An efficient parallel algorithm for the calculation of canonical MP2 energies

We present the parallel version of a previous serial algorithm for the efficient calculation of canonical MP2 energies (Pulay, P.; Saebo, S.; Wolinski, K. Chem Phys Lett 2001, 344, 543). It is based on the Saebo-Alml?f direct-integral transformation, coupled with an efficient prescreening of the AO integrals. The parallel algorithm avoids synchronization delays by spawning a second set of slaves during the bin-sort prior to the second half-transformation. Results are presented for systems with up to 2000 basis functions. MP2 energies for molecules with 400-500 basis functions can be routinely calculated to microhartree accuracy on a small number of processors (6-8) in a matter of minutes with modern PC-based parallel computers.     

New parallel algorithm for MP2 energy gradient calculations

A new parallel algorithm has been developed for calculating the analytic energy derivatives of full accuracy second order Møller‐Plesset perturbation theory (MP2). Its main projected application is the optimization of geometries of large molecules, in which noncovalent interactions play a significant role. The algorithm is based on the two‐step MP2 energy calculation algorithm developed recently and implemented into the quantum chemistry program, GAMESS. Timings are presented for test calculations on taxol (C₄₇H₅₁NO₁₄) with the 6‐31G and 6‐31G(d) basis sets (660 and 1032 basis functions, 328 correlated electrons) and luciferin (C₁₁H₈N₂O₃S₂) with aug‐cc‐pVDZ and aug‐cc‐pVTZ (530 and 1198 basis functions, 92 correlated electrons). The taxol 6‐31G(d) calculations are also performed with up to 80 CPU cores. The results demonstrate the high parallel efficiency of the program. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007     

A new parallel algorithm of MP2 energy calculations

A new parallel algorithm has been developed for second‐order Møller–Plesset perturbation theory (MP2) energy calculations. Its main projected applications are for large molecules, for instance, for the calculation of dispersion interaction. Tests on a moderate number of processors (2–16) show that the program has high CPU and parallel efficiency. Timings are presented for two relatively large molecules, taxol (C₄₇H₅₁NO₁₄) and luciferin (C₁₁H₈N₂O₃S₂), the former with the 6‐31G* and 6‐311G** basis sets (1032 and 1484 basis functions, 164 correlated orbitals), and the latter with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets (530 and 1198 basis functions, 46 correlated orbitals). An MP2 energy calculation on C₁₃₀H₁₀ (1970 basis functions, 265 correlated orbitals) completed in less than 2 h on 128 processors. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 407–413, 2006     

The GPU‐enabled divide‐expand‐consolidate RI‐MP2 method (DEC‐RI‐MP2)

We report porting of the Divide‐Expand‐Consolidate Resolution of the Identity second‐order Møller–Plesset perturbation (DEC‐RI‐MP2) method to the graphic processing units (GPUs) using OpenACC compiler directives. It is shown that the OpenACC compiler directives implementation efficiently accelerates the rate‐determining step of the DEC‐RI‐MP2 method with minor implementation effort. Moreover, the GPU acceleration results in a better load balance and thus in an overall scaling improvement of the DEC algorithm. The resulting cross‐platform hybrid MPI/OpenMP/OpenACC implementation has scalable and portable performance on heterogeneous HPC architectures. The GPU‐enabled code was benchmarked using a reduced version of the S12L test set of Stefan Grimme (Grimme, Chem. Eur. J. 2012, 18, 9955) consisting of supramolecular complexes up to 158 atoms and 4292 contracted basis functions (cc‐pVTZ). The test set results demonstrate the general applicability of the DEC‐RI‐MP2 method showing results consistent with the DEC‐RI‐MP2 introductory paper (Baudin et al., J. Chem. Phys. 2016, 144, 054102) on molecules of complicated electronic structures. © 2016 Wiley Periodicals, Inc.     

An efficient parallel algorithm for the calculation of unrestricted canonical MP2 energies

We present details of our efficient implementation of full accuracy unrestricted open‐shell second‐order canonical Møller–Plesset (MP2) energies, both serial and parallel. The algorithm is based on our previous restricted closed‐shell MP2 code using the Saebo–Almlöf direct integral transformation. Depending on system details, UMP2 energies take from less than 1.5 to about 3.0 times as long as a closed‐shell RMP2 energy on a similar system using the same algorithm. Several examples are given including timings for some large stable radicals with 90+ atoms and over 3600 basis functions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Potential energy surface of the (H2)2 dimer: an MP2 study

Fifteen structures of the (H₂)₂ dimer have been investigated at the MP2/[4s3p] level. The SCF and MP2 (2nd order Møller-Plesser treatment) interaction energies have been corrected for the basis set superposition error. Only the T-shaped structure has been established as a minimum on the potential energy surface. Two equivalent T-shaped structures are connected by a saddle point with a rhomboid structure.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

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.     

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…     

First-order relativistic corrections to MP2 energy from standard gradient codes: Comparison with results from density functional theory

The evaluation of the first-order scalar relativistic corrections to MP2 energy based on either direct perturbation theory or the mass–velocity and Darwin terms is discussed. In a basis set of Lévy-Leblond spinors the one- and two-electron matrix elements of the relativistic Hamiltonian can be decomposed into a nonrelativistic part and a relativistic perturbation. Thus, a program capable of calculating nonrelativistic energy gradients can be used to calculate the cross-term between relativity and correlation. The method has been applied to selected closed-shell atoms (He, Be, Ne, and Ar) and molecules (CuH, AgH, and AuH). The calculated equilibrium distances and harmonic frequencies were compared with results from first-order relativistic density functional calculations. It was found that the cross-term is not the origin of the nonadditivity of relativistic and correlation effects. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1596–1603, 1998     

Fragment interaction analysis based on local MP2

We have developed a fragment interaction analysis based on local MP2 (FILM) in the context of the fragment molecular orbital (FMO) scheme. The primary purpose of this work is to provide a tool for analyzing inter-fragment interaction associated with dispersion interactions in a large molecule such as protein and DNA. Our implementation of local MP2 (LMP2) is based on the algorithm developed by Pulay and Werner. A potential of FILM was demonstrated using the human immunodeficiency virus type 1 protease (HIV-1 PR) complexed with lopinavir (LPV). The total energy, binding affinity, and inter-fragment interaction energy (IFIE) by the FMO method using LMP2 were compared with those obtained by canonical MP2 and the site-specific information in dispersion interaction was obtained. It turned out that the FILM is a useful tool for analyzing the dispersion interaction between an amino acid residue and a specific site of a ligand.     

Towards the versatile DFT and MP2 computational schemes for 31P NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the calculation of ³¹P NMR chemical shifts in the representative series of organophosphorous compounds are examined at the density functional theory (DFT) and second‐order Møller–Plesset perturbation theory (MP2) levels. At the DFT level, the best functionals for the calculation of ³¹P NMR chemical shifts are those of Keal and Tozer, KT2 and KT3. Both at the DFT and MP2 levels, the most reliable basis sets are those of Jensen, pcS‐2 or larger, and those of Pople, 6‐311G(d,p) or larger. The reliable basis sets of Dunning's family are those of at least penta‐zeta quality that precludes their practical consideration. An encouraging finding is that basically, the locally dense basis set approach resulting in a dramatic decrease in computational cost is justified in the calculation of ³¹P NMR chemical shifts within the 1–2‐ppm error. Relativistic corrections to ³¹P NMR absolute shielding constants are of major importance reaching about 20–30 ppm (ca 7%) improving (not worsening!) the agreement of calculation with experiment. Further better agreement with the experiment by 1–2 ppm can be obtained by taking into account solvent effects within the integral equation formalism polarizable continuum model solvation scheme. We recommend the GIAO‐DFT‐KT2/pcS‐3//pcS‐2 scheme with relativistic corrections and solvent effects taken into account as the most versatile computational scheme for the calculation of ³¹P NMR chemical shifts characterized by a mean absolute error of ca 9 ppm in the range of 550 ppm. Copyright © 2014 John Wiley & Sons, Ltd.     

Enhanced second‐order treatment of electron pair correlation

Ab initio calculations have been performed for F₂, HCCH, H₂O, HF, (HF)₂, and (H₂O)₂, comparing certain electron pair correlation methods, or methods for doubly substituted configurations. In these model systems, the reweighting of substituted configurations that occurs beyond a second‐order perturbative treatment of electron correlation can be partly built into the second‐order analysis in a computationally trivial step. Specific means for doing this are explored, and they offer improvement in certain cases or else very little change. A consistent improvement in the correlation energy when judged against treatment with double substitution coupled cluster theory for the test species is obtained through one of these schemes. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 226–236, 2000     

Direct MP2 molecular dynamics studies of H atom reaction with CD4 and CH4

The mechanism and dynamics of the H + CD₄ → CD₃ + HD (I) and H + CH₄ → CH₃ + H₂ (II) reactions have been investigated by electronic structure methods. The minimum‐energy path and vibrational frequencies along the intrinsic reaction coordinate are calculated at MP2/cc‐pVDZ level. Energy distributions of the products are also obtained by the direct classical trajectory calculations at the MP2/ cc‐pVDZ level. It is found that most of the available energy appears as product translational energy, and very little of the available energy is partitioned into internal excitation of the HD (H₂) product for reaction I (II), which is in agreement with the experimental evidence. The results indicate that the experimental results could be reproduced by the direct MP2 molecular dynamics calculations. The rotational state distributions of the products show the HD (H₂) products are formed with lower rotational quantum numbers than the CD₃ (CH₃) products. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The MC‐DFT approach including the SCS‐MP2 energies to the new minnesota‐type functionals

We have applied the multicoefficient density functional theory (MC‐DFT) to four recent Minnesota functionals, including M06‐2X, M08‐HX, M11, and MN12‐SX on the performance of thermochemical kinetics. The results indicated that the accuracy can be improved significantly using more than one basis set. We further included the SCS‐MP2 energies into MC‐DFT, and the resulting mean unsigned errors (MUEs) decreased by approximately 0.3 kcal/mol for the most accurate basis set combinations. The M06‐2X functional with the simple [6–311+G(d,p)/6–311+G(2d,2p)] combination gave the best performance/cost ratios for the MC‐DFT and MC‐SCS‐MP2|MC‐DFT methods with MUE of 1.58 and 1.22 kcal/mol, respectively. © 2014 Wiley Periodicals, Inc.     

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.     

胸腺嘧啶-BH3构型与性质的DFT和MP2研究

Geometries and combination energies are predicated at B3LYP / 6-31G（d）and MP2 / 6-31G（d）level for thymine-BH3 complexes and 5 geometries have been obtained. Then single point energy calculations using larger basis sets（6-311 + G（2df）and aug-cc-pVDZ）and vibrational analysis and natural bond orbital analysis are carried out on the 5 optimized conformers. The outcome indicates that the conformers with the boron atom combined with O directly are relatively stable ones,（a）and（b）,with the combination energies of 90. 4 and 88. 0 kJ / mol （B3LYP / 6-31G（d）,BSSE corrected）. The fact is that the nitrogen atom offers electron to the empty atomic orbital of boron which produces the conformers（c）and（d）. Only one conformer is found which is formed because two carbon atoms offer π electron to the empty orbital of boron. The charge transference exists in all the conformers. The combination energies have a good line relation with their charge transference. The calculated results show that when the complex forms their IR spectrum moved to the red side and the frequency shifts are relative to the stabilities of the complexes.     

MP2 Study on the Proton Transfer Mechanism of Glycine Assisted by Water

The geometries of glycine-nH2O （n = 1-5） complexes and the transition states of proton transfer in glycine-H2O system were calculated at the MP2/6-31＋＋G＊＊//MP2/6-31G＊ level, upon which we discovered the proton transfer mechanisms, including the number of water molecules necessary for the stabilization of zwitterions and the effect of increasing water molecules on the proton transfer. To our interest, we found that only one water molecule can stabilize the zwitterions; in addition, with the increment of water molecules, the activation energy of positive reaction decreases and that of reverse reaction increases gradually. Glycine will be ionized completely while the water molecules reach to a certain number.