Geometry-dependent atomic charges: Methodology and application to alkanes,aldehydes, ketones,and amides

A general methodology for deriving geometry-dependent atomic charges is presented. The main ingredient of the method is a model that describes the molecular dipole moment in terms of geometry-dependent point charges. The parameters of the model are determined from ab initio calculations of molecular dipole moments and their Cartesian derivatives at various molecular geometries. Transferability of the parameters is built into the model by fitting ab initio calculations for various molecules simultaneously. The results show that charge flux along the bonds is a major contributing factor to the geometry dependence of the atomic charges, with additional contributions from fluxes along valence angles and adjacent bonds. Torsion flux is found to be smaller in magnitude than the bond and valence angle fluxes but is not always unimportant. A set of electrostatic parameters is presented for alkanes, aldehydes, ketones, and amides. Transferability of these parameters for a host of molecules is established to within 3 ?5% error in the predicted dipole moments. A possible extension of the method to include atomic dipoles is outlined. With the inclusion of such atomic dipoles and with the set of transferable point charges and charge flux parameters, it is demonstrated that molecular electrostatic potentials as well as electrostatic forces on nuclei can be reproduced much better than is possible with other models (such as potential derived charges). © 1995 by John Wiley & Sons, Inc.     

An atomic charge-charge flux-dipole flux atom-in-molecule decomposition for molecular dipole-moment derivatives and infrared fundamental intensities

The molecular dipole moment and its derivatives are determined from atomic charges, atomic dipoles, and their fluxes obtained from AIM formalism and calculated at the MP2(FC)/6-311++G(3d,3p) level for 16 molecules: 6 diatomic hydrides, CO, HCN, OCS, CO2, CS2, C2H2, C2N2, H2O, H2CO, and CH4. Root-mean-square (rms) errors of 0.052 D and 0.019 e are found for the dipole moments and their derivatives calculated using AIM parameters when compared with those obtained directly from the MP2(FC)/6-311++G(3d,3p) calculations and 0.097 D and 0.049 e when compared to the experimental values. The major deviations occur for the NaH, HF, and H2O molecules. Parallel polar tensor elements for the diatomic and linear polyatomic molecules, except H2, HF, LiH, and NaH, have values resulting from cancellations of substantial contributions from atomic charge fluxes and atomic dipole fluxes. These fluxes have a large negative correlation coefficient, -0.97. IR fundamental intensity sums for CO, HCN, OCS, CO2, CS2, C2H2, C2N2, H2CO, and CH4 calculated using AIM charges, charge fluxes, and atomic dipole fluxes have rms errors of 14.9 km mol(-1) when compared with sums calculated directly from the molecular wave function and 36.2 km mol(-1) relative to experimental values. The classical model proposed here to calculate dipole-moment derivatives is compared with the charge-charge flux-overlap model long used by spectroscopists for interpreting IR vibrational intensities. The utility of the AIM atomic charges and dipoles was illustrated by calculating the forces exerted on molecules by a charged particle. AIM quantities were able to reproduce forces due to a +0.1 e particle over a 3-8-A separation range for the CO and HF molecules in collinear and perpendicular arrangements. These results show that IR intensities do contain information relevant to the study of intermolecular interactions.     

ChelpG and QTAIM atomic charge and dipole models for the infrared fundamental intensities of the fluorochloromethanes

ChelpG atomic charges and dipoles and the charge–charge flux–dipole flux (CCFDF) model have been used to quantitatively estimate the fundamental infrared intensities of the fluorochloromethanes. Since the ChelpG calculational procedure includes the constraint that the atomic charges and dipoles reproduce the equilibrium dipole moments the model results in accurate intensity values that have a root mean square error of 0.7 km mol^?1 compared to those determined directly from the MP2/6-311G++(3d,3p) electronic density and 23.1 km mol^?1 relative to the experimental intensities. Although these ChelpG results for total dipole moment derivatives are almost the same as those obtained previously using QTAIM (Quantum Theory of Atoms in Molecules) atomic charges and dipoles in the CCFDF model, their charge, charge flux and dipole flux contributions are completely different. Whereas the contributions calculated using the QTAIM parameters have values following expectations based on electronegativity concepts this is not true for those obtained from the ChelpG parameters. Mean dipole moment derivatives determined from experimental fundamental infrared intensities are compared with the ChelpG and QTAIM atomic charges. Furthermore, Generalized Atomic Polar Tensor Charges (GAPT) are found to need correction for their dynamic contributions if they are to be used as static atomic charges.     

A charge–charge flux–dipole flux decomposition of the dipole moment derivatives and infrared intensities of the AB3 (A = N,P; B = H,F) molecules

The quantum theory of atoms in molecules (AIM) has been used to decompose dipole moment derivatives and fundamental infrared intensities of the AB₃ (A = N,P; B = H,F) molecules into charge–charge flux–dipole flux (CCFDF) contributions. Calculations were carried out at the MP2(FC)/6-311++G(3d,3p) level. Infrared intensities calculated from the AIM atomic charges and atomic dipoles are within 13.8 km mol⁻¹ of the experimental values not considering the NH₃ and PH₃ stretching vibrations for which the experimental bands are severely overlapped. Group V atomic dipoles are very important in determining the molecular dipole moments of NF₃, PH₃ and PF₃ although the atomic charges account for almost all of the NH₃ molecular moment. Dipole fluxes on the Group V atom are important in determining the stretching band intensities of all molecules whereas they make small contributions to the bending mode intensities. Consideration of dipole flux contributions from the terminal atoms must also be made for accurately describing the intensities of all these molecules. As expected from a simple bond moment model, charge contributions dominate for most of the NH₃, NF₃, and PF₃ dipole moment derivatives and intensities. Charge flux and dipole flux contributions are very substantial for all the PH₃ vibrations, cancelling each other for the stretching modes and reinforcing one another for the bending modes.     

Transfer of molecular property tensors in cartesian coordinates: A new algorithm for simulation of vibrational spectra

A direct transfer of Cartesian molecular force fields (FF) and electric property tensors is tested on model systems and compared to transfer in internal coordinates with an aim to improve simulation of vibrational spectra for larger molecules. This Cartesian transformation can be implemented easily and offers greater flexibility in practical computations. It can be also applied for transfer of anharmonic derivatives. The results for model calculations of the force field and vibrational frequencies for N-methylacetamide show that our method removes errors associated with numerical artifacts caused by nonlinearity of the otherwise required Cartesian to internal coordinate transformation. For determination of IR absorption and vibrational circular dichroism intensities, atomic polar and axial tensors were also transferred in the Cartesian representation. For the latter, which are dependent upon the magnetic dipole operator, a distributed origin gauge is used to avoid an origin dependence. Comparison of the results of transferring ab initio FF and intensity parameters from an amide dimer fragment onto a tripeptide with those from a conventionally determined tripeptide FF document some limitations of the transfer method and its possible applications in the vibrational spectroscopy. Finally, application to determination of the FF and spectra for helical heptapeptide are presented and compared to experimental results. © 1997 by John Wiley & Sons, Inc.     

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.     

QTAIM charge-charge flux-dipole flux models for the infrared fundamental intensities of the fluorochloromethanes

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the fluoro-, chloro-, and fluorochloromethanes are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square (rms) errors of 0.01 D and 5.6 km mol(-1) are found for the dipole moments and fundamental IR intensities calculated using QTAIM parameters when compared with those obtained directly from the MP2/6-311++(3d,3p) calculations and 0.04 D and 23.1 km mol(-1) when compared with the experimental values. Charge, charge flux, and dipole flux contributions are calculated for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.92 is calculated between the charge flux and dipole flux contributions and indicates that electron transfer from one side of the molecule to the other during vibrations is accompanied by relaxation with electron density polarization in the opposite direction. The CF, CCl, and CH stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions. Although the FCF and ClCCl deformation normal modes can also be discriminated from one another based on the sizes and signs of these contributions, some HCH deformations have contributions that are similar to those for some of the ClCCl deformations.     

Variation of atomic charges during proton transfer in hydrogen bonds

The point atomic charges in a number of ionic H-bonded systems are studied by ab initio calculations as functions of the proton transfer coordinate. In the proton-bound complexes of water–water, ammonia–ammonia, formamide–water, formamide–ammonia, and dimethylether–ammonia, the net atomic charges were obtained using Mulliken population analysis and from the diagonal elements of the atomic polar tensors calculated at the HF/4–31G and MP2/6–31 + G** levels. The dependence of the atomic charges upon the coordinate of the transferring proton was found to be close (within an error of 0.02 e) to a linear function for intermolecular distances in the 2.5–2.8 Å range. The obtained charge and charge flux dependencies highlight the electron redistribution during the proton transfer process and provide insights into the source of the high infrared (IR) intensities of stretching modes of N? H and O? H bonds undergoing hydrogen bonding. © 1994 by John Wiley & Sons, Inc.     

A polarizable electrostatic model of the N‐methylacetamide dimer

Our previously developed polarizable electrostatic model is applied to isolated N‐methylacetamide (NMA) and to three hydrogen‐bonded configurations of the NMA dimer. Two versions of the model are studied. In the first one (POL1), polarizability along the valence bonds is described by induced bond charge increments, and polarizability perpendicular to the bonds is described by cylindrically isotropic induced atomic dipoles. In the other version (POL2), the induced bond charge increments are replaced by induced atomic dipoles along the bonds. The parameterization is done by fitting to ab initio MP2/6‐31++G(d,p) electric potentials. The polarizability parameters are determined by subjecting the NMA molecule to various external electric fields. POL1 turns out to be easier to optimize than POL2. Both models reproduce well the ab initio electric potentials, molecular dipole moments, and molecular polarizability tensors of the monomer and the dimers. Nonpolarizable models are also investigated. The results show that polarization is very important for reproducing the electric potentials of the studied dimers, indicating that this is also the case in hydrogen bonding between peptide groups in proteins. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1933–1943, 2001     

Polarization energy gradients in combined quantum mechanics, effective fragment potential, and polarizable continuum model calculations

A method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a self-consistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFPPCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges.     

Dipole preserving and polarization consistent charges

A method for estimating dipole preserving and polarization consistent (DPPC) charges is described, which reproduces exactly the molecular dipole moment as well as the local, atomic hybridization dipoles determined from the corresponding wave function and can yield accurate molecular polarization. The method is based on a model described by Thole and van Duijnen and a new feature is introduced to treat molecular polarization. Thus, the DPPC method offers a convenient procedure to describe molecular polarization in applications using semiempirical models and ab initio molecular orbital theory with relatively small basis functions such as 6‐31+G(d,p) or without inclusion of electron correlation; these methods tend to underestimate molecular polarizability. The trends of the DPPC partial atomic charges are found to be in good accord with those of the CM2 model, a class IV charge analysis method that has been used in a variety of applications. The DPPC method is illustrated to mimic the correct molecular polarizability in a water dimer test case and in water‐halide ion complexes using the explicit polarization (X‐Pol) potential with the Austin model 1 Hamiltonian. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A simple model of hydrogen bonding with particular application to trends in hydrogen‐bonded dimers

A simple model has been proposed to explain trends in the computed interaction energy, bond length changes, frequency shifts and infrared intensities for the chlorofluoromethanes CF_nCl_mH, FH and FArH on complexation with the isoelectronic diatomics BF, CO, N₂ and the rare gas atoms Kr, Ar, Ne to form a series of linear or nearly linear hydrogen‐bonded complexes. The dipole moment derivative of the proton donor (with respect to the stretching coordinate) and the chemical hardness of the hydrogen‐bonded atom of the proton acceptor are identified as two useful parameters for rationalizing the changes in some of the molecular properties of the proton donor when the hydrogen bond is formed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes

A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler–Lagrange equations for molecular fragments ϕ_n described by internal parameters ζ_n. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k_a, adiabatic force constants. Minimization of the kinetic energy of the vibrating fragment ϕ_n yields the adiabatic mass m_a (corresponding to 1/G_nn of Wilson's G matrix) and, by this, adiabatic frequencies ω_a. Adiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 : 1–9, 1998     

Harmonic IR spectra from empirical force fields and ab initio dipole-moment derivatives

Infrared spectra simulations require ab initio techniques to get reliable intensities. On the other hand, recent force fields can provide accurate molecular geometries and frequencies. Therefore, it is suggested that these new force fields could be used to simulate infrared spectra, dipole-moment surfaces being described at high levels of theory in order to get satisfactory intensities. As pointed out, for a system with N atoms, the cost of such a simulation would be reduced N-fold with respect to standard quantum approaches. Preliminary calculations based on this scheme are reported here. Encouraging results are obtained since no significant lost of accuracy is noted on going from the ab initio to the molecular mechanics potential energy surface. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 705–711, 1998     

Ab initio calculations of the ultraviolet resonance Raman spectra of uracil

An equation been derived to calculate, ab initio, the frequencies and intensities of a resonant Raman spectrum from the transform theory of resonance Raman scattering. This equation has been used to calculate the intensities of the ultraviolet resonance Raman spectra from the first π-π* excited state of uracil and 1,3-dideuterouracil. The protocol for this calculation is as follows: (1) The force constant matrix elements in Cartesian coordinate space, the vibrational frequencies, and the minimum energy ground and excited state geometries of the molecule are calculated ab initio using the molecular orbital program Gaussian 92, (2) the force constants in Cartesian coordinates are transformed into force constants in the space of a set of 3N – 6 nonredundant symmetrized internal coordinates, (3) the G matrix is constructed from the energy minimized ground state Cartesian coordinates and the GFL = LΛ eigenvalue equation is solved in internal coordinate space, (4) the elements of the L and L^?1 matrices are calculated, (5) the changes in all of the internal coordinates in going from the ground to the excited state are calculated, and (6) these results are used in combination with the transform theory of resonance Raman scattering to calculate the relative intensities of each of the 3N – 6 vibrations as a function of the exciting laser frequency. There are no adjustable parameters in this calculation, which reproduces the experimental frequencies and intensities with remarkable fidelity. This indicates that the Dushinsky rotation of the modes in the excited state of these molecules is not important and that the simplest form of the transform theory is adequate. © 1995 John Wiley & Sons, Inc.     

Characterization of intramolecular hydrogen bonds by atomic charges and charge fluxes

The electronic charge redistribution and the infrared intensities of the two types of intramolecular hydrogen bonds, O-H···O and O-H···π, of o-hydroxy- and o-ethynylphenol, respectively, together with a set of related intermolecular hydrogen bond complexes are described in terms of atomic charges and charge fluxes derived from atomic polar tensors calculated at the B3LYP/cc-pVTZ level of theory. The polarizable continuum model shows that both the atomic charges and charge fluxes are strongly dependent on solvent. It is shown that their values for the OH bond in an intramolecular hydrogen bond are not much different from those for the "free" OH bond, but the changes are toward the values found for an intermolecular hydrogen bond. The intermolecular hydrogen bond is characterized not only by the decreased atomic charge but also by the enlarged charge flux term of the same sign producing thus an enormous increase in IR intensity. The overall behavior of the charges and fluxes of the hydrogen atom in OH and ≡CH bonds agree well with the observed spectroscopic characteristics of inter- and intramolecular hydrogen bonding. The main reason for the differences between the two types of the hydrogen bond lies in the molecular structure because favorable linear proton donor-acceptor arrangement is not possible to achieve within a small molecule. The calculated intensities (in vacuo and in polarizable continuum) are only in qualitative agreement with the measured data.     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

Molecular mobility of substituted poly(p-phenylenes) characterized by a range of polymer relaxation techniques

The free volume and related mobility properties of substituted poly(p-phenylene) polymers are examined. The techniques used range from positron annihilation, dielectric relaxation, and dynamic mechanical spectroscopy to thermally stimulated currents. Fractional free volume is determined for the samples with different substituted side groups and related to the glass transition temperature. Bulkier groups lead to a greater fractional free volume and lower glass transition temperatures. Comparison of molecular relaxation times using the different characterization techniques demonstrates that there is strong coupling between motion of the main chain and the side groups, on which the dipoles reside. Intermolecular coupling between the main chains at the primary relaxation is shown in this work to be related to the nature of the side chains and resultant free volume, as are the temperature locations of local, secondary relaxations. A qualitative model describing the effect of regiochemistry on the motions and packing of these materials is also proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1465–1481, 1998