Distributed Multipole Moments Research Articles

Multipole moments for embedding potentials: Exploring different atomic allocation algorithms

Polarizable quantum mechanical (QM)/molecular mechanics (MM)-embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins and RNA/DNA, and of molecules in solution. Our aim is to develop a computational methodology for distributed multipole moments and their associated multipole polarizabilities which is accurate, computationally efficient, and with smooth convergence with respect to multipole order. As the first step toward this goal, we herein investigate different ways of obtaining distributed atom-centered multipole moments that are used in the construction of the electrostatic part of the embedding potential. Our objective is methods that not only are accurate and computationally efficient, but which can be consistently extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well-known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we show that the classical embedding potential can be systematically improved, also when using basis sets with diffuse functions, and that very accurate embedding potentials suitable for QM/MM embedding calculations can be acquired. © 2016 Wiley Periodicals, Inc.

Transferable Atomic Multipole Machine Learning Models for Small Organic Molecules.

Accurate representation of the molecular electrostatic potential, which is often expanded in distributed multipole moments, is crucial for an efficient evaluation of intermolecular interactions. Here we introduce a machine learning model for multipole coefficients of atom types H, C, O, N, S, F, and Cl in any molecular conformation. The model is trained on quantum-chemical results for atoms in varying chemical environments drawn from thousands of organic molecules. Multipoles in systems with neutral, cationic, and anionic molecular charge states are treated with individual models. The models' predictive accuracy and applicability are illustrated by evaluating intermolecular interaction energies of nearly 1,000 dimers and the cohesive energy of the benzene crystal.

Vibrational solvatochromism. II. A first-principle theory of solvation-induced vibrational frequency shift based on effective fragment potential method.

Vibrational solvatochromism is a solvation-induced effect on fundamental vibrational frequencies of molecules in solutions. Here we present a detailed first-principle coarse-grained theory of vibrational solvatochromism, which is an extension of our previous work [B. Błasiak, H. Lee, and M. Cho, J. Chem. Phys. 139(4), 044111 (2013)] by taking into account electrostatic, exchange-repulsion, polarization, and charge-transfer interactions. By applying our theory to the model N-methylacetamide-water clusters, solute-solvent interaction-induced effects on amide I vibrational frequency are fully elucidated at Hartree-Fock level. Although the electrostatic interaction between distributed multipole moments of solute and solvent molecules plays the dominant role, the contributions from exchange repulsion and induced dipole-electric field interactions are found to be of comparable importance in short distance range, whereas the charge-transfer effect is negligible. The overall frequency shifts calculated by taking into account the contributions of electrostatics, exchange-repulsion, and polarization terms are in quantitative agreement with ab initio results obtained at the Hartree-Fock level of theory.

The multi-configuration self-consistent field method within a polarizable embedded framework

We present a detailed derivation of Multi-Configuration Self-Consistent Field (MCSCF) optimization and linear response equations within the polarizable embedding scheme: PE-MCSCF. The MCSCF model enables a proper description of multiconfigurational effects in reaction paths, spin systems, excited states, and other properties which cannot be described adequately with current implementations of polarizable embedding in density functional or coupled cluster theories. In the PE-MCSCF scheme the environment surrounding the central quantum mechanical system is represented by distributed multipole moments and anisotropic dipole-dipole polarizabilities. The PE-MCSCF model has been implemented in DALTON. As a preliminary application, the low lying valence states of acetone and uracil in water has been calculated using Complete Active Space Self-Consistent Field (CASSCF) wave functions. The dynamics of the water environment have been simulated using a series of snapshots generated from classical Molecular Dynamics. The calculated shifts from gas-phase to water display between good and excellent correlation with experiment and previous calculations. As an illustration of another area of potential applications we present calculations of electronic transitions in the transition metal complex, [Fe(NO)(CN)5](2-) in a micro-solvated environment. This system is highly multiconfigurational and the influence of solvation is significant.

Accurate Molecular Crystal Lattice Energies from a Fragment QM/MM Approach with On-the-Fly Ab Initio Force Field Parametrization.

We combine quantum and classical mechanics in a fragment-based many-body interaction model to predict organic molecular crystal lattice energies. Individual molecules in the central unit cell and their short-range pairwise interactions are modeled quantum mechanically, while long-range pairwise and many-body interactions are approximated classically. The classical contributions are evaluated using an accurate ab initio force field that is constructed on-the-fly from quantum mechanical calculations on the individual molecules in the unit cell. The force field parameters include ab initio distributed multipole moments, distributed polarizabilities, and isotropic two- and three-body atomic dispersion coefficients. This QM/MM fragment model reproduces full periodic MP2 lattice energies to within a couple kJ/mol at substantially reduced cost. When high-level electronic structure methods are coupled with the ab initio force field, molecular crystal lattice energies are predicted to within 2 kJ/mol of their experimental values for six of the seven crystals examined here. Finally, Axilrod-Teller-Muto three-body dispersion energy plays a nontrivial role in several of the molecular crystals studied here.

Is the Induction Energy Important for Modeling Organic Crystals?

We compare two methods for estimating the induction energy in organic molecular crystals by approximating the charge density polarization in the crystalline state. The first is a distributed atomic polarizability model combined with distributed multipole moments, derived from ab initio monomer properties. The second uses an ab initio calculation of the molecular charge density in a point-charge field. Various parameters of the models, such as the rank of polarizability model, effect of self-consistent iterations, and damping, are investigated. The methods are applied to a range of observed and predicted crystal structures of three particularly challenging molecules, namely oxalyl dihydrazide, 3-azabicyclo[3,3,1]nonane-2,4-dione, and carbamazepine, as well as demonstrating the importance of induction in the naphthalene crystal. The two models agree well considering the different approximations made, and it is shown that the induction energy can be an important discriminator in the relative lattice energies of structures with substantially different hydrogen-bonding motifs.

Van der Waals Complexes of Small Molecules with Benzenoid Rings: Influence of Multipole Moments on Their Mutual Orientation

Intermolecular interaction between some small molecules (HF, H2O, NH3, and CH4) and certain benzenoid ring systems (benzene, hexafluorobenzene, and 1,3,5-trifluorobenzene) has been investigated in detail at MP2 level of theory using 6-311++G** basis set, and the results are corrected for basis set superposition error (BSSE). Vibrational frequencies were calculated for all the geometries at the same level of theory and basis sets to ensure that the geometries obtained correspond to true minima. In the complexes with benzene, which has a large negative quadrupole moment, the preferred geometry has the electropositive end of the small molecule (HF, H2O, and NH3) pointing toward the ring and the corresponding interaction energies are -3.24, -2.43, and -1.57 kcal/mol, respectively. For the complexes with hexafluorobenzene which has a large positive quadrupole moment, the most stable geometries are those in which the electropositive end of HF, H2O, and NH3 points away from the ring and the corresponding interaction energies are -1.59, -2.73, and -3.14 kcal/mol, respectively. Methane, which has neither a dipole nor a quadrupole moment, is weakly bound and is oriented differently in different systems. 1,3,5-Trifluorobenzene has a negligible quadrupole moment, and the complexes with small molecules are stabilized by cyclic hydrogen bonding. Although the point dipole-quadrupole and point quadrupole-quadrupole interactions present in these complexes account qualitatively for the preferred orientations, distributed multipole moments of the constituent atoms are found to give a quantitative description of the interaction in such complexes.

Cumulative coordinates for approximations of high‐order atomic multipole moments in aluminosilicate and aluminophosphate sieves*

AbstractA scheme to obtain approximate analytical functions for the atomic distributed multipole moments of the crystallographically different atoms within aluminosilicate and aluminophosphate sieves is discussed. Respective atomic multipole moments are derived within the CRYSTAL95 ab initio periodic Hartree–Fock code with different basis sets, from minimal STO‐3G to 6‐21G*. In order to illustrate the possible applications, distributed analyses are carried out for various structural models from all‐siliceous zeolites and aluminophosphates with ratio Al/P=1 to hydrogen forms of aluminosilicates. Simple approximate forms based on charge and geometry coordinates are proposed for the high‐order moments of each atom, which are further required for the calculation of the electrostatic field within the structures. The possibility to use this analytical approach to evaluate the electrostatic field within embedded cluster models is also shortly discussed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 70–85, 2001

A distributed electrostatic model for field gradients at nuclei in van der Waals molecules: application to complexes of HCl

A distributed model for the response of the electric field gradient at a nucleus to perturbation by external fields is proposed, and an implementation using perturbation of distributed multipole moments by a test nuclear quadrupole is described. Calculations on the HCl and Cl 2 molecules show the response of the electric field gradient at Cl to be dominated by induced σ charge flow. Application to hydrogen-bonded complexes of HCl gives a qualitative explanation of 35Cl quadrupole coupling constants in B…HCl where B is a base such as H 3N, HCN, CH 3CN, H 3P and OC.

Modeling amino acid side chains. 3. Influence of intra- and intermolecular environment on point charges

Modifications of the molecular charge distributions of simplified models of amino acids due to intra- and intermolecular environment have been analyzed. Point charges of the extended conformers of Me-L-Ala-Me, Me-L-Asp-Me, Me-Gly-Me, Me-L-Ser-Me, and the extended (C 5 ) as well as the C 7 -equatorial conformations of N'-acetyl-L-methyl-L-aspartylamide (NANMAsp) have been computed from ab initio optimized geometries, using the split-valence 6-31G ** basis set. Point charge models were determined from the resulting self-consistent-field (SCF) wave functions by means of least-squares fits to the exact ab initio electrostatic potential and to the approximate electrostatic potential created by distributed multipole moments (DMM)

Induced dipole moments in acetylene complexes

The induced dipole moments of a number of van der Waals complexes containing acetylene have been calculated from the distributed multipole moments and the distributed polarizabilities of the monomers. The induced moments calculated for the equilibrium structures are generally in close agreement with the experimental values (where available), and differences can be understood in terms of zero-point motion in the loosely bound complexes

Central or distributed multipole moments? Electrostatic models of aromatic dimers

Multipole moments up to rank six are calculated at the SCF level for sym-triazine and 1,3,5-trifluorobenzene. Staggered face-to-face configurations of the homodimers are stabilized by both electrostatic and dispersion interactions. Low-order central multipole models fail to show the electrostatic attraction; high-order central multipole expansions are strongly divergent. Distributed multipoles derived either by fitting to ab initio central multipoles, or by analysis of the electron density, predict the correct orientational minimum and give reasonable estimates of electrostatic interaction energies.

Vibration–rotation spectrum of the carbon dioxide–acetylene van der Waals complex in the 3 μ region

The infrared absorption spectrum of the carbon dioxide–acetylene van der Waals complex has been observed in a pulsed molecular beam. A color center laser was used to excite the vibration associated with the antisymmetric hydrogen stretching mode of the acetylene monomer. The vibrational origin is 3281.740 cm−1 and the rotational constants are A″=8876, B″=2859, C″=2155, A′=8864, B′=2855, and C′=2154 MHz. The axes of the two monomer are parallel to one another and the complex has C2v symmetry. The separation of the monomer units is 3.285 Å. The angular part of the intermolecular potential function is discussed in terms of electrostatic interactions between distributed multipole moments.