Interpolated potential energy surfaces: How accurate do the second derivatives have to be?

A global potential energy surface for the water dimer is constructed using the modified Shepard interpolation scheme of Collins et al. According to this interpolation scheme, the energy at an arbitrary geometry is expressed as a weighted sum of Taylor series expansions from neighboring data points, where the energy and derivative data required are obtained from ab initio calculations. For some ab initio methods, errors are introduced into the second derivative matrix, either by numerical differencing of ab initio energies or numerical integration during the ab initio calculation. Therefore, we test the accuracy required of the second derivative data by truncation of the exact second derivatives to a series of approximate second derivatives, and assess the effect on the results of a quantum diffusion Monte Carlo (QDMC) simulation. Our results show that the calculated zero-point energy and wave function histograms converge to within the numerical uncertainty of the QDMC simulation by inclusion of either three significant figures or three decimal places in the second derivatives.     

A heuristic potential function for intramolecular and intrasupermolecular chemical reactions

A heuristic fitting procedure to obtain an analytical potential function for describing a reactive potential energy surface in the neighborhood of the intrinsic reaction coordinate (IRC ) has been developed. For discussion, the pairwise potential function form, ∑a_nr^?n, is assumed in order to fit ab initio quantum mechanical calculations of intramolecular (or intrasupermolecular) interaction energies and its use is found advantageous because all the calculation can be carried out by the linear least squares method. Normal modes perpendicular to IRC are utilized to prepare an initial data base for the potential fitting in the neighborhood of IRC . Some trial molecular dynamics (MD ) simulations are performed in order to check the fitted potential function and, unless they lead to reasonable energies within the tolerance assumed, their results are utilized to construct an improved data base (the dynamic sampling). The present systematic optimization procedure has been applied to the proton transfer reaction of the formamidine–water (FW ) system. The normal mode analysis in both the transition state (TS ) and the stable state (SS ) regions suggests that the present fitted potential function can reproduce satisfactorily the Born–Oppenheimer (BO ) adiabatic surface obtained by ab initio molecular orbital (MO ) calculations. We conclude that our procedure works well for the chemical reaction molecular dynamics (CRMD ) simulation.     

The ionization potential of the BeH molecule

The ionization potential of the BeH molecule is derived from a few Rydberg states observed in the absorption spectrum and from “ab initio” calculations of the energies of the ground states of the BeH and BeH⁺ molecules at their equilibrium distances. The values are in agreement and yield PI(BeH, X²Σ⁺) = 66 100 ± 500 cm^?1.     

定域分子轨道模型——含H、C、N、O有机小分子的研究

应用STO_(-3)G从头算方法和Fostre-Boys定域化分子轨道程序, 我们研究了20多个有机小分子(含H、C、N,O)的定域化分子轨道, 获得了它们的能量和相互作用参数。采用定域分子轨道模型和统一的参数, 对正醇类分子进行了计算, 与光电子能谱数据比较, 得到的电离能的计算结果是相当令人满意的。     

Pyramidal distortions in the ethylene triplet π,π* state

Pyramidal distortions which may stabilize the triplet π,π* state of ethylene are investigated using ab initio molecular orbital calculations. Using a minimal basis set, the calculated stabilization energies are 5.1 kcal mole^?1 for a cis flapped conformation, 3.6 kcal mole^?1 for a trans flapped conformation, and 0.8 kcal mole^?1 for a twisted flapped conformation. With a double zeta basis set the predicted stabilization energies are much smaller: 1.3, 0.7, and 0.0 kcal mole^?1, respectively.     

Computational studies on aspartic proteases. I. Active-site protonation and hydration in the substrate-free crystalline state

We performed semiempirical molecular orbital calculations on the free and hydrated states of the HCOO^?…HCOOH couple in crystals of an aspartic protease, rhizopuspepsin, in order to gain information not available by conventional X-ray diffraction studies. The reliability of the MNDO /PM 3 method was proven for the model system HCOO^?…HOH, for which we could reproduce geometry and energetics of the complex, obtained by sophisticated ab initio calculations, with astonishing accuracy. Comparing the geometries of the active-site models to experiment and their relative energies, we suggest that in the substrate-free crystalline state the carboxyl–carboxylate–hydroxonium triad exists most probably in the neutral form. The carboxyl–carboxylate dyad attracts a hydroxonium ion better than does ammonium, indicating that the nonhydrogen atom, located by X-ray crystallography near the active site, is oxygen and not nitrogen. We located the most probable hydrogen positions by geometry optimization.     

Highly accurate O(N) method for delocalized systems

The elongation method, developed in our groups, is an ab initio method approaching order O(N) type scalability with high efficiency and high accuracy (error <10^?8?au/atom in total energy compared to the conventional calculation) that can be applied to any one-dimensional (polymer), two-dimensional (surface) or three-dimensional (solid material) systems. For strongly delocalized systems, however, the accuracy of the original elongation method for the targeted entire systems declines by approximately two orders of magnitude in the total energy as compared to the value obtained by the earlier implemented version of the elongation method for nondelocalized systems. The relatively small differences (10^?6?C10^?8 au) between the elongation method and conventional method total energies have caused more serious errors in the second hyperpolarizability, ??, especially in nano-scale systems which have accompanying strong delocalization. In order to solve this problem, we have incorporated a simple correction technique based on an additional ??orbital basis?? to the ??region basis?? in our original elongation method procedures. Some not so-well-localized orbitals are incorporated into the interaction with the attacking molecule. This treatment has been applied to some model nano- and bio-systems that previously have shown strong delocalization, and the high accuracy in the energy obtained for nonstrongly delocalized systems was retained even for the strongly delocalized systems, both for the energies and for the second hyperpolarizabilities. This is a major breakthrough and now expands the systems for which the elongation method can be used to calculate and predict second-order nonlinear optical properties for delocalized systems.     

The determination of intrinsic reaction coordinates by density functional theory

The first implementation of the intrinsic reaction coordinate (IRC ) method within the density functional theory (DFT ) framework is presented. The implementation has been applied to four different types of chemical reactions represented by the isomerization process, HCN ? HNC (A); the S_N2 process, H^? + CH₄ ? CH₄ + H^? (B); the exchange process, H˙ + HX ? HX + H˙ (X ? F,Cl) (C); and the elimination process, C₂H₅Cl ? C₂H₄ + HCl (D). The present study presents for each process optimized structures and calculated harmonic vibrational frequencies for the reactant(s), the transition state, and the product(s) along with the IRC path connecting the stationary points. The calculations were carried out within the local density approximation (LDA ) as well as the LDA/NL scheme where the LDA energy expression is augmented by Perdew's and Becke's nonlocal (NL ) corrections. The LDA and LDA/NL results are compared with each other as well as the best available ab initio calculations and experimental data. For reaction (D), ab initio calculations based on MP 2 geometries and MP 4SDTQ energies have been added due to the lack of accurate published post-HF calculations on this process. A detailed discussion is provided on the efficiency of the IRC algorithms, the relative accuracy of the DFT and ab initio schemes, as well as the reaction mechanisms of the four reactions. It is concluded that the LDA/NL scheme affords the same accuracy as does the MP 4 method. The post-HF methods seem to overestimate activation energies, whereas the corresponding LDA/NL estimates are too low. The LDA activation energies are even lower than the LDA/NL counterparts. The incorporation of the IRC method into the DFT framework provides a promising and reliable tool for probing the chemical reaction path on the potential energy surfaces, even for large-size systems. IRC calculations by ab initio methods of an accuracy similar to the LDA/NL scheme, such as the MP 4 scheme, are not feasible. © John Wiley & Sons, Inc.     

DNA base trimers: empirical and quantum chemical ab initio calculations versus experiment in vacuo

A complete scan of the potential‐energy surfaces for selected DNA base trimers has been performed by a molecular dynamics/quenching technique using the force field of Cornell et al. implemented in the AMBER7 program. The resulting most stable/populated structures were then reoptimized at a correlated ab initio level by employing resolution of the identity, Møller–Plesset second‐order perturbation theory (RI‐MP2). A systematic study of these trimers at such a complete level of electronic structure theory is presented for the first time. We show that prior experimental and theoretical interpretations were incorrect in assuming that the most stable structures of the methylated trimers corresponded to planar systems characterized by cyclic intermolecular hydrogen bonding. We found that stacked structures of two bases with the third base in a T‐shape arrangement are the global minima in all of the methylated systems: they are more stable than the cyclic planar structures by about 10 kcal mol^?1. The different behaviors of nonmethylated and methylated trimers is also discussed. The high‐level geometries and interaction energies computed for the trimers serve also as a reference for the testing of recently developed density functional theory (DFT) functionals with respect to their ability to correctly describe the balance between the electrostatic and dispersion contributions that bind these trimers together. The recently reported M052X functional with a polarized triple‐zeta basis set predicts 11 uracil trimer interaction energies with a root‐mean‐square error of 2.3 kcal mol^?1 relative to highly correlated ab initio theoretical calculations.     

Modulation of Stacking Interactions by Transition‐Metal Coordination: Ab Initio Benchmark Studies

A series of ab initio calculations are used to determine the C? H???π and π???π‐stacking interactions of aromatic rings coordinated to transition‐metal centres. Two model complexes have been employed, namely, ferrocene and chromium benzene tricarbonyl. Benchmark data obtained from extrapolation of MP2 energies to the basis set limit, coupled with CCSD(T) correction, indicate that coordinated aromatic rings are slightly weaker hydrogen‐bond acceptors but are significantly stronger hydrogen‐bond donors than uncomplexed rings. It is found that π???π stacking to a second benzene is stronger than in the free benzene dimer, especially in the chromium case. This is assigned, by use of energy partitioning in the local correlation method, to dispersion interactions between metal d and benzene π orbitals. The benchmark data is also used to test the performance of more efficient theoretical methods, indicating that spin‐component scaling of MP2 energies performs well in all cases, whereas various density functionals describe some complexes well, but others with errors of more than 1 kcal mol^?1.     

Analytical potential from ab initio calculations for the Fe+-H2O and Feo-H2O systems

Analytical intermolecular potentials for the Fe⁺?H₂O and Fe^o?H₂O systems have been determined from ab initio calculations. Interaction energies for a lot of points along the two potential energy surfaces were calculated using Huzinga's MINI ?2 basis set. The results obtained were fitted to an analytical function containing 11 adjustable parameters that we have already used with success for the Fe²⁺?H₂O system. The goodness of the generated intermolecular potentials is discussed.     

Structures and energies of D-galactose and galabiose conformers as calculated by ab initio and semiempirical methods

Optimized geometries and total energies of some conformers of alpha- and beta-D-galactose have been calculated using the RHF/6-31G* ab initio method. Vibrational frequencies were computed at the 6-31G* level for the conformers that favor internal hydrogen bonding, in order to evaluate their enthalpies, entropies, Gibbs free energies, and then their structural stabilities. The semiempirical AM1, PM3, MNDO methods have also been performed on the conformers GG, GT, and TG of alpha- and beta-D-galactose. In order to test the reliability of each semiempirical method, the obtained structures and energies from the AM1, PM3, and MNDO methods have been compared to those achieved using the RHF/6-31G* ab initio method. The MNDO method has not been investigated further, because of the large deviation in the structural parameters compared with those obtained by the ab initio method for the galactose. The semiempirical method that has yielded the best results is AM1, and it has been chosen to perform structural and energy calculations on the galabiose molecule (the disaccharides constituted by two galactose units alpha 1,4 linked). The goal of such calculations is to draw the energy surface maps for this disaccharide. To realize each map, 144 different possible conformations resulting from the rotations of the two torsional angles psi and phi of the glycosidic linkage are considered. In each calculation, at each increment of psi and phi, using a step of 30 degrees from 0 to 330 degrees, the energy optimization is employed. In this article, we report also calculations concerning the galabiose molecule using different ab initio levels such as RHF/6-31G*, RHF/6-31G**, and B3Lyp/6-31G*.     

Ab initio studies of the 3nπ* states of glyoxal and methyl glyoxal

Results of ab initio calculations on the ³nπ* states of glyoxal and methyl glyoxal are reported. The symmetry unconstrained ΔE_SCF transition energies, unlike the symmetry constrained results, are found to be very similar. These calculations explain some anomalies which have appeared in the literature recently.     

A semiempirical HAM/3 study of core-electron binding energies for uracil its related molecules

The semiempirical HAM/3 molecular orbital method is used to calculate core-electron binding energies of common pyrimidine bases and some of their aza analogs. Average percent difference (error) is found to be 0.91 ± 0.12% which is substantially smaller than the error obtained from ab initio calculations with the application of Koopmans' theorem. HAM/3 chemical shifts are as good as those of ab initio direct hole state calculations reported in the literature. The molecular charge distributions calculated by HAM/3 agree fairly well with those of experiment and other theoretical methods. A large error in the HAM/3 core-electron binding energy of carbon in a CH₃ group has been detected.     

Ab initio energies and tunneling lifetimes of the doubly charged AH2+ (A = Mg—Ar) diatomics

Potential energy curves for the ground and low-lying excited states of the AH²⁺ (A = Mg—Ar) dications have been calculated using high-level ab initio methods with large atomic orbital basis sets. Quasi-bound potential energy curves with local minima and deprotonation barriers have been found for most of the dications studied. The energies, tunneling lifetimes, and widths of the quasi-bound states have been calculated by numerical solution of the radial Schrodinger equation using the Numeov method. All these dications except ArH²⁺ have low-lying states which support quasi-bound vibrational states. The ArH²⁺ dication has a ²∏_i potential energy curve with a minimum so shallow that it does not support any quasi-bound vibrational states. Results of our calculations are compared with previous ab initio calculations and available experimental data. © 1995 John Wiley & Sons, Inc.     

Performance of semiempirical methods in fullerene chemistry: relative energies and nucleus-independent chemical shifts

Semiempirical MNDO, AM1, and PM3 calculations are reported for 153 fullerene isomers in an attempt to assess the reliability of these methods through comparisons with ab initio and density functional results. B3LYP/6-31G^* relative energies are generally reproduced quite well by these calculations. Qualitative trends in ab initio nucleus-independent chemical shifts at the cage centers are captured by the semiempirical GIAO-MNDO approach while underestimating their absolute values. The agreement between the semiempirical results and the ab initio or density functional reference data is generally better for the larger fullerenes (C₆₀–C₁₀₂) than for the smaller ones (C₂₀–C₅₀). These systematic comparisons clarify the accuracy that may be expected from semiempirical computations in fullerene chemistry.     

An AB initio SCF MO CI study of the n → π* transition of methylenimine

The electron correlation energies of both the ground and n → π* excited states of methylenimine (CH₂NH) are investigated by means of ab initio SCF MO CI calculations. Then n → π* singlet and triplet state energies of methylenimine are obtained through 3461-dimensional CI including the singly, doubly and triply excited configurations. the excitation energy from the ground state to the ¹(n → π*) state nearly coincides with that obtained in the framework of the singly excited configuration interaction (SECI) procedure. This result suggests that there is good cancellation of the correlation energy between the ground and the excited singlet sates, proving the usefulness of the SECI method for the excitation energies.     

An efficient, fragment-based electronic structure method for molecular systems: self-consistent polarization with perturbative two-body exchange and dispersion

We report a fragment-based electronic structure method, intended for the study of clusters and molecular liquids, that incorporates electronic polarization (induction) in a self-consistent fashion but treats intermolecular exchange and dispersion interactions perturbatively, as post-self-consistent field corrections, using a form of pairwise symmetry-adapted perturbation theory. The computational cost of the method scales quadratically as a function of the number of fragments (monomers), but could be made to scale linearly by exploiting distance-dependent thresholds. Extensive benchmark calculations are reported using the S22 database of high-level ab initio binding energies for dimers, and we find that average errors can be reduced to <1 kcal/mol with a suitable choice of basis set. Comparison to ab initio benchmarks for water clusters as large as (H(2)O)(20) demonstrates that the method recovers ?90% of the binding energy in these systems, at a tiny fraction of the computational cost. As such, this approach represents a promising path toward accurate, systematically improvable, and parameter-free simulation of molecular liquids.     

Potential energy surfaces for simple chemical reactions: Li + F2 → LiF + F

A potential energy surface is calculated for the Li + F₂ → LiF + F reaction using an ab initio multistructure valence-bond approach. The orthogonalized Moffit (OM) method is employed to apply a correction for the large errors made by the ab initio calculation in representing the F⁻ ion relative to the F atom. The OM method predicts the potential surface to be of the highly “attractive” or “early downhill” type and to possess a potential energy well with respect to dissociation to the products LiF + F. The attributes of the surface predicted by the OM method are compared with those suggested by experiment and used in trajectory calculations for analogous systems.     

Force field for computation of conformational energies,structures, and vibrational frequencies of aromatic polyesters

A CFF93¹ all-atom force field for aromatic polyesters based on ab initio calculations is reported. The force field parameters are derived by fitting to quantum mechanical data which include total energies, first and second derivatives of the total energies, and electrostatic potentials. The valence parameters and the ab initio electrostatic potential (ESP) derived charges are then scaled to correct the systematic errors originating from the truncation of the basis functions and the neglect of electron correlation in the HF/6-31G* calculations. Based on the force field, molecular mechanics calculations are performed for homologues of poly(p-hydroxybenzoic acid) (PHBA) and poly(ethylene terephthalate) (PET). The force field results are compared with available experimental data and the ab initio results. © 1994 by John Wiley & Sons, Inc.