Analytic energy gradients for orbital‐optimized MP3 and MP2.5 with the density‐fitting approximation: An efficient implementation

Efficient implementations of analytic gradients for the orbital‐optimized MP3 and MP2.5 and their standard versions with the density‐fitting approximation, which are denoted as DF‐MP3, DF‐MP2.5, DF‐OMP3, and DF‐OMP2.5, are presented. The DF‐MP3, DF‐MP2.5, DF‐OMP3, and DF‐OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density‐fitted perturbation theory (DF‐MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF‐MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z‐vector equation, back‐transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc‐pCVQZ basis set, is 0.0001–0.0002 Å. © 2017 Wiley Periodicals, Inc.     

An ab initio and density functional theory study on the mechanism for the reaction of OH with 2-ethylfuran

The mechanism of the reaction of OH + 2-ethylfuran has been investigated using the G3MP2 and G3MP2B3 levels of theory. The geometric parameters of all species involved in the reaction have been optimized at the MP2 and B3LYP levels of theory with 6-311G(d,p) basis set. The overall profile of doublet potential energy surface (PES) for the OH + 2-ethylfuran reaction has been constructed using the G3MP2 and G3MP2B3 methods. The results show that the addition-elimination mechanism dominates the OH + 2-ethylfuran reaction and the major products are CH₃CH₂C(OH)CHCHCHOH (P8) and CH₃CH₂COCHCHCHOH (P6).     

The effect of electron correlation on the conformational space of melatonin

The pineal gland hormone melatonin regulates several physiological processes including circadian rhythm and also alleviates oxidative stress‐induced degenerative diseases. In spite of its important biological roles, no high level ab initio conformational study has been conducted to reveal its structural features. In this work, the conformational flexibility of melatonin was investigated using correlated ab initio calculations. Conformers, obtained previously at the Hartree‐Fock level (HF/6‐31G*), were fully optimized using second order Møller‐Plesset perturbation theory applying the frozen core approximation (MP2(FC)/6‐31G*). Furthermore, single‐point MP4(SDQ,FC)/6‐31G*//MP2(FC)/6‐31G* computations were performed to investigate the effect of higher order perturbation terms. The HF and MP2 conformational spaces are considerably different: the initial 128 structures converged into 102 different local minima as confirmed by frequency calculations; 28 new minima appeared and 26 previous HF local minima disappeared; no “all‐trans” C3 side chain conformations are seen at the MP2(FC) level. The MP2 global minimum conformation is stabilized by an aromatic‐side chain interaction. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008     

On the significance of the trigger reaction in the action of the calicheamicin γ1I anti-cancer drug

The significance of the so-called trigger reaction in the reaction mechanism of the calicheamicin γ₁ ^I anti-cancer drug has been studied with ab initio quantum chemical methods. The structures of four fragments of calicheamicin γ₁ ^I , consisting of either 39 or 41 atoms, have been fully optimized using the Becke-Perdew86 density functional method and the 6-31G* basis sets. The four structures constitute members of an isodesmic reaction for which the reaction energy is a direct measure of the change in activation energy of the Bergman reaction, caused by the structural rearrangements of the preceding trigger reaction. This difference in activation energy has been calculated with density functional theory, using the exchange-correlation functional mentioned above, and with second-order M?ller-Plesset perturbation theory (MP2), employing an ANO-type basis set. In both cases a value of 12 kcal/mol is obtained. The study firmly supports the hypothesis that the significance of the trigger reaction is to saturate a double bond in the vicinity of the enediyne group, which counteracts the formation of the biradical state of the drug. The MP2 computations became feasible by a novel implementation of an integral-direct, distributed-data, parallel MP2 algorithm. Received: 10 January 1997 / Accepted: 1 April 1997     

Theoretical study on the mechanism and kinetics of addition of hydroxyl radicals to fluorobenzene

Geometries, frequencies, reaction barriers, and reaction rates were calculated for the addition of OH radical to fluorobenzene using Möller–Plesset second‐order perturbation (MP2) and G3 methods. Four stationary points were found along each reaction path: reactants, prereaction complex, transition state, and product. A potential for association of OH radical and fluorobenzene into prereaction complex was calculated, and the associated transition state was determined for the first time. G3 calculations give higher reaction barriers than MP2, but also a significantly deeper prereaction complex minimum. The rate constants, calculated with Rice–Ramsperger–Kassel–Marcus (RRKM) theory using G3 energies, are much faster and in much better agreement with the experiment than those calculated with MP2 method, as the deeper well favors the formation of prereaction complex and also increases the final relative populations of adducts. The discrepancies between the experimental and calculated rate constants are attributed to the errors in calculated frequencies as well as to the overestimated G3 reaction barriers and underestimated prereaction complex well depth. It was possible to rectify those errors and to reproduce the experimental reaction rates in the temperature range 230–310 K by treating the relative translation of OH radical and fluorobenzene as a two‐dimensional particle‐in‐the‐box approximation and by downshifting the prereaction complex well and reaction barriers by 0.7 kcal mol^?1. The isomeric distribution of fluorohydroxycyclohexadienyl radicals is calculated from the reaction rates to be 30.9% ortho, 22.6% meta, 38.4% para, and 8.3% ipso. These results are in agreement with experiment that also shows dominance of ortho and para channels. © 2012 Wiley Periodicals, Inc.     

Mechanism for the gas‐phase reaction between OH and 3‐methylfuran: A theoretical study

The mechanism for the OH + 3‐methylfuran reaction has been studied via ab initio calculations to investigate various reaction pathways on the doublet potential energy surface. Optimizations of the reactants, products, intermediates, and transition structures are conducted using the MP2 level of theory with the 6‐311G(d,p) basis set. The single‐point electronic energy of each optimized geometry is refined with G3MP2 and G3MP2B3 calculations. The theoretical study suggests that the OH + 3‐methylfuran reaction is dominated by the formation of HC(O)CH?C(CH₃)CHOH (P7) and CH(OH)CH?C(CH₃)C(O)H (P9), formed from two low‐lying adducts, IM1 and IM2. The direct hydrogen abstraction pathways and the S_N2 reaction may play a minor or negligible role in the overall reaction of OH with 3‐methylfuran. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Au10团簇结构与电性质的理论研究

使用4种流行的泛函(BPW91, B3PW91, PW91和B3LYP)考查了若干Au10团簇结构的稳定结构, 获得了能量最有利的6种异构体(其中2种以前未见报道), 并在此基础上进一步用MP2方法校准了它们的相对稳定性, 分析了它们的电子性质以及最稳定异构体与氧分子的化学反应性能. 计算结果表明Au10团簇异构体的相对稳定性明显依赖所使用的理论方法和泛函, 密度泛函结果显示Au10倾向于采用平面结构, 且不同的泛函给出异构体的相对稳定性次序也不相同, 而MP2计算则显示三维空间结构的Au10团簇更稳定, Au10可能是金团簇从二维结构到三维结构演化的一个临界点.     

An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: application to alanine tetrapeptide conformational analysis

We present a new algorithm for analytical gradient evaluation in resolution‐of‐the‐identity second‐order Møller‐Plesset perturbation theory (RI‐MP2) and thoroughly assess its computational performance and chemical accuracy. This algorithm addresses the potential I/O bottlenecks associated with disk‐based storage and access of the RI‐MP2 t‐amplitudes by utilizing a semi‐direct batching approach and yields computational speed‐ups of approximately 2–3 over the best conventional MP2 analytical gradient algorithms. In addition, we attempt to provide a straightforward guide to performing reliable and cost‐efficient geometry optimizations at the RI‐MP2 level of theory. By computing relative atomization energies for the G3/99 set and optimizing a test set of 136 equilibrium molecular structures, we demonstrate that satisfactory relative accuracy and significant computational savings can be obtained using Pople‐style atomic orbital basis sets with the existing auxiliary basis expansions for RI‐MP2 computations. We also show that RI‐MP2 geometry optimizations reproduce molecular equilibrium structures with no significant deviations (>0.1 pm) from the predictions of conventional MP2 theory. As a chemical application, we computed the extended‐globular conformational energy gap in alanine tetrapeptide at the extrapolated RI‐MP2/cc‐pV(TQ)Z level as 2.884, 4.414, and 4.994 kcal/mol for structures optimized using the HF, DFT (B3LYP), and RI‐MP2 methodologies and the cc‐pVTZ basis set, respectively. These marked energetic discrepancies originate from differential intramolecular hydrogen bonding present in the globular conformation optimized at these levels of theory and clearly demonstrate the importance of long‐range correlation effects in polypeptide conformational analysis. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007     

Improving the accuracy of ab initio methods with summation approximants and singularity analysis

The accuracy of Møller–Plesset (MP) perturbation theory and coupled‐cluster (CC) theory can be significantly improved, at essentially no increase in computational cost, by using summation approximants that model the way in which these theories converge to the full configuration interaction limit. Approximants for MP4 and CCSD(T) are presented, their size scaling is analyzed, and the functional analysis of the MP energy, on which the MP4 approximant is based, is discussed. The MP approximants are shown to have a form that is appropriate for describing resonance energies. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

高级量子化学从头计算法研究N2和H2O分子间相互作用

在MP2/6-311++G(3d,3p)电子相关校正水平上,对N₂和H₂O分子间可能存在的氢键复合物进行全自由度能量梯度优化,发现了一个接近于直线的弱氢键总能量极小结构(1),进一步在高级电子相关校正的MP4SDTQ和CCSD(T)水平,用6-311++G(3d,3p)基组加上(3s3p2d1f)键函数,用MP4和CCSD(T)计算的结构1的结合能分别为-5.061kJ/mol和-4.715kJ/mol.     

Correlated ab initio quantum chemical calculations of di- and trisaccharide conformations

High level correlated quantum chemical calculations, using MP2 and local MP2 theory, have been performed for conformations of the disaccharide, beta-maltose, and the trisaccharide, 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranose. For beta-maltose, MP2 and local MP2 calculations using the 6-311++G** basis set are in good agreement, predicting a global minimum gas-phase conformation with a counterclockwise hydrogen bond network and the experimentally-observed intersaccharide hydrogen bonding arrangement. For conformations of 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranose, MP2/6-311++G**, and local MP2/6-311++G** calculations do not provide a consensus prediction of relative energetics, with the MP2 method finding large differences in stability between extended and folded trisaccharide conformations. Local MP2 calculations, less susceptible to intramolecular basis set superposition errors, predict a narrower range of trisaccharide energetics, in line with estimates from Hartree-Fock theory and B3LYP and BP86 density functionals. All levels of theory predict compact, highly hydrogen-bonded conformations as lowest in energy on the in vacuo potential energy surface of the trisaccharide. These high level, correlated local MP2/6-311++G** calculations of di- and trisaccharide energetics constitute potential reference data in the development and testing of improved empirical and semiempirical potentials for modeling of carbohydrates in the condensed phase.     

等电子-等自旋与非等旋反应的G2(MP2)和G2研究

我们在前文［1－2］中分别用MP2－4／6－31G**／／MP2／6－31G**及MP4／6－311G（2df，Zpd）／／MP2／6－31G**研究了一些双原子氢化物、卤化物、硫化物和氧化物的化学反应的烂变·这些化学反应按如下类型分为四组，即（1）反应物与生成物之间为等电子一等自旋关系，（2）价层等电一等旅，（3）等施和（4）非等旅·结果表明，MP4／6－3fiG（2才，ZPd）对于（1），（2）和（3）类反应，基本上与实验误差小于士15kJ·mo－‘而对非等旋反应仍有较大误差；MPZ－4／6－31G””只对（1）类反应较好．由于PoPle等人近几年来创立的Gaussi…     

Revealing the physical nature and the strength of charge‐inverted hydrogen bonds by SAPT(DFT), MP2, SCS‐MP2, MP2C,and CCSD(T) methods

The physical nature of charge‐inverted hydrogen bonds in H₃XH YH₃ (X = Si, Ge; Y = Al, Ga) dimer systems is studied by means of the SAPT(DFT)‐based decomposition of interaction energies and supermolecular interaction energies based on MP2, SCS‐MP2, MP2C, and CCSD(T) methods utilizing dimer‐centered aug‐cc‐pCVnZ (n = D, T, Q) basis sets as well as an extrapolation to the complete basis set limit. It is revealed that charge‐inverted hydrogen bonds are inductive in nature, although dispersion is also important. Computed interaction energies form the following relation: . It is confirmed that the aug‐cc‐pCVDZ basis set performs poorly and that very accurate values of interaction and dispersion energies require basis sets of at least quadrupole‐ζ quality. Considerably large binding energies suggest potential usefulness of charge‐inverted hydrogen bonds as an important structural motif in molecular binding. Terminology applying to σ‐ and π‐hole interactions as well as to triel and tetrel bonds is discussed. According to this new terminology the charge‐inverted hydrogen bond would become the first described case of a hydride‐triel bond. © 2017 Wiley Periodicals, Inc.     

Evaluation of density functional theory methods for the electronic interactions between indole and substituted benzene: Applications to horseradish peroxidase

In an effort to evaluate and design fast, accurate density functional theory (DFT) methods for calculating electrostatic and dispersion interactions between proteins and ligands, we have set up a model system examining interactions between mono‐substituted benzene and indole in seven different stable conformations. We first optimized the geometries of the monomers at the B3LYP/6‐31G level, and then scanned the potential curves with MP2, HF, B3LYP, SVWN, and HCTH407 [all at the 6‐311++G(d,p) level] to find the optimum separation. We used the approximate counterpoise method to calculate the basis set superposition error‐corrected interaction energies at the optimum geometries. We then applied these methods to the interactions between aromatic active site residues of horseradish peroxidase C with indole‐3‐propionic acid at two different binding sites. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007