Molecular photoionization cross sections in electron propagator theory: angular distributions beyond the dipole approximation

Corrections to dipole approximation results for angular distributions in photoionization of first-row hydrides have determined by using Dyson orbitals calculated with ab initio electron propagator theory and by considering the full multipole expansion for the incident photon representation. The relative importance of first-order corrections which consist of electric quadrupole and magnetic dipole terms and of higher-order terms has been estimated as a function of photon energy. Multipole corrections to the dipole approximation depend on photon energy and on the characteristics of the Dyson orbitals.     

Accuracy of distributed multipoles and polarizabilities: comparison between the LoProp and MpProp models

Localized multipole moments up to the fifth moment as well as localized dipole polarizabilities are calculated with the MpProp and the newly developed LoProp methods for a total of 20 molecules, predominantly derived from amino acids. A comparison of electrostatic potentials calculated from the multipole expansion obtained by the two methods with ab initio results shows that both methods reproduce the electrostatic interaction with an elementary charge with a mean absolute error of approximately 1.5 kJ/mol at contact distance and less than 0.1 kJ/mol at distances 2 A further out when terms up to the octupole moments are included. The polarizabilities are tested with homogenous electric fields and are found to have similar accuracy. The MpProp method gives better multipole moments unless diffuse basis sets are used, whereas LoProp gives better polarizabilities.     

Limitations of the molecular multipole expansion treatment of electrostatic interactions for C-H...O and O-H...O hydrogen bonds and application of a general charge density approach

A molecular multipole expansion treatment (up to hexadecapole) is examined for its accuracy in describing hydrogen-bond electrostatic interactions, with particular reference to explaining the differences between blue-shifted C-H...O and red-shifted O-H...O bonds. In interactions of H2O and CH4 with point charges at hydrogen-bonding distances, we find that the molecular multipole treatment not only fails to reproduce ab initio energies but also forces on OH or CH bonds, and therefore cannot properly account for the electrostatic component of the interaction. A treatment based on a molecule's permanent charge density and its derivatives and the charge density and its derivatives induced by an external multipole distribution is in full accord with ab initio results, as shown by application to models of the H2O-H2O and CH4-FH systems. Such a charge density approach provides a fundamental basis for understanding the importance of interaction forces in initiating structural change and thereby altering molecular properties.     

Benchmarking the multipole shielding polarizability/reaction field approach to solvation against QM/MM: applications to the shielding constants of N-methylacetamide

We present a benchmark study of a combined multipole shielding polarizability/reaction field (MSP/RF) approach to the calculation of both specific and bulk solvation effects on nuclear magnetic shielding constants of solvated molecules. The MSP/RF scheme is defined by an expansion of the shielding constants of the solvated molecule in terms of electric field and field gradient property derivatives derived from single molecule ab initio calculations. The solvent electric field and electric field gradient are calculated based on data derived from molecular dynamics simulations, thereby accounting for solute-solvent dynamical effects. The MSP/RF method is benchmarked against polarizable quantum mechanics/molecular mechanics (QM/MM) calculations. The best agreement between the MSP/RF and QM/MM approaches is found by truncating the electric field expansion in the MSP/RF approach at the linear electric field level which is due to the cancelation of errors. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the ab initio calculations of the property derivatives and find that these derivatives are affected by the basis set in a way similar to the shielding constants themselves.     

The coupling constant polarizability and hyperpolarizabilty of 1J(NH) in N-methylacetamide, and its application for the multipole spin-spin coupling constant polarizability/reaction field approach to solvation

We present a benchmark study of a combined multipole spin-spin coupling constant (SSCC) polarizability/reaction field (MJP/RF) approach to the calculation of both specific and bulk solvation effects on SSCCs of solvated molecules. The MJP/RF scheme is defined by an expansion of the SSCCs of the solvated molecule in terms of coupling constant dipole and quadrupole polarizabilities and hyperpolarizabilities derived from single molecule ab initio calculations. The solvent electric field and electric field gradient are calculated based on data derived from molecular dynamics (MD) simulations thereby accounting for solute-solvent dynamical effects. The MJP/RF method is benchmarked against polarizable QM/MM calculations for the one-bond N-H coupling constant in N-methylacetamide. The best agreement between the MJP/RF and QM/MM approaches is found by truncating the electric field expansion in the MJP/RF approach at the linear electric field level. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the ab initio calculations of the coupling constant (hyper-)polarizabilities and find that they are affected by the basis set in a way similar to the coupling constants themselves.     

A fragment multipole approach to long-range Coulomb interactions in Hartree–Fock calculations on large systems

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short- and long-range contributions, leading to a reduction of the computational effort from the original fourth-power size-dependence to one that is approximately quadratic. The short-range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long-range interactions are evaluated using a two-center multipole expansion formalism. The number of short-range contributions grows only linearly with the number of subunits, while the long-range contributions grow as N². Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one-stranded chains, three-stranded chains, and three-dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as N^K where 1 < K < 2.     

Dispersion energy in rare gas dimers from an ab initio perturbative procedure: Ne + Ne,Ar + Ar

The dispersion energy between two neon and two argon atoms is computed from an ab initio perturbative procedure not based on the multipole expansion. A comparison with the multipole expansion provides C₆ = 5.36 for Ne and 76.6 for Ar. It is seen that one d polarization function provides the main part of the C₆R^?6 contribution, the exponent of this function probably being related to the polarizability of the molecule. The multipole expansion seems acceptable up to the van der Waals minimum but quite invalid for smaller distances, and doubtful at the van der Waals minimum itself.     

Nonempirical Atom-Atom Potentials for Main Components of Intermolecular Interaction Energy

Atom-atom potentials representing separate contributions to the nonempirical interaction energy have been derived in the SCF decomposition scheme corrected for basis set superposition error by the counterpoise method. The nontransferable long-range electrostatic multipole and classical induction terms have been evaluated directly from cumulative atomic multipole expansions, whereas the short-range exchange, charge-transfer, and electrostatic penetration contributions have been represented by simplified potentials of the form (β + δR^?1) exp(?δR) fitted to the corresponding ab initio results for 336 dimer configurations formed by HF, H₂O, NH₃, CH₄, CO, and CO₂. The dominant anisotropic character of electrostatic multipole atom-atom potentials and much more isotropic nature of the potentials representing short-range terms is illustrated in the Appendix for head-on interactions in CO ‥ OC and HF ‥ FH dimers.     

Ab initio computed diabatic potential energy surfaces of OH-HCl

The two four-dimensional diabatic potential energy surfaces (DPESs) for OH-HCl are computed that correlate with the twofold degenerate (2)Pi ground state of the free OH radical. About 20 000 points on the surface are obtained by the ab initio coupled-cluster and multi-reference configuration interaction methods. Analytic forms for the diabatic potential energy surfaces are derived as expansions in complete sets of orthogonal functions depending on the three intermolecular angles. The numeric computation of the angular expansion coefficients is discussed. The distance-dependence of the angular coefficients is represented by the reproducing kernel Hilbert space method. It is checked that both diabatic potentials converge for large intermolecular separations to the values computed directly from the electrostatic multipole expansion. The final DPESs are discussed and illustrated by some physically meaningful one- and two-dimensional cuts through them.     

An analysis of the electrostatic interaction between nucleic acid bases

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.     

Application of a simple quantum chemical approach to ligand fragment scoring for<Emphasis Type="Italic"> Trypanosoma brucei</Emphasis> pteridine reductase 1 inhibition

There is a need for improved and generally applicable scoring functions for fragment-based approaches to ligand design. Here, we evaluate the performance of a computationally efficient model for inhibitory activity estimation, which is composed only of multipole electrostatic energy and dispersion energy terms that approximate long-range ab initio quantum mechanical interaction energies. We find that computed energies correlate well with inhibitory activity for a compound series with varying substituents targeting two subpockets of the binding site of Trypanosoma brucei pteridine reductase 1. For one subpocket, we find that the model is more predictive for inhibitory activity than the ab initio interaction energy calculated at the MP2 level. Furthermore, the model is found to outperform a commonly used empirical scoring method. Finally, we show that the results for the two subpockets can be combined, which suggests that this simple nonempirical scoring function could be applied in fragment–based drug design.     

An overlap expansion method for improving ab initio model potentials: anisotropic intermolecular potentials of N2, CO, and C2H2 with He*(2(3)S)

An overlap expansion method is proposed for improving ab initio model potentials. Correction terms are expanded in terms of overlap integrals between orbitals of the interacting system. The method is used to improve ab initio model potentials for N2+He*(2(3)S), CO+He*(2(3)S), and C2H2+He*(2(3)S). Physical meanings of the optimization are elucidated in terms of target orbitals. Correction terms are found to be dominated by the components of HOMO, LUMO, next-HOMO, and next-LUMO on the target molecule. The present overlap expansion method using a limited number of correction terms related to frontier orbitals provides an efficient and intuitive approach for construction of highly anisotropic intermolecular interaction potentials.     

Potential energy surface and MULTIMODE vibrational analysis of C2H3+

A full dimensional, ab initio-based semiglobal potential energy surface for C(2)H(3) (+) is reported. The ab initio electronic energies for this molecule are calculated using the spin-restricted, coupled cluster method restricted to single and double excitations with triples corrections [RCCSD(T)]. The RCCSD(T) method is used with the correlation-consistent polarized valence triple-zeta basis augmented with diffuse functions (aug-cc-pVTZ). The ab initio potential energy surface is represented by a many-body (cluster) expansion, each term of which uses functions that are fully invariant under permutations of like nuclei. The fitted potential energy surface is validated by comparing normal mode frequencies at the global minimum and secondary minimum with previous and new direct ab initio frequencies. The potential surface is used in vibrational analysis using the "single-reference" and "reaction-path" versions of the code MULTIMODE.     

The elusive atomic rationale for DNA base pair stability

A systematic analysis of the electrostatic interaction between 27 natural DNA base pairs was carried out, based on ab initio correlated wave functions and the topology of the electron density. Using high rank multipole moments we show that the atomic partitioning of the interaction energy contains many substantial contributions between distant atoms. Profiles of cumulative energy versus internuclear distance show large fluctuations and provide an electrostatic fingerprint of the partitioning of interaction energy in a complex. A quantified comparison between each pair of energy profiles, one for each base pair, makes clear that there is no correlation between the total base pair interaction energy and the shape of the profile. In other words, base pairs with similar interaction energy are not stable for the same reasons in terms of atomic partitioning. In summary, simple rules to rationalize the pattern of energetic stability of naturally occurring base pairs in terms of subsets of atoms are elusive. Our work cautions against inappropriate use of Jorgensen's secondary interaction hypothesis.     

Ab initio-based double many-body expansion potential energy surface for the first excited triplet state of the ammonia molecule

A global single-sheeted double many-body expansion potential energy surface is reported for the first excited triplet state of NH(3). It employs an approximate cluster expansion of the molecular potential that utilizes previously reported functions of the same family for the triatomic fragments. Four-body energy terms have been calibrated from extensive accurate ab initio data so as to reproduce the main features of the title system. A new switching function formalism has been reported to approximate the true multisheeted nature of NH(3)((3)A(2) (')) potential energy surface, thus allowing the correct behavior at the NH(2)((2)A(")) + H((2)S) and NH(2)((4)A(")) + H((2)S) dissociation limits. The resulting fully six-dimensional potential energy function reproduces the correct symmetry under the permutation of identical atoms, and predicts the correct behavior at all dissociation channels while providing a realistic representation at all interatomic separations. The major attributes of the NH(3) double many-body expansion potential energy surface have also been characterized, and found to be in good agreement, both with the calculated ones from the raw ab initio energies and the theoretical results available in the literature.     

The convergence of energy expansions for molecules in electrostatic fields: A linear‐response coupled‐cluster study

The radii of convergence of power series expansions describing energy of a molecule in external electrostatic field are investigated usingD’Alembert ratio test, standard and generalized Cauchy–Hadamardcriteria, and Padé approximants. The corresponding coefficients at various field and field‐gradient components, representing multipole moments and (hyper)polarizabilities and including terms of tenth or even twentieth order, are determined using an ab initio linear responsecoupled‐cluster theory. Most calculations are performed for the HF molecule described by the basis set of double zeta quality, while the role of basis set is discussed by comparing the results with estimates of the radii of convergence obtained with the basis set of [5s3p2d/3s2p] quality. Emphasis is placed on the dependence of the interval of convergence of power series expansion describing energy of a molecule in applied electrostatic field on the nuclear geometry. The results might have important implications for various numerical methods used to calculate electrostatic molecular properties as functions of the internuclear geometry, including the finite‐field andfixed‐point‐charge approaches. This revised version was published online in July 2006 with corrections to the Cover Date.     

Resolving the aluminum ordering in aluminosilicates by a combined experimental/theoretical study of 27Al electric field gradients

The discrimination between atomic species in light-element materials is a challenging question. An archetypal example is the resolution of the Al/Si ordering in aluminosilicates. Only an average long-range order can be deduced from powder X-ray or neutron diffraction, while magic-angle-spinning NMR provides an accurate picture of the short-range order. The long- and short-range orders thus obtained usually differ, hence raising the question of whether the difference between local and extended orders is intrinsic or caused by the difficulty of obtaining an accurate picture of the long-range order from diffraction techniques. In this communication we resolve this question for the monoclinic phases of BaAl2Si2O8 and SrAl2Si2O8 on the basis of 27Al NMR measurements and ab initio simulation of electric field gradient. Although the long- and short-range orders deduced from our XRD and NMR experiments differ, they become similar when the XRD atomic positions are optimized by ab initio electronic structure calculations.     

Mixed quantum—classical calculations on the water molecule in liquid phase: Influence of a polarizable environment on electronic properties

Electronic properties of a water molecule embedded in a water droplet are studied in the framework of the generalized self-consistent reaction field approach, using ab initio Hartree-Fock and configuration interaction wave functions. Electrostatic and inductive effects of the surrounding water molecules were calculated with the help of configurations drawn from a classical molecular dynamics simulation. Basis-set effects and solute-solvent interaction operator representation are examined. Embedding energies and liquid-phase multipole moments obtained from the present mixed quantum-classical model are compared with corresponding quantities for purely classical water models. © 1996 John Wiley & Sons, Inc.