Cumulative potential-derived atomic multipoles

A method to derive the atomic multipole moments cumulatively up to quadrupole moments was developed. The multipole moments are obtained by least-square simulating the molecular electrostatic potentials. Only the components of the term of highest order in the atomic multipole expansion are optimized while the lower terms remain fixed. The calculations on HF, H₂O and NH₃ show that the cumulative method can give reasonable qualitative and fairly good quantitative results.     

Molecular electrostatic potentials and partial atomic charges from correlated wave functions: Applications to the electronic ground and excited states of 3-methylindole

Procedures have been developed to generate molecular electrostatic potentials based on correlated wave function from ab initio or semiempirical electronic structure programs. A new algorithm for point-wise sampling of the potential is described and used to obtain partial atomic charges via a linear, least squares fit between classical and quantum mechanical electrostatic potentials. The proposed sampling algorithm is efficient and promises to introduce less rotational variance in the potential derived partial charges than algorithms applied previously. Electrostatic potentials and fitted atomic charges from ab initio (HF/6–31G* and MP2/6-31G*) and semiempirical (INDO/S; HF, SECI, and SDCI) wave functions are presented for the electronic ground (S₀) and excited (¹L_b, ¹L_a) states of 3-methylindole. © 1992 by John Wiley & Sons, Inc.     

A multipole approximation of the electrostatic potential of molecules

The problem of approximating three-dimensional spatial distributions of quantum-mechanical electrostatic potentials of molecules by analytic potentials on the basis of atomic charges, real dipoles, and atomic multipoles up to quadrupoles inclusive was considered. Real dipole potentials are created by pairs of point charges of opposite signs, and the search for their arrangement in the volume of a molecule is part of the approximation problem. A FitMEP program was developed for the optimization of the parameters of models of the types specified taking into account molecular symmetry. It was shown for the example of several molecules (HF, CO, H₂O, NH₃, CH₄, formaldehyde, methanol, formamide, ethane, cyclopropane, cyclobutane, cyclohexane, tetrahedrane, cubane, adamantane, ethylene, and benzene) that the real dipole and atomic multipole models gave errors in approximated quantum-mechanical electrostatic potential values smaller by one or two orders of magnitude compared with the atomic charge model. The atomic charge model was shown to be virtually inoperative as applied to saturated hydrocarbons. Real dipole models were slightly inferior to atomic multipole models in quality but had all the advantages of the potential of point charges as concerned simplicity and compactness, and their use in potential energy calculations did not require changes in the existing program codes.     

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.     

New approach to the rapid semiempirical calculation of molecular electrostatic potentials based on the am1 wave function: Comparison with ab initio hf/6-31g* results

A new approach to the computation of molecular electrostatic potentials based on the AM1 wave function is described. In contrast to the prevailing philosophy, but consistent with the underlying NDDO approximation, no deorthogonalization of the wave function is carried out. The integrals required for the computation of the electronic contributions to the molecular electrostatic potential are evaluated in a manner similar to that of the AM1 core-electron attraction integrals, while the nuclear contributions are computed using a new semiempirical function—Z_A(S^AS^A, S^pS^p)[1 + exp[ – ω_A(R_Ai – δ_A)]]—where the atomic parameters ω_A and δ_A are obtained by calibration against the results of ab initio HF/6-31G* calculations. Isopotential contour maps for guanine and cytosine obtained with the new method are qualitatively almost indistinguishable from their HF/6-31G* counterparts, while quantitative comparisons for the minima for a wide range of molecules are reproduced with an rms error of 5.2 kcal mol^?1. The locations of the “lone-pair” minima for a wide range of heterosubstituted organic molecules generally fall within 0.02 Å of the corresponding HF/6-31G* minima while those in the π-regions of unsaturated molecules are generally within 0.2 Å. Because of the rapid integral evaluation, the fully semiempirical method described here is extremely economical. For example, for the guanine–cytosine base pair it is >500 times faster than calculations in which the complete integral matrix is computed analytically from the deorthogonalized AM1 wave function. © John Wiley & Sons, Inc.     

Multipole electrostatic model for MNDO-like techniques with minimal valence spd-basis sets

We report an implementation of an atomic multipole model (up to quadrupole) for calculating the electrostatic properties of molecules based on electron densities derived from MNDO-like NDDO-based semiempirical MO calculations with minimal s,p,d valence basis sets. The results were validated by a comparison of the calculated values of the molecular electrostatic potential with those obtained from fine grain numerical integrations (both with AM1*), B3LYP/6–31G(d) and MP2/6–31G(d). The DFT and ab initio potentials can be reproduced remarkably well (mean unsigned error <2 kcal mol⁻¹ e⁻¹) using simple linear regression equations to correct the AM1* (multipole) results. Dedicated to Prof. Karl Jug on the occasion of his 65th birthday     

Ab initio MO calculations on the stable conformations and their binding energies of the ion-molecule complexes: Ion = H+, Li+, Na+, K+ Be2+, and molecule = CO and N2

The most stable conformation of ion-molecule complexes involving a CO molecule were surveyed by the use of Hartree-Fock (HF) MO and third-order Moller-Plesset perturbation (MP3) methods with a 6–31G* basis set ion = H⁺, Li⁺, Na⁺, K⁺, Bc²⁺, Mg²⁺, and Ca²⁺. The MP3 level of theory reveals the ion-CO conformation in which the ion bonds to a carbon atom of CO to be the most stable; these MP3 results are contrary to the HF ones. Binding energies of ion-molecule complexes involving CO and N₂ were computed; MP3 energies are in good agreement with the experimental ones. The computed binding energies of cation-N₂ are about one-third of cation-NH₃ due to the absence of dipole moment and the smaller polarizability of N₂. The decrease in binding energy in cation-CO and -N₂ complexes, with increasing cation size, is mainly caused by the decrease of the electrostatic and polarization stabilizations.     

Extended Koopmans' theorem: Approximate ionization energies from MCSCF wave functions

The extended Koopmans' theorem has been implemented using multiconfigurational self-consistent field wave functions calculated with the GAMESS, HONDO, and SIRIUS programs. The results of illustrative calculations are presented for the molecules HF, H₂O, NH₃, CH₄, N₂, CO, HNC, HCN, C₂H₂, H₂CO, and B₂H₆. The lowest extended Koopmans' theorem ionization potentials agree well within the experimental values and the ionization potentials representing excited states of the ions show some improvements over the Koopmans' theorem values in most cases. The extended Koopmans' theorem is easily implemented and the time required to calculate the ionization energies is insignificant compared to the time required to calculate the wave function of the un-ionized molecule. © 1992 by John Wiley & Sons, Inc.     

Effective potentials for spectator groups in molecular systems I. Potential curves and binding energies

Summary A method for representing inactive groups, i.e. spectator groups, in a molecular system by an effective potential is presented. The matrix elements for the spectator's short-range Hartree-Fock potential is stored in an intermediate AO basis, from which it can be transferred into the user basis for the active part of the molecular system. The longer-range of the potential is transferred via a (distributed) multipole expansion. The method is illustrated for the NH₃·X (X=NH₃, H₂O, HF) complexes: binding energies could be reproduced to within 5% by employing the effective NH₃ potential (whereby the lone pair was included in the active system), the entire NH₃·HF potential curve with a depth of 50 kJ/mol is reproduced within 2 kJ/mol if various intermediate basis sets are chosen. Technical details are discussed; the effective potential can directly be introduced in CI calculations.     

The Nature of Nonclassical Carbonyl Ligands Explained by Kohn–Sham Molecular Orbital Theory

When carbonyl ligands coordinate to transition metals, their bond distance either increases (classical) or decreases (nonclassical) with respect to the bond length in the isolated CO molecule. C−O expansion can easily be understood by π-back-donation, which results in a population of the CO's π*-antibonding orbital and hence a weakening of its bond. Nonclassical carbonyl ligands are less straightforward to explain, and their nature is still subject of an ongoing debate. In this work, we studied five isoelectronic octahedral complexes, namely Fe(CO)₆²⁺, Mn(CO)₆⁺, Cr(CO)₆, V(CO)₆⁻ and Ti(CO)₆²⁻, at the ZORA-BLYP/TZ2P level of theory to explain this nonclassical behavior in the framework of Kohn–Sham molecular orbital theory. We show that there are two competing forces that affect the C−O bond length, namely electrostatic interactions (favoring C−O contraction) and π-back-donation (favoring C−O expansion). It is a balance between those two terms that determines whether the carbonyl is classical or nonclassical. By further decomposing the electrostatic interaction ΔV_elstat into four fundamental terms, we are able to rationalize why ΔV_elstat gives rise to the nonclassical behavior, leading to new insights into the driving forces behind C−O contraction.     

Bonding in FHF−, (HF)2, and FHF

Bonding in FHF^?, (HF)₂, and FHF is compared from the molecular orbital and electrostatic bonding viewpoint. The electrostatic force is dominant in the formation of FHF^? and HF dimer. Exchange repulsion dominates in preventing the formation of FHF and leads to a D_∞h transition state for H exchange. At the D_∞h stationary points for FHF^? and FHF the electronic structure can be understood using delocalized symmetry orbitals, but this delocalization is not the primary driving force along the potential energy surface leading to these structures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Point charge representation of multicenter multipole moments in calculation of electrostatic properties

Summary Distributed Point Charge Models (PCM) for CO, (H₂O)₂, and HS-SH molecules have been computed from analytical expressions using multicenter multipole moments. The point charges (set of charges including both atomic and non-atomic positions) exactly reproduce both molecular and segmental multipole moments, thus constituting an accurate representation of the local anisotropy of electrostatic properties. In contrast to other known point charge models, PCM can be used to calculate not only intermolecular, but also intramolecular interactions. Comparison of these results with more accurate calculations demonstrated that PCM can correctly represent both weak and strong (intramolecular) interactions, thus indicating the merit of extending PCM to obtain improved potentials for molecular mechanics and molecular dynamics computational methods.Dedicated to Prof. Alberte PullmanPacific Northwest Laboratory is operated for the US Department of Energy by Battelle Memorial Institute under contract DE-ACO6-76RLO 1830     

Origins of relative acidity: First and second period hydrides

The origins of the trends of relatively acidity across and between the first and second period hydrides (BH₃, CH₄, NH₃, H₂O, HF, AIH₃, SiH₄, PH₃, H₂S, and HCl) were investigated using molecular and subsystem quantum mechanics at the Hartree-Fock (HF)/6–31 + + G ^**//HF/6–31 + + G ^** level of theory. The total deprotonation energies, Δ E_acid, are interpreted in terms of three component processes: Δ E₁; deprotonation without electronic and nuclear relaxation; Δ E₂, electronic relaxation within the acid geometry; and Δ E₃, nuclear relaxation. Δ E₁ is given from the electrostatic potential at the acidic proton, Δ E₃ + Δ E₂ (= Δ E ^*) is given from the calculated energy of the conjugate anion at the acid geometry. The increased acidity across a given period is shown to be already mostly an inherent property of the acid. © 1996 by John Wiley & Sons, Inc.     

Molecular relaxation processes in triatomic molecules. II. The N2–CO2 system

Translation–vibration (T–V) and vibration–vibration (V–V) energy transfer processes in the N₂–CO₂ system were investigated using classical trajectory techniques. Two empirical interaction potentials were employed. One is comprised of independent, atom–atom Morse-type functions operating between nonbonded atoms. The other included these atom–atom Morse functions plus Coulombic terms to account for the quadrupole–quadrupole intertion. Both interaction potentials led to similar T–V results. However, the result that CO₂(v₃) is excited ～10³ times more efficiently than N₂(v = 1) was obtained, which is at variance with existing analytical theories of T–V energy transfer employing purely repulsive short-range potentials. Different V–V energy transfer probabilities were obtained from the two interaction potentials. The most important finding is that only when electrostatic orientation effects are combined with short-range repulsive interactions is the near-resonant V–V transfer found to be the dominant energy transfer path. This interaction potential also crudely accounts for the negative temperature dependence observed for this near-resonant V–V transfer at low temperatures (300–1000°K).     

The solid-state electronic structure and the nature of the chemical bond of the ternary Zintl-phase Li8MgSi6. A tight-binding analysis

The electronic strcuture of the ternary Zintl-phase Li₈MgSi₆ has been investigated in the computational framework of a semi-empirical crystal orbital (CO) formalism based on the tight-binding approximation. Li₈MgSi₆ crystallizes in the space group P2₁/m-C_2h² with a = 12.701 Å, b = 4.347 Å, c = 10.507 Å and β = 107.58°. A self-consistent-field (SCF) Hartree-Fock (HF) INDO CO procedure has been employed for the numerical approach. In order to reduce the computational expenditure of the CO calculations we have adopted a one-dimensional (ID) model simulating the real solid. To allow for a clear theoretical analysis the ID system is divided into simpler subfragments (MgSi^2-, Li₃MgSi⁺, Li₅Si₅^?); the solid-state electronic structures of these moieties can be rationalized in a straightforward way. The band structure properties, density of states distributions, net charges and atomic orbital populations of Li₈MgSi₆ are interpreted. A forbidden band gap of 0.62 eV is calculated by the semi-empirical tight-binding scheme, a value that is in excellent agreement to the measured band gap of the semiconducting compound which amounts to = 0.7 eV. The nature of chemical bond in the Li₈MgSi₆ phase is analyzed by fragmenting the net diatomic interaction energies between SiSi, SiLi and MgSi pairs into covalent resonance elements as well as exchange and classical electrostatic (Coulomb) contributions. Partial coordination numbers (PCN) are defined for the various atomic species of the ternary phase that are labels of strongly stabilizing interactions (bonds) in the low-dimensional units. The calculated charge distributions show a striking 1:1 correspondence between the present CO results and the expectations derived on the basis of classical (Zintl-Klemm) electron-counting rules thus corroborating the utility of extended Zintl-Klemm conceptions in solids with atoms beyond the first two rows.     

Molecular surface electrostatic potentials and local ionization energies of Group V–VII hydrides and their anions: Relationships for aqueous and gas-phase acidities

We have computed ab initio HF /6-31+G * electrostatic potentials and average local ionization energies on the molecular surfaces of the Group V–VII hydrides and corresponding anions of the first three rows of the periodic table. The surfaces were defined to be specified contours (0.002 or 0.001 au) of the molecular electronic density. The most negative potentials, V_S,min, and lowest ionization energies ī_S,min, were located and determined. Their magnitudes separately satisfy limited correlations with gas-phase protonation enthalpies and aqueous pK_a values. Our results indicate that V_S,min, and ī_S,min are complementary, the former reflecting electrostatic factors and the latter being related to charge transfer/polarization. More general relationships for protonation enthalpies are obtained when both V_S,min and ī_S,min are explicitly included. Solution-phase and gas-phase acidities are shown to correlate very well if electrostatic effects are explicitly taken into account. © 1993 John Wiley & Sons, Inc.     

Vibrational and rotational energy transfer upon molecular collisions

The cross section of the rotational and vibrational energy transfer is derived by using the first Born approximation which quantizes the translational motion of the colliding particles. The theory developed here integrates the intermolecular potential V(R) over all regions of the internuclear distance R by obtaining a Fourier transform of V(R). This differs from previous semiclassical (impact-parameter) treatments which either considered the short-range repulsive interaction or expanded V(R) into a long-range multipole expansion. The cross section obtained here is expressed in a very simple algebraic expression which can be readily calculated. This will be illustrated by examples of CO₂(001)+N₂(υ=0)=CO₂(000)+N₂(υ=1)+18.6 cm^?1 and CO(υ=1)+CO(υ=1)=CO(υ=0)+CO(υ=2)+27 cm^?1. Calculations have been made both for the exothermic and for the endothermic reactions. The comparison of the present results with experimental results as well as with previously calculated results will be discussed.     

Relative binding orientations of adenosine A1 receptor ligands — A test case for Distributed Multipole Analysis in medicinal chemistry

Summary The electrostatic properties of adenosine-based agonists and xanthine-based antagonists for the adenosine A₁ receptor were used to assess various proposals for their relative orientation in the unknown binding site. The electrostatic properties were calculated from distributed multipole representations of SCF wavefunctions. A range of methods of assessing the electrostatic similarity of the ligands were used in the comparison. One of the methods, comparing the sign of the potential around the two molecules, gave inconclusive results. The other approaches, however, provided a mutually complementary and consistent picture of the electrostatic similarity and dissimilarity of the molecules in the three proposed relative orientations. This was significantly different from the results obtained previously with MOPAC AM1 point charges. In the standard model overlay, where the aromatic nitrogen atoms of both agonists and antagonists are in the same position relative to the binding site, the electrostatic potentials are so dissimilar that binding to the same receptor site is highly unlikely. Overlaying the N⁶-region of adenosine with that near C8 of theophylline (the N⁶-C8 model) produces the greatest similarity in electrostatic properties for these ligands. However, N⁶-cyclopentyladenosine (CPA) and 1,3-dipropyl-8-cyclopentylxanthine (DPCPX) show greater electrostatic similarity when the aromatic rings are superimposed according to the flipped model, in which the xanthine ring is rotated around its horizontal axis. This difference is mainly attributed to the change in conformation of N⁶-substituted adenosines and could result in a different orientation for theophylline and DPCPX within the receptor binding site. However, it is more likely that DPCPX also binds according to the N⁶-C8 model, as this model gives the best steric overlay and would be favoured by the lipophilic forces, provided that the binding site residues could accommodate the different electrostatic properties in the N⁶/N7-region. Finally, we have shown that Distributed Multipole Analysis (DMA) offers a new, feasible tool for the medicinal chemist, because it provides the use of reliable electrostatic models to determine plausible relative binding orientations.Abbreviations DMA distributed multipole analysis - SCF self-consistent field - CPA N⁶-cyclopentyladenosine - DPCPX 1,3-dipropyl-8-cyclopentylxanthine - R-PIA R-1-phenyl-2-propyladenosine - S-PIA S-1-phenyl-2-propyladenosine