Parameterization of charge model 3 for AM1, PM3, BLYP,and B3LYP

We have recently developed a new Class IV charge model for calculating partial atomic charges in molecules. The new model, called Charge Model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree-Fock theory and by hybrid density functional theory (DFT) based on the modified Perdew-Wang density functional with several basis sets. In the present article we extend CM3 to semiempirical molecular orbital theory, in particular Austin Model 1 (AM1) and Parameterized Model 3 (PM3), and to the popular BLYP and B3LYP DFT and hybrid DFT methods, respectively. For the BLYP extension, we consider the 6-31G(d) basis set, and for the B3LYP extension, we consider three basis sets: 6-31G(d), 6-31+G(d), and MIDI!6D. We begin with the previous CM3 strategy, which involves 34 parameters for 30 pairs of elements. We then refine the model to improve the charges in compounds that contain N and O. This modification, involving two new parameters, leads to improved dipole moments for amides, bifunctional H, C, N, O compounds, aldehydes, ketones, esters, and carboxylic acids; the improvement for compounds not containing N results from obtaining more physical parameters for carbonyl groups when the O=C-N conjugation of amides is addressed in the parameterization. In addition, for the PM3 method, we added an additional parameter to improve dipole moments of compounds that contain bonds between C and N. This additional parameter leads to improved accuracy in the dipole moments of aromatic nitrogen heterocycles with five-membered rings.     

Linear Approximation of Basis Set Orbital Exponents for Isoelectronic Series of Atoms

The orbital exponents of Slater type atomic orbitals (AOs) in isoelectronic series of atoms may be approximated by the linear dependence on the nuclear charge using a technique developed for optimization of AO basis sets in Hartree–Fock–Roothaan calculations. This approach yields the analytical Hartree–Fock wave functions for any ion in the isoelectronic atomic series without optimization of orbital exponents. The approximated linear equations for atomic orbital basis sets of B, C, O, and F in the ground state are presented as an example.     

IR, Raman and SERS spectra of 2-phenoxymethylbenzothiazole

The FT-IR and FT-Raman spectra of 2-phenoxymethylbenzothiazole were recorded and analyzed. The surface enhanced Raman scattering (SERS) spectrum was recorded in a silver colloid. The vibrational wavenumbers of the compound have been computed using the Hartree–Fock/6-31G* basis and compared with the experimental values. The appearance of the Ag–O stretching mode at 237 cm⁻¹ in the SERS spectrum along with theoretically calculated atomic charge density, leads us to suggest that the molecule is adsorbed through the oxygen atom with the molecular plane tilted on the colloidal silver surface. The direction of charge transfer contribution to SERS has been discussed from the frontier orbital theory.     

Density-functional theory and hybrid density-functional theory continuum solvation models for aqueous and organic solvents: universal SM5.43 and SM5.43R solvation models for any fraction of Hartree-Fock exchange

Hybrid density functional theory, which is a combined Hartree–Fock and density functional method, provides a simple but effective way to incorporate nonlocal exchange effects and static and dynamical correlation energy into an orbital-based theory with affordable computational cost for many important problems of gas-phase chemistry. The inclusion of a reaction field representing an implicit solvent in a self-consistent hybrid density functional calculation provides an effective and efficient way to extend this approach to problems of liquid-phase chemistry. In previous work, we have parameterized several models based on this approach, and in the present article, we present several new parameterizations based on implicit solvation models SM5.43 and SM5.43R. In particular, we extend the applicability of these solvation models to several combinations of the MPWX hybrid-density functional with various one-electron basis sets, where MPWX denotes a combination of Barone and Adamos modified version of Perdew and Wangs exchange functional, Perdew and Wangs correlation functional, and a percentage X of exact Hartree–Fock exchange. SM5.43R parameter optimizations are presented for the MPWX/MIDI!, MPWX/MIDI!6D, and MPWX/6-31+G(d,p) combinations with X=0 (i.e., pure density functional theory), 25, 42.8, and 60.6, and for MPWX/6-31G(d) and MPWX/6-31+G(d), with X=0, 42.8, and 60.6; this constitutes a total of 18 new parameter sets. [Note that parameter optimizations using MPW25/6-31G(d) and MPW25/6-31+G(d) were carried out in a previous SM5.43R parameterization.] For each of the five basis sets, we found no significant loss in the accuracy of the model when parameters averaged over the four values of X are used instead of the parameters optimized for a specific value of X. Therefore for each of the five basis sets used here, the SM5.43R and SM5.43 models are defined to have a single parameter set that can be used for any value of X between 0 and 60.6. The new models yield accurate free energies of solvation for a broad range of solutes in both water and organic solvents. On the average, the mean-unsigned errors, as compared with those from experiment, of the free energies of solvation of neutral solutes range from 0.50 to 0.55 kcal/mol and those for ions range from 4.5 to 4.9 kcal/mol. Since the SM5.43R model computes the free energy of solvation as a sum of bulk-electrostatic and non-bulk-electrostatic contributions, it may be used for detailed analysis of the physical effects underlying a calculation of the free energy of solvation. Several calculations illustrating the partitioning of these contributions for a variety of solutes in n-hexadecane, 1-octanol, and water are presented.Acknowledgement This work was supported by a Department of Defense Multidisciplinary University Research Initiative (MURI) grant managed by the Army Research Office and by the National Science Foundation.     

A comparative study of finite nucleus models for low-lying states of few-electron high-Z atoms

We studied low-lying states of lithium-like and beryllium-like ions with Z=80 and 100≤Z≤120 for differential effects due to variation of the nuclear charge density distribution. The latter was represented by exponential, Gauss-type, and Fermi-type models, standardized to a common rms radius. Numerical Hartree–Fock and Dirac–Fock–Coulomb calculations were performed. Changes in total energies due to the use of different models become increasingly important for high Z in relativistic approaches. Different models may even lead to different sequences of atomic states, and thus energy differences between those states may vary by an order of magnitude.     

VBSM: a solvation model based on valence bond theory

A new solvation model, called VBSM, is presented. The model combines valence bond (VB) theory with parameters determined for the SM6 solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). VBSM, like SM6, is based on the generalized Born (GB) approximation for bulk electrostatics and atomic surface tensions to account for cavitation, dispersion, and solvent structure (CDS). The solvation free energy of VBSM includes (i) a self-consistent polarization term obtained by using VB atomic charges in a GB reaction field with a VB self-consistent field procedure that minimizes the total energy of the system with respect to the valence bond orbitals and (ii) a geometry-dependent CDS term to account for deviations from bulk-electrostatic solvation. Test calculations for a few systems show that the liquid-phase partial atomic charges obtained by VBSM are in good agreement with liquid-phase charges obtained by charge model CM4 (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). Free energies of solvation are calculated for two prototype test cases, namely, for the degenerate S(N)2 reaction of Cl(-) with CH(3)Cl in water and for a Menshutkin reaction in water. These calculations show that the VBSM method provides a practical alternative to single-configuration self-consistent field theory for solvent effects in molecules and chemical reactions.     

Accuracy of free energies of hydration using CM1 and CM3 atomic charges

Absolute free energies of hydration (DeltaGhyd) have been computed for 25 diverse organic molecules using partial atomic charges derived from AM1 and PM3 wave functions via the CM1 and CM3 procedures of Cramer, Truhlar, and coworkers. Comparisons are made with results using charges fit to the electrostatic potential surface (EPS) from ab initio 6-31G* wave functions and from the OPLS-AA force field. OPLS Lennard-Jones parameters for the organic molecules were used together with the TIP4P water model in Monte Carlo simulations with free energy perturbation theory. Absolute free energies of hydration were computed for OPLS united-atom and all-atom methane by annihilating the solutes in water and in the gas phase, and absolute DeltaGhyd values for all other molecules were computed via transformation to one of these references. Optimal charge scaling factors were determined by minimizing the unsigned average error between experimental and calculated hydration free energies. The PM3-based charge models do not lead to lower average errors than obtained with the EPS charges for the subset of 13 molecules in the original study. However, improvement is obtained by scaling the CM1A partial charges by 1.14 and the CM3A charges by 1.15, which leads to average errors of 1.0 and 1.1 kcal/mol for the full set of 25 molecules. The scaled CM1A charges also yield the best results for the hydration of amides including the E/Z free-energy difference for N-methylacetamide in water.     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

The MIDI! basis set for quantum mechanical calculations of molecular geometries and partial charges

We present a series of calculations designed to identify an economical basis set for geometry optimizations and partial charge calculations on medium-size molecules, including neutrals, cations, and anions, with special emphasis on functional groups that are important for biomolecules and drug design. A new combination of valence basis functions and polarization functions, called the MIDI! basis set, is identified as a good compromise of speed and accuracy, yielding excellent geometries and charge balances at a cost that is as affordable as possible for large molecules. The basis set is optimized for molecules containing H, C, N, O, F, P, S, and Cl. Although much smaller than the popular 6-31G* basis set, in direct comparisons it yields more accurate geometries and charges as judged by comparison to MP2/cc-pVDZ calculations.     

Hydrogen bonding and dimeric self-association of 2-pyrrolidinone: An ab initio study

Ab initio calculations on the different associated structures of 2-pyrrolidinone with water and with itself were carried out using 3-21G and 6-31G^* basis sets at the Hartree–Fock level, including electron correlation using second-order Møller–Plesset perturbation theory. The calculated free energy changes for the intermolecular hydrogen bonded dimer and hydrated species indicated that the molecular systems with cyclic dimerization and association with two water molecules are dominant. The results are compared to the available experimental data in the literature.     

Various atomic charge calculation schemes of CoMFA on HIF‐1 inhibitors of moracin analogs

Selection of appropriate partial charges in a molecule is crucial to derive good quantitative structure–activity relationship models. In this work, several partial atomic charges were assigned and tested in a comparative molecular field analysis (CoMFA) models. Many CoMFA models were generated for a series of hypoxia inducible factor 1 (HIF‐1) inhibitors using various partial atomic charges including charge equalization, Mülliken population analysis (MPA), natural population analysis, and electrostatic potential (ESP)‐derived charges. These atomic charges were investigated at various theoretical levels such as empirical, semiempirical, Hartree–Fock (HF), and density functional theory (DFT). Among them, Merz‐Singh‐Kollman (MK) ESP‐derived charges at the level of HF/6‐31G* gave the highest predictive q² with experimental pIC₅₀ values. With this charge scheme, a detailed analysis of CoMFA model was performed to understand the electrostatic interactions between ligand and receptor. More elaborate charge calculation schemes such as HF and DFT correlated more strongly with activity than empirical or semiempirical schemes. The choice of optimization methods was important. As geometries were fully optimized at the given levels of theory, the aligned structures were different. They differed considerably, especially for the flexible parts. This was likely the source of the substantial variation of q² values, even when the same steric factor was considered without electrostatic parameters. ESP‐derived charges were most appropriate to describe CoMFA electrostatic interactions among MPA, NBA, and ESP charges. Overall q² values vary considerably (0.8–0.5) depending on the charge schemes applied. The results demonstrate the need to consider more appropriate atomic charges rather than default CoMFA charges. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A fast empirical GAFF compatible partial atomic charge assignment scheme for modeling interactions of small molecules with biomolecular targets

We report here a new and fast approach [Transferable Partial Atomic Charge Model (TPACM4)-upto four bonds] for deriving the partial atomic charges of small molecules for use in protein/DNA-ligand docking and scoring. We have created a look-up table of 5302 atom types to cover the chemical space of C, H, O, N, S, P, F, Cl, and Br atoms in small molecules together with their quantum mechanical RESP fit charges. The atom types defined span diverse plausible chemical environments of each atom in a molecule. The partial charge on any atom in a given molecule is then assigned by a reference to the look-up table. We tested the sensitivity of the TPACM4 partial charges in estimates of hydrogen bond dimers energies, solvation free energies and protein-ligand binding free energies. An average error ±1.11 kcal/mol and a correlation coefficient of 0.90 is obtained in the calculated protein-ligand binding free energies vis-à-vis an RMS error of ±1.02 kcal/mol and a correlation coefficient of 0.92 obtained with RESP fit charges in comparison to experiment. Similar accuracies are realized in predictions of hydrogen bond energies and solvation free energies of small molecules. For a molecule containing 50-55 atoms, the method takes on the order of milliseconds on a single processor machine to assign partial atomic charges. The TPACM4 programme has been web-enabled and made freely accessible at http://www.scfbio-iitd.res.in/software/drugdesign/charge.jsp.     

Optimized Atomic Partial Charges and Radii Defined by Radical Voronoi Tessellation of Bulk Phase Simulations

We present a novel method for the computation of well-defined optimized atomic partial charges and radii from the total electron density. Our method is based on a two-step radical Voronoi tessellation of the (possibly periodic) system and subsequent integration of the total electron density within each Voronoi cell. First, the total electron density is partitioned into the contributions of each molecule, and subsequently the electron density within each molecule is assigned to the individual atoms using a second set of atomic radii for the radical Voronoi tessellation. The radii are optimized on-the-fly to minimize the fluctuation (variance) of molecular and atomic charges. Therefore, our method is completely free of empirical parameters. As a by-product, two sets of optimized atomic radii are produced in each run, which take into account many specific properties of the system investigated. The application of an on-the-fly interpolation scheme reduces discretization noise in the Voronoi integration. The approach is particularly well suited for the calculation of partial charges in periodic bulk phase systems. We apply the method to five exemplary liquid phase simulations and show how the optimized charges can help to understand the interactions in the systems. Well-known effects such as reduced ion charges below unity in ionic liquid systems are correctly predicted without any tuning, empiricism, or rescaling. We show that the basis set dependence of our method is very small. Only the total electron density is evaluated, and thus, the approach can be combined with any electronic structure method that provides volumetric total electron densities—it is not limited to Hartree–Fock or density functional theory (DFT). We have implemented the method into our open-source software tool TRAVIS.     

Charge distributions for molecular dynamics simulations from self-consistent polarization method

Partial atomic charges are important force field parameters. They are usually computed by applying quantum-chemical calculations and the assumed population scheme. In this study polarization consistent scheme of deriving a charge distribution inside solute molecule is proposed. The environment effect is explicitly taken into account by distributing solvent molecules around the solute target. The performed analysis includes a few computational schemes (HF, MP2, B3LYP, and M026X), basis sets (cc-pvnz, n = 2, 3, …, 6), and electrostatically derived charge distributions (KS, CHELP, CHELPG, and HLY). It is demonstrated that the environment effect is very important and cannot be disregarded. The second solvation shell should be included to achieve the charge convergence. Huge corrections to charge distribution are due to induction and dispersion. The B3LYP/cc-pvqz level of theory is recommended for deriving the charges within self-consistent polarization scheme.     

Can STO basis sets do a good job in evaluating molecular electromagnetic properties? I. First hyperpolarizability of H2O, CH4, and NH3 according to the TDHF theory

The performance of STO basis sets for the ab initio estimation of the nonlinear electromagnetic response properties of molecules, in terms of a time-dependent Hartree–Fock procedure, is investigated. Applications to the case of the first dynamic hyperpolarizability of three simple polyatomics (H₂O, CH₄, NH₃) adopting several extended basis sets are reported and discussed. Independent estimates for the observables investigated obtained by the same approach in terms of Gaussian basis sets are confronted with our findings in the search for recipes of possible utility.Acknowledgements This research has been partially supported by funds provided by the Italian Consiglio Nazionale delle Ricerche (contribution n. CTB 00.00650.PF34) and Pisa University (fondi di Ateneo, ex 60%, years 2001–2002).Contribution to the Jacopo Tomasi Honorary Issue     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Ab initio and density functional studies on the structure and vibrational spectra of 2-hydroxy-1,4-naphthoquinone-1-oxime derivatives

Structure and vibrational frequencies of lawsoneoxime and its C₃-substituted (R=CH₃, NH₂, Cl, NO₂) derivatives in keto and nitrosophenol forms have been obtained employing the Hartree–Fock and density functional methods. Charge distributions in different conformers have been studied using the molecular electrostatic potential topography as a tool. For all these derivatives except for nitrolawsoneoxime the amphi conformer in the keto form is predicted to be of lowest energy, which can partly be attributed to hydrogen bonding through the oximino nitrogen. In the nitro derivative, however, the preference to form a six membered ring owing to O–H–O hydrogen-bonded interactions makes the anti conformer (keto) the stablest. Further one of the nitrosophenol conformers of nitrolawsoneoxime turns out to be very close in energy (0.21 kJ mol^–1 higher) to this anti conformer. The consequences of hydrogen bonding on charge distribution and vibrational spectra are discussed.     

Electron localizability indicator for correlated wavefunctions. II Antiparallel-spin pairs

The electron localizability indicator for anti parallel-spin pairs is closely associated with the correlation of the motion of opposite-spin electrons. At the Hartree–Fock level this functional is constant throughout the whole space, whereas for correlated wavefunctions structures resembling atomic shells and the bonding situation emerges.