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.     

DIESEL-MP2: a new program to perform large-scale multireference-MP2 computations

This article presents a new MR‐MP2 code (Multi‐Reference Møller–Plesset 2nd order) suitable for the computation MR‐MP2 energies of extended systems with strong near degeneracy effects (e.g., open shell systems). It is based on the DIESEL program package developed by Hanrath and Engels. Due to improved algorithms the new code is able to handle systems with 400–500 basis functions and more than 100 electrons. The code is made for parallel computers with distributed memory, but can also be run on local machines. It possesses two integral interfaces (MOLCAS, TURBOMOLE). The algorithms are briefly introduced and timings for the Neocarzinostatin chromophore are presented. The efficiencies of the codes obtained with Intel or GNU compilers are compared. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1055–1062, 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.     

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.     

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 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     

Intermolecular interactions of formic acid with benzene: Energy decomposition analyses with ab initio MP2 and double‐hybrid density functional computations

The intermolecular interactions of formic acid (HCOOH) with benzene (C₆H₆) have been investigated using localized molecular orbital energy decomposition analyses (LMO‐EDA) with ab initio MP2 and several double‐hybrid density functionals. The molecular geometries of five HCOOH…C₆H₆ complexes and corresponding benchmark total interaction energies at the CCSD(T)/CBS level are taken from literature (Zhao et al., J. Chem. Theory Comput. 2009, 5, 2726). According to the results of LMO‐EDA with the MP2 method, the dispersion energies are found to be as important as the electrostatic energies for the total interaction energies of the five HCOOH…C₆H₆ complexes. Based on LMO‐EDA with the double‐hybrid density functionals of B2PLYP, B2K‐PLYP, B2T‐PLYP, and B2GP‐PLYP computations, two new parameters for the framework of B2PLYP are extrapolated. These two new parameters are tested with other 10 complexes involving C₆H₆ (Crittenden, J. Phys. Chem. A 2009, 113, 1663), and they perform well on predicting the corresponding total interaction energies. Interestingly, these two new parameters for the framework of B2PLYP also perform well on the noncovalent complexation energies database (NCCE31/05) developed by Truhlar's group (Zhao and Truhlar, J. Phys. Chem. A 2005, 109, 5656). Therefore, these two new parameters appear to be suitable for investigating the noncovalent interactions, and they are denoted as B2N‐PLYP, where N stands for the noncovalent interaction. This study is expected to provide new insight into the derivation of double‐hybrid density functionals for studying the noncovalent interactions. © 2013 Wiley Periodicals, Inc.     

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.     

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…     

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     

Application of resolution of identity approximation of second-order M?ller�CPlesset perturbation theory to three-body fragment molecular orbital method

The resolution of identity (RI) approximation of second-order M?ller?CPlesset perturbation (MP2) theory, termed as RI-MP2, is applied to three-body fragment molecular orbital (FMO3) method. New implementation of FMO3 RI-MP2 is developed based on an efficient parallel RI-MP2 code developed recently in our group. Using this new implementation, the accuracy and computational time of FMO3 RI-MP2 calculations are assessed for water clusters, polyalanines, and proteins. The errors arising from RI-MP2 are sufficiently small in the FMO3 MP2 calculations that they give quantitative accuracy for practical chemical applications. Considerable time savings are attained in the FMO3 MP2 calculations with the application of RI-MP2.     

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     

MPI/OpenMP hybrid parallel algorithm for resolution of identity second‐order Møller–Plesset perturbation calculation of analytical energy gradient for massively parallel multicore supercomputers

A massively parallel algorithm of the analytical energy gradient calculations based the resolution of identity Møller–Plesset perturbation (RI‐MP2) method from the restricted Hartree–Fock reference is presented for geometry optimization calculations and one‐electron property calculations of large molecules. This algorithm is designed for massively parallel computation on multicore supercomputers applying the Message Passing Interface (MPI) and Open Multi‐Processing (OpenMP) hybrid parallel programming model. In this algorithm, the two‐dimensional hierarchical MP2 parallelization scheme is applied using a huge number of MPI processes (more than 1000 MPI processes) for acceleration of the computationally demanding O (N ⁵) step such as calculations of occupied–occupied and virtual–virtual blocks of MP2 one‐particle density matrix and MP2 two‐particle density matrices. The new parallel algorithm performance is assessed using test calculations of several large molecules such as buckycatcher C₆₀@C₆₀H₂₈ (144 atoms, 1820 atomic orbitals (AOs) for def2‐SVP basis set, and 3888 AOs for def2‐TZVP), nanographene dimer (C₉₆H₂₄)₂ (240 atoms, 2928 AOs for def2‐SVP, and 6432 AOs for cc‐pVTZ), and trp‐cage protein 1L2Y (304 atoms and 2906 AOs for def2‐SVP) using up to 32,768 nodes and 262,144 central processing unit (CPU) cores of the K computer. The results of geometry optimization calculations of trp‐cage protein 1L2Y at the RI‐MP2/def2‐SVP level using the 3072 nodes and 24,576 cores of the K computer are presented and discussed to assess the efficiency of the proposed algorithm. © 2017 Wiley Periodicals, Inc.     

A general efficient implementation of the BSSE-free SCF and MP2 methods based on the chemical Hamiltonian approach

We describe some details related to a new, general, and efficient implementation of the BSSE‐free SCF and second‐order Møller–Plesset perturbation theories of intermolecular interactions, based on the “Chemical Hamiltonian Approach” (CHA). The program is applicable for both open‐shell and closed‐shell systems and for an arbitrary number of interacting subsystems. With the new program the CHA method is faster than the usual “counterpoise correction” scheme for single point calculations, especially for clusters consisting of several molecules. The numerical results provided by these conceptually different schemes, however, have again found to be very close to each other. The CHA scheme is particularly good for providing truly BSSE‐free MP2 data for intermolecular potentials. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1505–1516, 2006     

Assessment of the performance of MP2 and MP2 variants for the treatment of noncovalent interactions

For many years, MP2 served as the principal method for the treatment of noncovalent interactions. Until recently, this was the only technique that could be used to produce reasonably accurate binding energies, with binding energy errors generally below ~35%, at a reasonable computational cost. The past decade has seen the development of many new methods with improved performance for noncovalent interactions, several of which are based on MP2. Here, we assess the performance of MP2, LMP2, MP2-F12, and LMP2-F12, as well as spin component scaled variants (SCS) of these methods, in terms of their abilities to produce accurate interaction energies for binding motifs commonly found in organic and biomolecular systems. Reference data from the newly developed S66 database of interaction energies are used for this assessment, and a further set of 38 complexes is used as a test set for SCS methods developed herein. The strongly basis set-dependent nature of MP2 is confirmed in this study, with the SCS technique greatly reducing this behavior. It is found in this work that the spin component scaling technique can effectively be used to dramatically improve the performance of MP2 and MP2 variants, with overall errors being reduced by factors of about 1.5-2. SCS versions of all MP2 variants tested here are shown to give similarly accurate overall results.     

Assessment of ab initio MP2 and density functionals for characterizing the potential energy profiles of the SN2 reactions at N center

The potential energy profiles of five selected bimolecular nucleophilic substitution (S_N2) reactions at nitrogen (N) center have been reinvestigated with the CCSD(T), G3[MP2,CCSD(T)], MP2, and some density functional methods. The basis sets of 6‐31+G(d,p) and 6‐311+G(3d,2p) are used for the MP2 and density functional calculations. Taking the relative energies at the CCSD(T)/CBS level of theory as benchmarks, we recommend the MP2, B97‐K, B2K‐PLYP, BMK, ωB97X‐D, M06‐2X, M05‐2X, CAM‐B3LYP, M08‐SO, and ωB97X methods to generally characterize the potential energy profiles for the S_N2 reactions at N center. Furthermore, these recommended methods with the relatively small 6‐31+G(d,p) basis set may also be used to perform direct classical trajectory simulations to uncover the dynamic behaviors of the S_N2 reactions at N center. © 2012 Wiley Periodicals, Inc.     

Ab initio quantum chemical calculation of electron density,electrostatic potential,and electric field of biomolecule based on fragment molecular orbital method

Efficient quantum chemical calculations of electrostatic properties, namely, the electron density (EDN), electrostatic potential (ESP), and electric field (EFL), were performed using the fragment molecular orbital (FMO) method. The numerical errors associated with the FMO scheme were examined at the HF, MP2, and RI‐MP2 levels of theory using 4 small peptides. As a result, the FMO errors in the EDN, ESP, and EFL were significantly smaller than the magnitude of the electron correlation effects, which indicated that the FMO method provides sufficiently accurate values of electrostatic properties. In addition, an attempt to reduce the computational effort was proposed by combining the FMO scheme and a point charge approximation. The error due to this approximation was examined using 2 proteins, prion protein and human immunodeficiency virus type 1 protease. As illustrative examples, the ESP values at the molecular surface of these proteins were calculated at the MP2 level of theory.