Charge Model 5: An Extension of Hirshfeld Population Analysis for the Accurate Description of Molecular Interactions in Gaseous and Condensed Phases.

We propose a novel approach to deriving partial atomic charges from population analysis. The new model, called Charge Model 5 (CM5), yields class IV partial atomic charges by mapping from those obtained by Hirshfeld population analysis of density functional electronic charge distributions. The CM5 model utilizes a single set of parameters derived by fitting to reference values of the gas-phase dipole moments of 614 molecular structures. An additional test set (not included in the CM5 parametrization) contained 107 singly charged ions with nonzero dipole moments, calculated from the accurate electronic charge density, with respect to the center of nuclear charges. The CM5 model is applicable to any charged or uncharged molecule composed of any element of the periodic table in the gas phase or in solution. The CM5 model predicts dipole moments for the tested molecules that are more accurate on average than those from the original Hirshfeld method or from many other popular schemes including atomic polar tensor and Löwdin, Mulliken, and natural population analyses. In addition, the CM5 charge model is essentially independent of a basis set. It can be used with larger basis sets, and thereby this model significantly improves on our previous charge models CMx (x = 1-4 or 4M) and other methods that are prone to basis set sensitivity. CM5 partial atomic charges are less conformationally dependent than those derived from electrostatic potentials. The CM5 model does not suffer from ill conditioning for buried atoms in larger molecules, as electrostatic fitting schemes sometimes do. The CM5 model can be used with any level of electronic structure theory (Hartree-Fock, post-Hartree-Fock, and other wave function correlated methods or density functional theory) as long as an accurate electronic charge distribution and a Hirshfeld analysis can be computed for that level of theory.

[1]  P. Kollman,et al.  Atomic charges derived from semiempirical methods , 1990 .

[2]  Donald G Truhlar,et al.  Density functional for spectroscopy: no long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states. , 2006, The journal of physical chemistry. A.

[3]  C. Cramer,et al.  Accurate partial atomic charges for high-energy molecules using class IV charge models with the MIDI! basis set , 2005 .

[4]  David J. Giesen,et al.  Class IV charge models: A new semiempirical approach in quantum chemistry , 1995, J. Comput. Aided Mol. Des..

[5]  Donald G. Truhlar,et al.  Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory , 2003 .

[6]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[7]  A. L. McClellan,et al.  Tables of experimental dipole moments , 1963 .

[8]  Wilfried Langenaeker,et al.  Atomic charges, dipole moments, and Fukui functions using the Hirshfeld partitioning of the electron density , 2002, J. Comput. Chem..

[9]  A. Becke Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[10]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[11]  A. Bondi van der Waals Volumes and Radii , 1964 .

[12]  Patrick Bultinck,et al.  Critical analysis and extension of the Hirshfeld atoms in molecules. , 2007, The Journal of chemical physics.

[13]  Donald G. Truhlar,et al.  New Class IV Charge Model for Extracting Accurate Partial Charges from Wave Functions , 1998 .

[14]  H. Stoll,et al.  Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements , 2003 .

[15]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[16]  Michael Dolg,et al.  Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-d main group elements: Application to PbH and PbO , 2000 .

[17]  C. W. Gillies,et al.  Rotational Spectra, Molecular Structure, and Electric Dipole Moment of Propanethial S-Oxide , 1999 .

[18]  Jun Li,et al.  Basis Set Exchange: A Community Database for Computational Sciences , 2007, J. Chem. Inf. Model..

[19]  B. Starck,et al.  2.6.1 Introduction and explanation of symbols , 1967 .

[20]  Donald G Truhlar,et al.  SM6:  A Density Functional Theory Continuum Solvation Model for Calculating Aqueous Solvation Free Energies of Neutrals, Ions, and Solute-Water Clusters. , 2005, Journal of chemical theory and computation.

[21]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[22]  Peter Politzer,et al.  Chemical Applications of Atomic and Molecular Electrostatic Potentials: "Reactivity, Structure, Scattering, And Energetics Of Organic, Inorganic, And Biological Systems" , 2013 .

[23]  G. A. Petersson,et al.  A complete basis set model chemistry. VI. Use of density functional geometries and frequencies , 1999 .

[24]  Michael Dolg,et al.  Energy‐adjusted ab initio pseudopotentials for the first row transition elements , 1987 .

[25]  István Mayer,et al.  Charge, bond order and valence in the AB initio SCF theory , 1983 .

[26]  David Feller The role of databases in support of computational chemistry calculations , 1996 .

[27]  Frank Weinhold,et al.  Natural hybrid orbitals , 1980 .

[28]  C. Cramer,et al.  Polarization Effects in Aqueous and Nonaqueous Solutions. , 2007, Journal of chemical theory and computation.

[29]  Ernest R. Davidson,et al.  A test of the Hirshfeld definition of atomic charges and moments , 1992 .

[30]  R. C. Weast CRC Handbook of Chemistry and Physics , 1973 .

[31]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[32]  Paul R. Gerber,et al.  Charge distribution from a simple molecular orbital type calculation and non-bonding interaction terms in the force field MAB , 1998, J. Comput. Aided Mol. Des..

[33]  D. Truhlar,et al.  Accuracy of Effective Core Potentials and Basis Sets for Density Functional Calculations, Including Relativistic Effects, As Illustrated by Calculations on Arsenic Compounds. , 2011, Journal of chemical theory and computation.

[34]  Bhyravabhotla Jayaram,et al.  A fast empirical GAFF compatible partial atomic charge assignment scheme for modeling interactions of small molecules with biomolecular targets , 2011, J. Comput. Chem..

[35]  Warren J. Hehre,et al.  AB INITIO Molecular Orbital Theory , 1986 .

[36]  Beatriz Cordero,et al.  Covalent radii revisited. , 2008, Dalton transactions.

[37]  D. Stalke Meaningful structural descriptors from charge density. , 2011, Chemistry.

[38]  D. Truhlar,et al.  A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. , 2006, The Journal of chemical physics.

[39]  Vincenzo Barone,et al.  Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models , 1998 .

[40]  Donald G. Truhlar,et al.  Polarization of the nucleic acid bases in aqueous solution , 1992 .

[41]  John A. Montgomery,et al.  A complete basis set model chemistry. VII. Use of the minimum population localization method , 2000 .

[42]  Donald G Truhlar,et al.  Density functionals with broad applicability in chemistry. , 2008, Accounts of chemical research.

[43]  F. L. Hirshfeld Bonded-atom fragments for describing molecular charge densities , 1977 .

[44]  P. Kollman,et al.  A well-behaved electrostatic potential-based method using charge restraints for deriving atomic char , 1993 .

[45]  David M. Gange,et al.  Charges fit to electrostatic potentials. II. Can atomic charges be unambiguously fit to electrostatic potentials? , 1996 .

[46]  Michael Dolg,et al.  Energy‐adjusted ab initio pseudopotentials for the rare earth elements , 1989 .

[47]  L. E. Chirlian,et al.  Atomic charges derived from electrostatic potentials: A detailed study , 1987 .

[48]  Elizabeth A. Amin,et al.  Zn Coordination Chemistry:  Development of Benchmark Suites for Geometries, Dipole Moments, and Bond Dissociation Energies and Their Use To Test and Validate Density Functionals and Molecular Orbital Theory. , 2008, Journal of chemical theory and computation.

[49]  R. S. Mulliken Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[50]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[51]  Alkali and alkaline earth metal compounds: core—valence basis sets and importance of subvalence correlation , 2003, physics/0301056.

[52]  F. Matthias Bickelhaupt,et al.  Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis , 2004, J. Comput. Chem..

[53]  Michael Dolg,et al.  Energy-adjusted pseudopotentials for the rare earth elements , 1989 .

[54]  Elizabeth A. Amin,et al.  Energies, Geometries, and Charge Distributions of Zn Molecules, Clusters, and Biocenters from Coupled Cluster, Density Functional, and Neglect of Diatomic Differential Overlap Models. , 2009, Journal of chemical theory and computation.

[55]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[56]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[57]  Giovanni Scalmani,et al.  Gaussian 09W, revision A. 02 , 2009 .

[58]  Donald E. Williams Representation of the molecular electrostatic potential by atomic multipole and bond dipole models , 1988 .

[59]  R. J. Abraham,et al.  Charge calculations in molecular mechanics. V. Silicon compounds and π bonding , 1988 .

[60]  P Coppens,et al.  Electron Density from X-Ray Diffraction , 1992 .

[61]  Timothy Clark,et al.  Efficient diffuse function‐augmented basis sets for anion calculations. III. The 3‐21+G basis set for first‐row elements, Li–F , 1983 .

[62]  Donald G Truhlar,et al.  Charge Model 4 and Intramolecular Charge Polarization. , 2007, Journal of chemical theory and computation.

[63]  Linus Pauling,et al.  Atomic Radii and Interatomic Distances in Metals , 1947 .

[64]  Jon Baker,et al.  Classical chemical concepts from ab initio SCF calculations , 1985 .

[65]  P. Kollman,et al.  An approach to computing electrostatic charges for molecules , 1984 .

[66]  P. Salvador,et al.  Overlap populations, bond orders and valences for fuzzy atoms , 2004 .

[67]  Patrick Bultinck,et al.  Electrostatic Potentials from Self-Consistent Hirshfeld Atomic Charges. , 2009, Journal of chemical theory and computation.

[68]  Steven M. Bachrach,et al.  Some methods and applications of electron density distribution analysis , 1987 .

[69]  James P. Ritchie Electron density distribution analysis for nitromethane, nitromethide, and nitramide , 1985 .

[70]  Dennis R. Salahub,et al.  Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation , 1992 .

[71]  F. Weinhold,et al.  Natural population analysis , 1985 .

[72]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[73]  Curtis L. Janssen,et al.  An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations , 1988 .

[74]  I. Mayer On bond orders and valences in the Ab initio quantum chemical theory , 1986 .

[75]  Chérif F. Matta,et al.  Atomic Charges Are Measurable Quantum Expectation Values: A Rebuttal of Criticisms of QTAIM Charges , 2004 .

[76]  J. Pople,et al.  Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions , 1980 .

[77]  Pekka Pyykkö,et al.  Molecular single-bond covalent radii for elements 1-118. , 2009, Chemistry.

[78]  Richard A. Friesner,et al.  Integrated Modeling Program, Applied Chemical Theory (IMPACT) , 2005, J. Comput. Chem..

[79]  Jerzy Cioslowski,et al.  A new population analysis based on atomic polar tensors , 1989 .

[80]  C. Van Alsenoy,et al.  An Extension of the Hirshfeld Method to Open Shell Systems Using Fractional Occupations. , 2011, Journal of chemical theory and computation.

[81]  Michael J. Frisch,et al.  Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets , 1984 .

[82]  A class IV charge model for boron based on hybrid density functional theory , 2003 .

[83]  D. Truhlar,et al.  Minimally augmented Karlsruhe basis sets , 2011 .

[84]  P. Kollman,et al.  Application of RESP charges to calculate conformational energies, hydrogen bond energies, and free energies of solvation , 1993 .

[85]  Donald G Truhlar,et al.  Universal Solvation Model Based on the Generalized Born Approximation with Asymmetric Descreening. , 2009, Journal of chemical theory and computation.

[86]  C. Breneman,et al.  Determining atom‐centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis , 1990 .

[87]  H. Stoll,et al.  Energy-adjustedab initio pseudopotentials for the second and third row transition elements , 1990 .

[88]  P. Winget,et al.  Charge Model 3: A class IV Charge Model based on hybrid density functional theory with variable exchange , 2002 .

[89]  E. Gross,et al.  Density-Functional Theory for Time-Dependent Systems , 1984 .

[90]  P. Löwdin On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals , 1950 .

[91]  Alessandro Laio,et al.  D-RESP: Dynamically Generated Electrostatic Potential Derived Charges from Quantum Mechanics/Molecular Mechanics Simulations , 2002 .

[92]  More reliable partial atomic charges when using diffuse basis sets , 2002 .