On the use of electrostatic potential derived charges in molecular mechanics force fields. The relative solvation free energy of cis- and trans-N-methyl-acetamide

We have carried out free energy perturbation calculations on the relative solvation free energy of cis- and trans-N-methyl-acetamide (NMA). Experimentally, the solvation free energy difference has been found to be near zero. Using 6-31G* ab initio electrostatic potential derived charges for both the cis and trans conformations, we calculate a solvation free energy difference of 0.1 ± 0.1 kcal/mol. Using the 6-31G* charges derived for the trans conformation for both the cis and trans models leads to a solvation free energy difference of 0.9 ± 0.1 kcal/mol, compared to the value of 2.2 kcal/mol determined for the OPLS model for trans-NMA.     

First‐Principles Prediction of Nucleophilicity Parameters for π Nucleophiles: Implications for Mechanistic Origin of Mayr’s Equation

Quantitative nucleophilicity scales are fundamental to organic chemistry and are usually constructed on the basis of Mayr’s equation [log k=s(N+E)] by using benzhydrylium ions as reference electrophiles. Here an ab initio protocol was developed for the first time to predict the nucleophilicity parameters N of various π nucleophiles in CH₂Cl₂ through transition‐state calculations. The optimized theoretical model (BH&HLYP/6‐311++G(3df,2p)//B3LYP/6‐311+G(d,p)/PCM/UAHF) could predict the N values of structurally unrelated π nucleophiles within a precision of ca. 1.14 units and therefore may find applications for the prediction of nucleophilicity of compounds that are not readily amenable to experimental characterization. The success in predicting N parameters from first principles also allowed us to analyze in depth the electrostatic, steric, and solvation energies involved in electrophile–nucleophile reactions. We found that solvation does not play an important role in the validity of Mayr’s equation. On the other hand, the correlations of the E, N, and log k values with the energies of the frontier molecular orbitals indicated that electrostatic/charge‐transfer interactions play vital roles in Mayr’s equation. Surprising correlations observed between the electrophile–nucleophile C? C distances in the transition state, the activation energy barriers, and the E and N parameters indicate the importance of steric interactions in Mayr’s equation. A method is then proposed to separate the attraction and repulsion energies in the nucleophile–electrophile interaction. It was found that the attraction energy correlated with N+E, whereas the repulsion energy correlated to the s parameter.     

Solving the low dimensional Smoluchowski equation with a singular value basis set

Reaction kinetics on free energy surfaces with small activation barriers can be computed directly with the Smoluchowski equation. The procedure is computationally expensive even in a few dimensions. We present a propagation method that considerably reduces computational time for a particular class of problems: when the free energy surface suddenly switches by a small amount, and the probability distribution relaxes to a new equilibrium value. This case describes relaxation experiments. To achieve efficient solution, we expand the density matrix in a basis set obtained by singular value decomposition of equilibrium density matrices. Grid size during propagation is reduced from (100–1000)^N to (2–4)^N in N dimensions. Although the scaling with N is not improved, the smaller basis set nonetheless yields a significant speed up for low‐dimensional calculations. To demonstrate the practicality of our method, we couple Smoluchowsi dynamics with a genetic algorithm to search for free energy surfaces compatible with the multiprobe thermodynamics and temperature jump experiment reported for the protein α₃D. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Conformational analysis of N,N-diisopropylamides by combined use of n.m.r. lanthanide-induced shifts and conformational energy calculations

A new method of conformational analysis has been developed, in which energy minimization calculations are combined with lanthanide-induced shift data. First, exhaustive energy calculations are carried out on the free molecules in order to determine the conformations of lowest energy. Then, the coordinates of all low energy conformations or pairs of conformations are used in the pseudocontact shift equation for lanthanide-induced shifts in order to find which of the theoretically obtained conformation(s) gives the best agreement with experiment. The molecules complexed to the lanthanide shift reagent were N,N-diisopropylformamide (DIPF) and N,N-diisopropylacetamide (DIPA). Two different lanthanide shift reagents were used, Eu(fod)₃

1 Fod is the anion of 1,1,1,2,2,3,3-heptafluoro-7,7-dimethyl-4,6-octanedione-d₂₇.

and Pr(fod)₃, in order to check the validity of the method. Proton magnetic resonance spectra were taken at 6 °C in carbon tetrachloride solution. The principal conformation found was different for each amide. DIPF was found to exist as a mixture of I (39 mol%) and II (61 mol%) with Eu(fod)₃, and a mixture of I (37%) and II (63%) with Pr(fod)₃. DIPA was found to exist as a mixture of I (79%) and IV (21%) with Eu(fod)₃ and a mixture of I (87%) and IV (13%) with Pr(fod)₃. For both molecules, the two conformations of lowest computed energy were also the pair which gave the best fit to the lanthanide shift reagent data. The location of the principal magnetic axis of the complex was found to lie between 0° and 14° from the lanthanide atom–oxygen atom bond axis. The technique of combining lanthanide shift reagent data with energy calculations shows great promise in conformational analysis.     

Valence type vacant orbitals for configuration interaction calculations

A method is proposed to determine the valence type vacant orbitals, which are suitable for CI calculations and for the initial guess orbitals in MC SCF calculations. The method was applied to calculate the ionization energies of series of molecules and to draw the potential energy curves of various states of N₂ and N⁺₂.     

Evaluation of compatibility in polymer blend systems by simultaneous DSC-FTIR measurement

The concept of crystallization dynamics method evaluating the miscibility of binary blend system including crystalline component was proposed. Three characteristic rates, nucleation, crystal growth rates (N*, G*) and growth rate of conformation (G _c*) were used to evaluate the miscibility of PVDF/at-PMMA and PVDF/iso-PMMA by the simultaneous DSC-FTIR. N*, G* and G _c* depended remarkably on both temperature and blend fraction (ϕ_PMMA) for PVDF/at-PMMA system, which indicated the miscible system. PVDF/iso-PMMA showed small ϕ_PMMA dependency of N*, G* and G _c*, was estimated the immiscible system. The ΔT/T _m⁰ values, corresponding to Gibbs energy required to attend the constant G* and G _c*, evaluated from G* and G _c* showed the good linear relationships with different slope. The experimental results suggested that the concentration fluctuation existed in PVDF/iso-PMMA system.     

Order-<Emphasis Type="Italic">N</Emphasis> and embedded-cluster first-principles DFT calculations using SIESTA/Mosaico

Order-N and embedded-cluster first-principles DFT calculations have been performed with the Mosaico method for energy optimization (Seijo and Barandiarán in J Chem Phys 121:6698, 2004) for the first time. The Hamiltonian matrix elements have been computed with the SIESTA code. The order-N behavior of the method in DFT calculations was shown in total energy calculations performed on bulk silicon using supercells up to Si₈₀₀₀. The sizes of the orbital-specific-basis-sets needed for precise calculations have been explored in demanding (bulk silicon) and favorable (water clusters) cases for a method based on the calculation of localized molecular orbitals. Embedded-cluster calculations, which are much faster than full-system calculations, have been performed on an Si-vacancy of bulk silicon and on a water cluster with a displacing water molecule. The feasiability of calculations of this type with Mosaico has been demonstrated. The sizes of the variationally free, active clusters which are needed for an agreement with full-system calculations have been explored and result to be reasonably small. Contribution to the Serafin Fraga Memorial Issue.     

Influence of substitution on the strength and nature of CH···N hydrogen bond in XCCH···NH3 complexes

The effect of substitution on the strength and nature of CH···N hydrogen bond in XCCH···NH₃ (X = F, Cl, Br, OH, H, Me) and NCH···NH₃ complexes were investigated by quantum chemical calculations. Ab initio calculations were performed using MP2 method with a wide range of basis sets. With tacking into account the BSSE and ZPVE, the values of BEs decrease. Replacement of the nonparticipatory hydrogen atom of HCCH by the electronegative atoms (F, Cl, and Br), lead to the BEs increases. The BE corresponding to the replacement of the nonparticipatory hydrogen atom of HCCH by the OH and CH₃ groups decreases. A far greater enhancement of the interaction energy arises from replacement of HCCH by the more acidic HCN. The natural bond orbital analysis and the Bader's quantum theory of atoms in molecules were also used to elucidate the interaction characteristics of these complexes. The electrostatic nature of H‐bond interactions is predicted from QTAIM analysis. In addition, the relationship between the isotropic and anisotropic chemical shifts of the bridging hydrogen and binding energy of complexes as well as electron density at N···H BCPs were investigated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spin coupling in shake-up processes

The treatment of spin coupling in calculations of shake-up states in core photoelectron processes is reviewed and the problems arising when the equivalent core approximation is used to model the core hole are discussed. A method for approximating the intensity of the triplet-coupled doublet state in semiempirical calculations is proposed. The intensities of the triplet-coupled doublet states in N₂, formaldehyde, and aniline core ionization spectra are calculated. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 189–196, 1997     

A density functional study of Fe(SINGLE BOND)N2, Fe(SINGLE BOND)N+2, and Fe(SINGLE BOND)N−2

The interaction of an iron atom with molecular nitrogen was studied using density functional theory. Calculations were of the all-electron type and both conventional local and gradient-dependent models were used. A ground state of linear structure was found for Fe(SINGLE BOND)N₂, with 2S + 1 = 3, whereas the triangular Fe(SINGLE BOND)N₂ geometry, of C_2v symmetry, was located 2.1 kcal/mol higher in energy, at least for the gradient-dependent model. The reversed order was found using the conventional local approximation. In Fe(SINGLE BOND)N₂, the N(SINGLE BOND)N bond is strongly perturbed by the iron atom: It has a bond order of 2.4, a vibrational frequency of 1886 cm⁻¹, and an equilibrium bond length of 1.16 Å: These values are 3.0, 2359 cm⁻¹, and 1.095 Å, respectively, for the free N₂ molecule. With the gradient-dependent model and corrections for nonsphericity of the Fe atom, a very small binding energy, 8.8 kcal/mol, was calculated for Fe(SINGLE BOND)N₂. Quartet ground states were found for both Fe(SINGLE BOND)N⁺₂ and Fe(SINGLE BOND)N⁻₂. The adiabatic ionization potential, electron affinity, and electronegativity were also computed; the predicted values are 7.2, 1.22, and 4.2 eV, respectively. © 1997 John Wiley & Sons, Inc.     

Role of twisting and sliding on the solvation of a stacked cytosine dimer: an ab initio study

Ab initio calculations with inclusion of correlation effects at the MP2/6-31G* level have been used to predict the interaction energy of stacked cytosine dimer (C/C) as a function of twisting and sliding in the gas phase. Systematic calculations have also been carried out on the solvation free energies of various rotated and translated C/C dimers using a polarized continuum model approach at the HF/6-31G* level with a view to probe the role of various degrees of freedom on the free energy of solvation of the C/C dimer. The interaction energy of the C/C dimer decreases upon changing from a parallel to an antiparallel conformation in the gas phase. The 180°-rotated conformation has been found to be the most stable arrangement when compared to other rotated positions. The rotated and translated dimers exhibit lower solvation free energy than the parallel conformation. The decrease in the dipole moment upon rotation from the parallel to the antiparallel conformation indicates the cancellation of charge distribution upon rotation in the z direction of one cytosine base with respect to the other. The calculation reveals that the present approach could not yield association energy, ΔΔG _Asso, in a solvent medium. This may be due to the fact that in the case of floppy molecules the contribution from translational, rotational and vibrational free energies plays a significant role in the calculation of ΔΔG _Asso. Received: 13 December 2001 / Accepted: 25 March 2002 / Published online: 13 June 2002     

Electrostatic and relaxation effects in ionization of molecular dimers and intermolecular complexes

The shifts in ionization energies which occur when a molecule is incorporated as an asymmetric dimer or in an intermolecular complex are analyzed theoretically. MO ? SCF calculations with 4–31G basis sets were performed on closed- and open-shell states of (HF)₂, H₂O·HF, and their valence–hole ions, as well as on the heterodimers incorporating the higher homologues CH₃F, CH₃OH, and (CH₃)₂O. The analysis concerns the influence of electrostatic, polarization, and charge transfer effects associated with complexation on the initial molecular state of each monomer system, as well as monomer–dimer differences in the electronic relaxation mechanism considered as a final state effect in the ionization process. The calculated ionization energy shifts which agree well with the experimental data available for (CH₃)₂O·HF, show that the shifts are dominated by electrostatic effects, but some effects arising from differences in molecular size and electric polarizability of the monomers can be discerned.     

Host-guest preorganization and complementarity: A molecular mechanics and molecular dynamics study of cation complexes of a cyclic urea-anisole spherand

Molecular mechanics and molecular dynamics calculations were carried out in vacuo for 1 and for the complexes of 1 with alkali metal cations and t-BuNH. The calculations identify perching and nesting conformations of the complexes not available from X-ray data. For the Li⁺ ? 1 complex, the MD simulations identify a new global minimum not found by the molecular mechanics calculation. In general, the net favorable ion-spherand complexation energy is due to the offset of the unfavorable reorganization energy of the spherand by the overwhelmingly favorable electrostatic component of the ion-spherand interaction energy. The host is least preorganized for the binding of Li⁺ and, even in its complexed conformation, presents the least steric complementarity to this ion. The complexation energy becomes significantly more favorable due to a large increase in the electrostatic complementarity of the ion binding site when the spherand adopts its complexed conformation. Correction of the calculated complexation energy by the experimental free energy of ion aqueous desolvation leads to results in line with the findings of Cram and co-workers that K⁺ is the most, and Li⁺ the least, favorably bound by 1 .     

A pH‐dependent computational approach to the effect of mutations on protein stability

This article describes a novel software implementation for high‐throughput scanning mutagenesis with a focus on protein stability. The approach combines molecular mechanics calculations with calculations of protein ionization and a Gaussian‐chain model of electrostatic interactions in unfolded state. Comprehensive testing demonstrates a state‐of‐the‐art accuracy for predicted free energy differences on single, double, and triple mutations with a correlation coefficient R above 0.7, which takes about 1.5 min per mutation on a single CPU. Unlike most of existing in silico methods for fast mutagenesis, the stability changes are reported as a continuous function of solution pH for wide pH intervals. We also propose a novel in silico strategy for searching stabilized protein variants that is based on combinatorial scanning mutagenesis using representative amino acid types. Our in silico predictions are in excellent agreement with the hyper‐stabilized variants of mesophilic cold shock protein found using the Proside method of direct evolution. © 2016 Wiley Periodicals, Inc.     

A new formulation of the PCM solvation method: PCM-QINTn

A new formulation of the PCM electrostatic solution problem is proposed. Through a new derivation of the PCM-CLSn expression we propose an interpolation formula that improved the convergence: PCM-QINTn. All the available formulations are applied to the evaluation of the electrostatic component of the free energy of solvation for some molecular systems. In addition, PCM-QINT derivatives of G _el with respect to atomic coordinates are evaluated. The computational costs are compared with those of PCM-direct formulation. Received: 21 October 1996 / Accepted: 7 January 1997     

The influence of the solvent on the conformational energy differences due to the anomeric effect

The solvation free energy ΔG^sol of molecules exhibiting the anomeric effect is computed in an approach that considers a continuous distribution for the solvent. A partition of ΔG^sol into separately evaluated contributions confirms that changes in the energy of the systems due to changes in conformation of the solute are ruled by the electrostatic contribution. A comparison with the “exact” values indicates that the approximate expression for the electrostatic contribution to ΔG^sol are not accurate enough to permit a proper modeling of the solvent influence on the anomeric effect. The systems are composed of methanediol, methoxymethanol, dimethoxymethane, and 2-methoxytetrahydropyran in carbon tetrachloride, chloroform, acetone, and water. The calculations have been performed at the SCF level with the STO -3G and 4–31G basis sets.     

Electrostatic,sequential bond energies and structures of Li+·(N2)n complexes: computational study

The MP2 and CCSD calculations of the geometries and binding energies of the Li⁺·(N₂)_n (n?=?1–4) complexes are obtained. The potential energy surface showed that these complexes exhibit one minimum state and one transition state. The mono- and di-ligated complexes exhibit linear configurations with a binding energy of 11.1 and 21.2 kcal mol^?1, respectively. Trigonal planar and tetrahedral configurations are obtained for tri- and tetra-ligated complexes, respectively. The computed sequential bond dissociation energies (BDEs) of Li⁺·(N₂)_n (n?=?1–4) complexes are also calculated in which the mono-ligated complex has the largest BDE value. The obtained trend is mainly dependent on the variation in the ion-quadrupole interaction of these ion complexes. These calculations predict that these complexes are of purely electrostatic nature.

     

Theoretical prediction of ionization potential,electron affinity,and electronic spectrum of the S2N radical

Ab initio MRD –CI calculations using a basis set of near Hartree–Fock quality have been carried out to calculate the ground-state electronic structure of S₂N⁺, S₂N, and S₂N^? and the ionization potential, electron affinity, and vertical electronic spectrum of S₂N. At the highest level of theory (estimated full CI or FCI ), S₂N⁺ is predicted to have a linear structure with r(N? S) = 1.51 Å. For S₂N and S₂N^?, the minimum in energy at the FCI level corresponds to a quasi-linear [with a barrier height to linearity of about 2.0 kcal mol^?1, ] and a bent structure , respectively. The adiabatic/vertical ionization potential and electron affinity of S₂N are predicted to be 7.26/7.82 and 1.60/0.79 eV, respectively. Of the several electronic transitions in S₂N considered, the ones with the excitation energy of 1.87 eV (X² A₁ → ²B₂) and 2.87 eV (X²A₁ → ²B₂) are somewhat intense (? = 0.005 and 0.002) and likely to be observed.     

B12N12 Nano-cage as Potential Sensor for NO2 Detection

The NO₂ molecule adsorption on B₁₂N₁₂ nano-cage was investigated using density func-tional theory calculations in terms of adsorption energy, HOMO/LUMO energy gap (Eg) changes, charge transfer, structural deformation, etc. Furthermore, some aspects of stability and properties of B₁₂N₁₂ including calculation of binding electronic and Gibbs free energies, density of states, and molecular electrostatic potential surfaces are investigated. Three pos-sible configurations for NO₂ adsorption on the B₁₂N₁₂ nano-cage are energetically found. Interestingly, the results reveals that the Eg of B₁₂N₁₂ cluster is very sensitive to the pres-ence of NO₂ molecules as its value reduces from 6.84 eV in free cluster to 3.23 eV in the most stable configuration of NO₂/cluster complex. This phenomenon dramatically increases the electrical conductivity of the cluster, suggesting that the B₁₂N₁₂ nano-cluster may be potential sensor for NO₂ gaseous molecule detection.