani et al. Opt Lett 27: 2118 (2002)]. The simulations that employ corrected polarizabilities give predictions in very good agreement with exact results obtained by solving Laplace's equation. In contrast, simulations that employ uncorrected Clausius-Mossotti polarizabilities substantially underestimate the extent of the electric field "hot spot" near the spheroid's sharp tip, and give predictions for the field enhancement factor near the tip that are 30 to 50% too small.

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy.

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.

Quasiclassical trajectory study of the vibrational quenching of hydroxyl radicals through collision with O atoms.

The collisional removal of vibrationally excited OH radicals by O atoms is studied by the quasiclassical trajectory method. To evaluate the effect of different topological features on the scattering processes two different global potential energy surfaces, DMBE IV and TU, are used. Results for reactive, exchange, and inelastic scattering probabilities are reported for central collisions (with zero total angular momentum) with a fixed relative translational energy for vibrational levels of OH ranging from nu=1 to v=8. Vibrational state distributions of product molecules are also compared on the two potential energy surfaces. Both surfaces predict higher probabilities for reaction than for exchange or inelastic scattering. The vibrational state distributions of the product diatomic molecules are different on the two surfaces. In particular, the two surfaces give substantially different probabilities for multiquantum OH vibrational relaxation transitions OH(v)+O-->OH(v')+O.

Interaction-induced dipole moment of the Ar-H2 dimer: dependence on the H2 bond length.

We present ab initio calculations of the interaction-induced dipole moment of the Ar-H2 van der Waals dimer. The primary focus of our calculations is on the H2 bond length dependence of the dipole moment, which determines the intensities of both the collision-induced H2 upsilon = 1 <-- 0 fundamental band in gaseous Ar-H2 mixtures and the dopant-induced H2 upsilon = 1 <-- 0 absorption feature in Ar-doped solid H2 matrices. Our calculations employ large atom-centered basis sets, diffuse bond functions positioned between the two monomers, and a coupled cluster treatment of valence electron correlation; core-valence correlation effects appear to make negligible contributions to the interaction-induced dipole moment for the Ar-H2 configurations considered here.

Vibrational dependence of the H2-H2 C6 dispersion coefficients.

We use the sum-over-states formalism to compute the imaginary-frequency dipole polarizabilities for H2, as a function of the H-H bond length, at the full configuration interaction level of theory using atom-centered d-aug-cc-pVQZ basis sets. From these polarizabilities, we obtain isotropic and anisotropic C6 dispersion coefficients for a pair of H2 molecules as functions of the two molecules' bond lengths.