An overlap criterion for selection of core orbitals

 An overlap criterion is defined that connects the identification of core orbitals in a molecular system, which can be problematic, to that in isolated atoms, which is well defined. This approach has been tested on a variety of troublesome systems that have been identified in the literature, including molecules containing third-row main-group elements, and is shown to remove errors of up to 100 kcal/mol arising from an inconsistent treatment of core orbitals at different locations on a potential-energy surface. For some systems and choices of core orbitals, errors as large as 19 kcal/mol can be introduced even when consistent sets of orbitals are frozen, and the new method is shown to identify these cases of substantial core–valence mixing. Finally, even when there is limited core–valence mixing, the frozen-core approximation can introduce errors of more than 5 kcal/mol, which is much larger than the presumed accuracy of models such as G2 and CBS-QB3. The source of these errors includes interatomic core–core and core–valence dispersion forces. Received: 31 August 2001 / Accepted: 11 October 2001 / Published online: 9 January 2002     

The inclusion of electrostatic hydration energies in molecular mechanics calculations

Summary The problem of including solvent effects in molecular mechanics calculations is discussed. It is argued that the neglect of charge-solvent (solvation) interactions can introduce significant errors. The finite difference Poisson-Boltzmann (FDPB) method for calculating electrostatic interactions is summarized and is used as a basis for introducing a new pairwise energy term which accounts for charge-solvent interactions. This term acts between all pairs of atoms usually considered in molecular mechanics calculations and can be easily incorporated into existing force fields. As an example, a parameterization is developed for the CHARMm force field and the results compared to the predictions of the FDPB method. An approach to the realistic incorporation of solvent screening into force fields is also outlined.     

Computation of hydration free energies of organic solutes with an implicit water model

A new approach for computing hydration free energies DeltaG(solv) of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component DeltaG(el) of DeltaG(solv) and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (DeltaG(nel)). The novel features include the following: (a) two different cavities are used for treating DeltaG(el) and DeltaG(nel). For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of DeltaG(nel) is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed.     

Conformation-dependent intermolecular interaction energies of the triphosphate anion with divalent metal cations. Application to the ATP-binding site of a binuclear bacterial enzyme. A parallel quantum chemical and polarizable molecular mechanics investigation

We have explored the conformation-dependent interaction energy of the triphosphate moiety, a key constituent of ATP and GTP, with a closed-shell divalent cation, Zn2+, used as a probe. This was done using the SIBFA polarizable molecular mechanics procedure. We have resorted to a previously developed approach in which triphosphate is built out from its elementary constitutive fragments, and the intramolecular, interfragment, interaction energies are computed simultaneously with their intermolecular interactions with the divalent cation. This approach has enabled reproduction of the values of the intermolecular interaction energies from ab initio quantum-chemistry with relative errors <3%. It was extended to the complex of a nonhydrolyzable analog of ATP with the active site of a bacterial enzyme having two Mg2+ cations as cofactors. We obtained following energy-minimization a very close overlap of the ATP analog over its position from X-ray crystallography. For models of the ATP analog-enzyme complex encompassing up to 169 atoms, the values of the SIBFA interaction energies were found to match their DFT counterparts with relative errors of <2%.     

Impact of Mn on the solution enthalpy of hydrogen in austenitic Fe‐Mn alloys: A first‐principles study

Hydrogen interstitials in austenitic Fe‐Mn alloys were studied using density‐functional theory to gain insights into the mechanisms of hydrogen embrittlement in high‐strength Mn steels. The investigations reveal that H atoms at octahedral interstitial sites prefer a local environment containing Mn atoms rather than Fe atoms. This phenomenon is closely examined combining total energy calculations and crystal orbital Hamilton population analysis. Contributions from various electronic phenomena such as elastic, chemical, and magnetic effects are characterized. The primary reason for the environmental preference is a volumetric effect, which causes a linear dependence on the number of nearest‐neighbour Mn atoms. A secondary electronic/magnetic effect explains the deviations from this linearity. © 2014 Wiley Periodicals, Inc.     

Quantum Monte Carlo calculations of bond dissociation energies for some nitro and amino molecules

Bond dissociation energies (BDEs) for some nitro or amino contained prototypical molecules in energetic materials are computed by fixed‐node diffusion quantum Monte Carlo method. The nodes are determined from a Slater determinant calculated within density functional theory at the B3LYP/6‐311G** level. The possible errors, the nodal error, and the cancellation of nodal errors in calculating BDE are discussed, and the accuracy is compared with other available ab initio computations and experimental results. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

A smooth permittivity function for Poisson–Boltzmann solvation methods

This work introduces a continuous smooth permittivity function into Poisson–Boltzmann techniques for continuum approaches to modeling the solvation of small molecules and proteins. The permittivity function is derived using a Gaussian method to describe volume exclusion. The new method allows a rigorous determination of solvent forces within a grid‐based technology. The generality of approach is demonstrated by considering a range of applications for small molecules and macromolecules. We also present a very complete statistical analysis of grid errors, and show that the accuracy of our Gaussian‐based method is improved over standard techniques. The method has been implemented in a new code called ZAP, which is freely available to academic institutions. 1 © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 608–640, 2001     

Some applications of local density functional theory to the calculation of reaction energetics

Summary We report the results of a local density functional investigation of the energetics of some isomerization reactions, involving the conversions of several unsaturated systems to highly strained molecules related to triprismane and tetrahedrane. The program DMol was used at the DNP level to compute the activation barriers and total energy changes associated with these processes. We also show, for more than 70 first- and second-row atoms and molecules, that the errors (non-local corrections) in their energies correlate very well with the number of electrons, within isonuclear series. This should provide a useful empirical means for improving dissociation energies obtained within the local approximation.     

Quantum chemical calculations of geometries and gas‐phase deprotonation energies of linear polyyne chains

The molecular geometries of polyyne chains H(CC)_nH with their deprotonated forms (anions) have been optimized using ab initio LCAO‐SCF molecular orbital (MO) method and density functional theory at different basis set levels. The polyynes possess a series of alternating single and triple bonds. On the theoretical side the persistence of bond alternation and the effect of chain lengthening on the individual bond length in linear conjugated polyyne chains has been investigated. The common conclusion has been drawn that the bond alternation will persist and that bond length variation will be small. The triple bond length increases progressively toward the asymptotic limits as the value of n increases progressively. If the split‐valence basis set was employed, the total charges obtained using the Mulliken population analysis yielded unrealistic values. Using natural bond orbital (NBO) analysis or Bader's analysis, the net charges of the individual atoms converge very rapidly to their asymptotic limits, and the central atoms have almost zero charges in contrast to the Mulliken population analysis results. The reliability of deprotonation energies of neutral polyynes and their monoanionic derivatives calculated from the differences in molecular energy of the parent chains and the corresponding anions E(H(CC)_n⁻)–E(H(CC)_nH) and E(⁻(CC)_n⁻)–E(H(CC)_n⁻) was tested for different basis sets. The increase of the number of CC bonds in the chain decreases these differences asymptotically. The studied compounds are the best available building blocks in bimetallic compounds with useful properties in molecular electronics and nonlinear optics. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 73–85, 2001     

Relativistic theory of an inhomogeneous electron liquid in relation to atomic binding energies

Experimentally determined ionization potentials in the literature are used to plot the binding energies for neutral atoms as a function of atomic number Z for Z?=?2–30, 32, 36, 42. From this pretty smooth plot we have subtracted non-relativistic Hartree–Fock binding energies, using both available numerical values and the almost analytical result, based on the non-relativistic Thomas–Fermi statistical theory valid for large Z. The difference is still relatively smooth. For Mo, with Z?=?42, the difference is about 70 atomic units. This difference is then analyzed using first relativistic theory of an inhomogeneous electron liquid and then the Local Density Approximation (LDA), and for Mo their results yield approximately 88 and 67 atomic units respectively. We infer that a highly accurate relativistic many-electron theory will therefore be needed before reliable electron correlation energies can be extracted from the experimental binding energies for atoms heavier than Argon. This fact has prompted us to use available LDA calculations to confront three theoretical predictions of the Z dependence of non-relativistic electron correlation energies at large Z.     

A new property of atom energies

A proof is given that the total nuclear‐electron attraction energy should be constant for all the light atoms, when calculated by various trial wave functions. If hydrogenic wave functions for effective nuclear charges are picked as standards, it is easy to calculate the value of this energy. This constraint should be added to the usual constraints (minimum energy and the virial theorem) of the variation method. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

New energy terms for reduced protein models implemented in an off‐lattice force field

Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (C_α atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229–1242, 2001     

Applying the concepts of density functional theory to simple systems

Equations are derived for the chemical potential and local hardness of the ground states of helium and the related two electron ions. With these properties it is possible to correct the energies of the simple single‐zeta wave functions to the nearly exact values. The calculations are simple for these simple systems. In principle, it is possible to extend this method to all atoms and molecules. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical investigation on sulfur‐containing chelating resin‐divalent metal complexes

The complex structures and interactions of sulfur‐containing chelating resin poly[4‐vinylbenzyl‐(2‐hydroxyethyl)]sulfide (PVBS), poly[4‐vinylbenzyl‐(2‐hydroxyethyl)]sulfoxide (PVBSO), and poly[4‐vinylbenzyl‐(2‐hydroxyethyl)]sulfone (PVBSO₂) with divalent metal chlorides (Cu(II), Ni(II), Zn(II), Cd(II), and Pd(II)) were investigated theoretically. Results indicate that PVBS tends to coordinate with metal ions by sulfur and oxygen atoms forming five‐membered ring chelating complexes; while PVBSO and PVBSO₂ prefer to interact with metal ions by the oxygen atom of the sulfoxide or sulfone and hydroxyl group to form six‐membered ring chelating compounds. Theoretical calculations reveal that sulfur atoms of PVBS are the main contributor when coordinate with metal ions, while oxygen atoms also take part in the coordination with Cu(II), Zn(II), and Cd(II). As for PVBSO, the oxygen atoms of sulfoxide group play a key role in the coordination, but sulfur and hydroxyl oxygen also participate in the coordination. Similarly, sulfone group oxygen atoms of PVBSO₂ dominate the coordination of Ni(II), Cu(II), and Pd(II), while the affinities of Zn(II) and Cd(II) are mainly attributed to the hydroxyl oxygen atoms. The computational results are in good agreement with the XPS analysis. Combined the theoretical and experimental results, further understanding of the structural information on the complexes was achieved and the adsorption mechanism was confirmed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

NDDO MO Calculations

Siegbahn's potential model as extended by Ellison et al. is used with density matrix elements calculated by the NDDO/2 procedure, to correlate the K-shell binding energy shifts of C, N and O atoms in a few molecules containing only the first-row atoms. The correlation is not superior to that obtained with the CNDO/2 method when only the monopole term is retained in calculating the Madelung potential energy. However, the results are in excellent agreement with experiment when the two-parameters model including the dipole and quadrupole terms is used.     

Temperature dependence of the HO2 + ClO reaction. 2. Reaction kinetics using the discharge-flow resonance-fluorescence technique

The total rate coefficient, k3, for the reaction HO2 + ClO --> products has been determined over the temperature range of 220-336 K at a total pressure of approximately 1.5 Torr of helium using the discharge-flow resonance-fluorescence technique. Pseudo-first-order conditions were used with both ClO and HO2 as excess reagents using four different combinations of precursor molecules. HO2 molecules were formed by using either the termolecular association of H atoms in an excess of O2 or via the reaction of F atoms with an excess of H(2)O(2). ClO molecules were formed by using the reaction of Cl atoms with an excess of O3 or via the reaction of Cl atoms with Cl(2)O. Neither HO2 nor ClO were directly observed during the course of the experiments, but these species were converted to OH or Cl radicals, respectively, via reaction with NO prior to their observation. OH fluorescence was observed at 308 nm, whereas Cl fluorescence was observed at approximately 138 nm. Numerical simulations show that under the experimental conditions used secondary reactions did not interfere with the measurements; however, some HO2 was lost on conversion to OH for experiments in excess HO2. These results were corrected to compensate for the simulated loss. At 296 K, the rate coefficient was determined to be (6.4 +/- 1.6) x 10(-12) cm3 molecule(-1) s(-1). The temperature dependence expressed in Arrhenius form is (1.75 +/- 0.52) x 10-12 exp[(368 +/- 78)/T] cm3 molecule(-1) s(-1). The Arrhenius expression is derived from a fit weighted by the reciprocal of the measurement errors of the individual data points. The uncertainties are cited at the level of two standard deviations and contain contributions from statistical errors from the data analysis in addition to estimates of the systematic experimental errors and possible errors from the applied model correction.     

Conformational dependence of electrostatic potential-derived charges: Studies of the fitting procedure

Atomic monopole “point charges” are routinely determined through a least squares fit to molecular electrostatic potentials [potential-derived (PD) charges]. Previously, it has been shown that these charges vary with variation in molecular conformation. Also, it has been observed that these swings in charges are highly correlated between neighboring atoms. Here, we examine the least squares variance–covariance data matrices for a set of data in the literature and find further indications of high colinearity within the data. These colinearities effectively reduce the dimensionality of the data to a value well below the number of atoms in the molecules. This suggests that the data is not of sufficient dimensionality to support calculation of the charges for all of the atoms in a statistically significant way. We experiment with fixing the charges of atoms whose PD charges reflect large errors in the fit. The resulting estimates of fit of the remaining charges are little degraded from the estimates of fit when the charges of all of the atoms are fit. In addition, the charges that are fit take what would be considered more reasonable and “chemically intuitive” values, often of smaller magnitude. Although most of the free charges continue to vary with molecular conformation, their range is no larger than when all charges were fit and, in some cases, the ranges of the charges for the fit atoms is actually reduced over those that are found when all of the atoms take part in the fitting procedure. The errors of fit are lower and the unconstrained charges appear more reasonable when more chemically “reasonable” charges are used for the fixed values. This suggests that in many cases charges are transferable between molecules. Further, it shows a way to justifiably reduce the large fluctuations in PD charges that occur with variations in conformation. © 1993 John Wiley & Sons, Inc.     

Monte Carlo configuration interaction applied to multipole moments,ionization energies,and electron affinities

The method of Monte Carlo configuration interaction (MCCI) (Greer, J. Chem. Phys. 1995a, 103, 1821; Tong, Nolan, Cheng, and Greer, Comp. Phys. Comm. 2000, 142, 132) is applied to the calculation of multipole moments. We look at the ground and excited state dipole moments in carbon monoxide. We then consider the dipole of NO, the quadrupole of N₂ and of BH. An octupole of methane is also calculated. We consider experimental geometries and also stretched bonds. We show that these nonvariational quantities may be found to relatively good accuracy when compared with full configuration interaction results, yet using only a small fraction of the full configuration interaction space. MCCI results in the aug‐cc‐pVDZ basis are seen to generally have reasonably good agreement with experiment. We also investigate the performance of MCCI when applied to ionisation energies and electron affinities of atoms in an aug‐cc‐pVQZ basis. We compare the MCCI results with full configuration interaction quantum Monte Carlo (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112) and “exact” nonrelativistic results (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112). We show that MCCI could be a useful alternative for the calculation of atomic ionisation energies however electron affinities appear much more challenging for MCCI. Due to the small magnitude of the electron affinities their percentage errors can be high, but with regards to absolute errors MCCI performs similarly for ionisation energies and electron affinities. © 2013 Wiley Periodicals, Inc.     

New dimension indices for the characterization of the solvent‐accessible surface

A method for the computation of a dimension index D is implemented in program TOPO and applied to calculate the solvent‐accessible surfaces of molecules. Our algorithm distinguishes external from internal atoms, and uses such a feature to give two fractal‐like dimension indices, D and D′. The D′−D difference is a sensitive method to elucidate the occurrence of atoms that are hidden to solvents. For molecules with buried atoms this difference is great (e.g., faujasite). The procedure is compared with the GEPOL code, which provides high‐quality results. TOPO systematic error can be easily corrected by simple addition of a small constant value (0.011). Correlation models between indices D and D′, globularity, rugosity, dipole moment and other properties make clear the existence of a homogeneous molecular structure in each series. Additional applications are the extrapolation of D to infinite polymers, the variation of the D with generations of dendrimers and a revision of D for lysozyme. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 477–487, 2001