Energy correctors for accurate prediction of molecular energies

Energy correctors are introduced for the calculation of molecular energies of compounds containing first row atoms (Li-F) to modify ab initio molecular orbital calculations of energies to better reproduce experimental results. Four additive correctors are introduced to compensate for the differences in the treatment of molecules with different spin multiplicities and multiplicative correctors are also calculated for the electronic and zero-point vibrational energies. These correctors, individually and collectively yield striking improvements in the atomization energies for several ab initio methods. We use as training set the first row subset of molecules from the G1 basis of molecules; when the correctors are applied to other molecules not included in the training set, selected from the G3 basis, similar improvements in the atomization energies are obtained. The special case of the B3PW91/cc-pVTZ yields an average error of 1.2 kcal/mol, which is already within a chemical accuracy and comparable to the Gaussian-n theories accuracy. The very inexpensive B3PW91/6-31G** yields an average error of 2.1 kcal/mol using the correctors. Methods considered unsuitable for energetics such as HF and LSDA yield corrected energies comparable to those obtained with the best highly correlated methods.     

The fragment molecular orbital method for geometry optimizations of polypeptides and proteins

The fragment molecular orbital method (FMO) has been used with a large number of wave functions for single-point calculations, and its high accuracy in comparison to ab initio methods has been well established. We have developed the analytic derivative of the electrostatic interaction between far separated fragments and performed a number of restricted Hartree-Fock (RHF) geometry optimizations using FMO and ab initio methods. In particular, the alpha-helix, beta-turn, and extended conformers of a 10-residue polyalanine were studied and the good FMO accuracy was established (the rms deviations for the former two forms were about 0.2 A and for the latter structure about 0.001 A). Met-enkephalin dimer was used as a model for the polypeptide binding and computed at the 3-21G and 6-31G* levels with a similar accuracy achieved; the error in the binding energy predictions (FMO vs ab initio) was 1-3 kcal/mol. Chignolin (PDB: 1uao) and an agonist polypeptide of the erythropoietin receptor protein (emp1) were optimized at the 3-21(+)G level, with the rms deviation from ab initio of about 0.2 A, or 0.5 degrees in terms of bond angles. The effect of solvation on the structure optimization was studied in chignolin and the Trp-cage miniprotein construct (PDB:1l2y), by describing water with TIP3P. The computed structures in gas phase and solution are compared to each other and experiment.     

Ab initio calculations of the melting temperatures of refractory bcc metals

We present ab initio calculations of the melting temperatures for bcc metals Nb, Ta and W. The calculations combine phase coexistence molecular dynamics (MD) simulations using classical embedded-atom method potentials and ab initio density functional theory free energy corrections. The calculated melting temperatures for Nb, Ta and W are, respectively, within 3%, 4%, and 7% of the experimental values. We compare the melting temperatures to those obtained from direct ab initio molecular dynamics simulations and see if they are in excellent agreement with each other. The small remaining discrepancies with experiment are thus likely due to inherent limitations associated with exchange-correlation energy approximations within density-functional theory.     

Theoretical study of C24N4 molecule

Both ab initio 6-31G, 3-21G and STO-3G basis sets and semiempirical PM3 and AM1 molecular orbital calculations are carried out on the C₂₄N₄ molecule of the T_d symmetry group. Results on the fully optimized structure which constrained T_d symmetry, molecular orbitals and vibrational frequency were obtained by both ab initio and semiempirical methods. The binding energy and various thermodynamic properties were also calculated via the PM3 and AM1 semiempirical methods. All the evidence of this work proves that the C₂₄N₄ molecule is stable and that its four six-membered rings with a remarkable delocalized C…C bond are similar to the related rings in the C₆₀ buckminsterfullerene structure.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Elucidating the Origin of Conformational Energy Differences in Substituted 1,3-Dioxanes: A Combined Theoretical and Experimental Study

13C NMR spectroscopy, ab initio quantum mechanics, and molecular mechanics have been used to investigate the trans-4-(trifluoromethyl)-2,2,6-trimethyl-1,3-dioxane chair/twist-boat equilibrium. The molecular mechanics calculations were based upon the MM3 and AMBER force fields. A 6-31G basis set was used for the ab initio calculations, and MP2 correlation corrections were applied. Both the ab initio and AMBER molecular mechanics calculations are consistent with the (13)C NMR chemical shift differences for the trans-4-(trifluoromethyl)-2,2,6-trimethyl-1,3-dioxane conformers. The predicted chair to twist-boat equilibrium suggested by the MM3 calculations is not consistent with the experimental data. These results support the suggestion by Howard et al. (Howard, A. E.; Cieplak, P.; Kollman, P. A. J. Comput.Chem. 1995, 16, 243-261) on the critical role of electrostatic interactions in determining the chair/twist-boat equilibrium.     

The Fourier transform infrared spectrum of the boron trifluoride–nitrous oxide complex

The Fourier transform infrared spectra of boron trifluoride and nitrous oxide, co-deposited in nitrogen and argon matrices at cryogenic temperatures, have been recorded. Concentration and temperature cycling experiments have established the existence of a 1:1 molecular complex, the spectrum of which is consistent with a structure similar to that of BF₃.N₂O in the gas phase. The structure derived from the infrared spectrum is also consistent with the results of a series of ab initio molecular orbital calculations reported by us recently. The experimental wavenumbers and complex-monomer wavenumber shifts compare reasonably well, by and large, with those predicted by the ab initio calculations.     

Ab initio prediction of the potential energy surface and vibrational-rotational energy levels of dialuminum monoxide, Al2O

The equilibrium structure and potential energy surface of dialuminum monoxide, Al(2)O, have been determined from large-scale ab initio calculations using the coupled-cluster method, CCSD(T), in conjunction with basis sets of triple- through quintuple-zeta quality. The effects of core-electron correlation on the calculated molecular parameters were investigated. The vibrational-rotational energy levels of the Al(2) (16)O and Al(2) (18)O isotopic species were calculated by a variational approach. The predicted energy levels are in remarkably good agreement with the available experimental spectroscopic data (from laser-induced fluorescence), demonstrating that the Al(2)O molecule is linear at equilibrium in its ground electronic state. The reported theoretical data settle controversies between the experimental studies about the equilibrium structure and assignment of vibrational fundamentals of the Al(2)O molecule.     

Theory and range of modern semiempirical molecular orbital methods

Semiempirical molecular orbital methods have a long history. They serve to tackle large systems and complicated processes beyond the reach of ab initio or density functional methods. Although their setup is derived from Hartree–Fock theory, the design of approximate energy expressions and the empirical parameters are used to achieve higher accuracy than the underlying ab initio theory. In this way the effect of larger basis sets or correlation can be partially simulated. All widely used semiempirical methods establish their accuracy by error statistics for molecular properties with experimental and high-level ab initio or density functional theory calculations as a reference. Their computational efficiency makes them suitable for the study of biochemical systems and solid materials. The present review presents a variety of applications which demonstrate the need for and success of semiempirical methods.     

Modeling water exchange on an aluminum polyoxocation

For the first time, water exchange on a polymeric complex has been modeled using a combination of gas-phase ab initio calculations and molecular dynamics (MD) simulations. The GaO4Al12(OH)24(H2O)12(7+)aq ion (GaAl12) was chosen because high-quality experimental data exist, including an activation enthalpy (+63 +/- 7 kJ/mol) and an activation volume (+3 +/- 1 cm3/mol). We took a two-step approach. First, the local solvent structure and the initial states for reaction were inferred from the molecular dynamics simulations. Second, we used this information to evaluate initial-state structures in the ab initio calculations. The energy differences between the initial and transition states from the ab initio calculations varied from +59 kJ/mol to +53 kJ/mol depending upon details, closely approximating the activation enthalpy.     

Quantum Topological Studies on the Molecular Complexes-CO_2-NCH and CO_2-OH_2

Topological properties of charge distribution for the title complexes and their constituent are analyzed by using ab initio calculations at 3-21G basis set. The results obtained are compared with those originated from ab initio and energy decomposition method. It has been determined that the title molecular complexes are T-shaped. The characteristics of the bonds and the changes originated from the formation of the complexes are discussed.     

An ab initio MO study on the structures and electronic states of hydrogen-bonded O3- HF and SO2-HF complexes

Ab initio molecular orbital (MO) calculations have been carried out for base-hydrogen fluoride (HF) complexes (base = O3 and SO2) in order to elucidate the structures and energetics of the complexes. The ab initio calculations were performed up to the QCISD(T)/6-311++G(d,p) level of theory. In both complexes, hydrogen-bonded structures where the hydrogen of HF orients toward one of the oxygen atoms of bases were obtained as stable forms. The calculations showed that cis and trans isomers exist in both complexes. All calculations for the SO2-HF complex indicated that the cis form is more stable in energy than the trans form. On the other hand, in O3-HF complexes, the stable structures are changed by the ab initio levels of theory used, and the energies of the cis and trans forms are close to each other. From the most sophisticated calculations (QCISD(T)/6-311++G(d,p)//QCISD/6-311+G(d) level), it was predicted that the complex formation energies for cis SO2-HF, trans SO2-HF, cis O3-HF, and trans O3-HF are 6.1, 5.7, 3.4, and 3.6 kcal/mol, respectively, indicating that the binding energy of HF to SO2 is larger than that of O3. The harmonic vibrational frequencies calculated for cis O3-HF and cis SO2-HF complexes were in good agreement with the experimental values measured by Andrews et al. Also, the calculated rotation constants for cis SO2-HF agreed with the experiment.     

Free energy perturbation study of water dimer dissociation kinetics

An efficient approach is described for using accurate ab initio calculations to determine the rates of elementary condensation and evaporation processes that lead to nucleation of aqueous aerosols. The feasibility of the method is demonstrated in an application to evaporation rates of water dimer at 230 K. The method, known as ABC-FEP (ab initio/classical free energy perturbation), begins with a calculation of the potential of mean force for the dissociation (evaporation) of small water clusters using a molecular dynamics (MD) simulation with a model potential. The free energy perturbation is used to calculate how changing from the model potential to a potential calculated from ab initio methods would alter the potential of mean force. The difference in free energy is the Boltzmann-weighted average of the difference between the ab initio and classical potential energies, with the average taken over a sample of configurations from the MD simulation. In principle, the method does not require a highly accurate model potential, though more accurate potentials require fewer configurations to achieve a small sampling error in the free energy perturbation step. To test the feasibility of obtaining accurate potentials of mean force from ab initio calculations at a modest number of configurations, the free energy perturbation method has been used to correct the errors when some standard models for bulk water (SPC, TIP4P, and TIP4PFQ) are applied to water dimer. To allow a thorough exploration of sampling issues, a highly accurate fit to results of accurate ab initio calculations, known as SAPT-5s, as been used a proxy for the ab initio calculations. It is shown that accurate values for a point on the potential of mean force can be obtained from any of the water models using ab initio calculations at only 50 configurations. Thus, this method allows accurate simulations of small clusters without the need to develop water models specifically for clusters.     

Interpolating moving least-squares methods for fitting potential energy surfaces: an application to the H2CN unimolecular reaction

Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.     

Kinetic isotope effects for Cl + CH4 ⇌ HCl + CH3 calculated using ab initio semiclassical transition state theory

Calculations were carried out for 25 isotopologues of the title reaction for various combinations of (35)Cl, (37)Cl, (12)C, (13)C, (14)C, H, and D. The computed rate constants are based on harmonic vibrational frequencies calculated at the CCSD(T)/aug-cc-pVTZ level of theory and X(ij) vibrational anharmonicity coefficients calculated at the CCSD(T) /aug-cc-pVDZ level of theory. For some reactions, anharmonicity coefficients were also computed at the CCSD(T)/aug-cc-pVTZ level of theory. The classical reaction barrier was taken from Eskola et al. [J. Phys. Chem. A 2008, 112, 7391-7401], who extrapolated CCSD(T) calculations to the complete basis set limit. Rate constants were calculated for temperatures from ～100 to ～2000 K. The computed ab initio rate constant for the normal isotopologue is in good agreement with experiments over the entire temperature range (～10% lower than the recommended experimental value at 298 K). The ab initio H/D kinetic isotope effects (KIEs) for CH(3)D, CH(2)D(2), CHD(3), and CD(4) are in very good agreement with literature experimental data. The ab initio (12)C/(13)C KIE is in error by ～2% at 298 K for calculations using X(ij) coefficients computed with the aug-cc-pVDZ basis set, but the error is reduced to ～1% when X(ij) coefficients computed with the larger aug-cc-pVTZ basis set are used. Systematic improvements appear to be possible. The present SCTST results are found to be more accurate than those from other theoretical calculations. Overall, this is a very promising method for computing ab initio kinetic isotope effects.     

Intramolecular SN2 reaction caused by photoionization of benzene chloride-NH3 complex: direct ab initio molecular dynamics study

Ionization processes of chlorobenzene-ammonia 1:1 complex (PhCl-NH3) have been investigated by means of full dimensional direct ab initio molecular dynamics (MD) method, static ab initio calculations, and density functional theory (DFT) calculations. The static ab initio and DFT calculations of neutral PhCl-NH3 complex showed that one of the hydrogen atoms of NH3 orients toward a carbon atom in the para-position of PhCl. The dynamics calculation for ionization of PhCl-NH3 indicated that two reaction channels are competitive with each other as product channels: one is an intramolecular SN2 reaction expressed by a reaction scheme [PhCl-NH3]+-->SN2 intermediate complex-->PhNH3++Cl, and the other is ortho-NH3 addition complex (ortho complex) in which NH3 attacks the ortho-carbon of PhCl+ and the trajectory leads to a bound complex expressed by (PhCl-NH3)+. The mechanism of the ionization of PhCl-NH3 is discussed on the basis of the theoretical results.     

Structure and bonding studies of ClX-C2H4 (X = H or Br) van der Waals complexes

High-quality ab initio calculations at the MPn (n = 2, 3 or 4) levels for the π-donor complex formed by HCl and ethene, and the recently characterized ClBr-ethene complex are presented. Interaction energies were calculated with the inclusion of both basis-set superposition error and zero-point energy corrections, resulting in values of about 1 kcal mol⁻¹ for both complexes. The total charge densities for both complexes yielded molecular graphs indicative of the weak binding in these molecules, and correspondingly, calculated charges showed that the XCl moiety has an overall slightly negative charge, while the ethene moiety is slightly positive. Analysis of the Laplacian of the charge density showed that the geometry of the ClBr- C₂H₄ complex may be understood in terms of the VSEPR model as an example of an AXYE₃ molecule.     

Research in the method of large molecular calculations utilizing transferability of LMO

The localized molecular orbitals of some saturated hydrocarbons and their derivatives have been formed using ab initio method and M. P. [1–2] localization procedure. Two models, SLMO and ELMO , a set of parameters of LMO Fock matrix elements, and a technique called “Group Effect” are proposed. Based on these, we developed a procedure to simulate the ab initio calculations on large molecules. Some test calculations have been done. The results are compared with those of the ab initio method. In general, absolute errors of orbital energies are about 10^?3 a.u., and the relative errors of total energies are about 10^?4. For the original applications, we applied this procedure to some large systems of alkane and their derivatives as well as three Crown-ether compounds. Satisfactory results are obtained.     

精密从头算与ABEEM/MM模型对水团簇(H2O)11 9种低能结构的计算

用精密从头算方法研究了(H2O)11的9种低能异构体的性质, 包括优化的几何结构、结合能、偶极矩和氢键个数等, 并且得出了515-a是(H2O)11的全局最低能结构. 同时, 也用ABEEM/MM(atom bond electronegativity equalization method/molecular mechanics) 模型研究了这些性质, 与从头算的结果进行了比较, 得到了相符合的结果. 这显示了ABEEM/MM模型在描述中等大小的水分子团簇结构上是成功的.