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     

Ab initio study of the π–π interactions between CO2 and benzene,pyridine, and pyrrole

The π–π interactions between CO₂ and three aromatic molecules, namely benzene (C₆H₆), pyridine (C₅H₅N), and pyrrole (C₄H₅N), which represent common functional groups in metal‐organic/zeoliticimidazolate framework materials, were characterized using high‐level ab initio methods. The coupled‐cluster with single and double excitations and perturbative treatment of triple excitations (CCSD(T)) method with a complete basis set (CBS) was used to calibrate Hartree–Fock, density functional theory, and second‐order M?ller–Plesset (MP2) with resolution of the identity approximation calculations. Results at the MP2/def2‐QZVPP level showed the smallest deviations (only about 1 kJ/mol) compared with those at the CCSD(T)/CBS level of theory. The strength of π–π binding energies (BEs) followed the order C₄H₅N > C₆H₆ ～ C₅H₅N and was roughly correlated with the aromaticity and the charge transfer between CO₂ and aromatic molecule in clusters. Compared with hydrogen‐bond or electron donor–acceptor interactions observed during BE calculations at the MP2/def2‐QZVPP level of theory, π–π interactions significantly contribute to the total interactions between CO₂ and aromatic molecules. © 2013 Wiley Periodicals, Inc.     

MPI/OpenMP hybrid parallel implementation of second-order M?ller�CPlesset perturbation theory using numerical quadratures

An algorithm for massively parallel computers is developed for energy calculations of second-order M?ller?CPlesset (MP2) perturbation theory with numerical quadratures. Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) technologies are utilized for inter-node and intra-node parallelization, respectively. Computational tasks and intermediates are distributed across nodes by dividing quadrature points, and the distributed data are stored in memory. Benchmark calculations were performed on 256?C8,192 CPU cores, and we observed the speed-ups 4,534?C6,266 for 8,192 cores. A large calculation for fullerene (C₆₀) with aug-cc-pCVTZ (3,540 basis functions) was completed in ca. 4.8?h on 8,192 cores without invoking molecular symmetry.     

Excited state properties,fluorescence energies,and lifetimes of a poly(fluorene‐phenylene), based on TD‐DFT investigation

The structural and electronic properties of fluorene‐phenylene copolymer (FP)_n, n = 1–4 were studied by means of quantum chemical calculations based on density functional theory (DFT) and time dependent density functional theory (TD‐DFT) using B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest singlet excited state. It was found that (FP)_n is nonplanar in its ground state while the electronic excitations lead to planarity in its S₁ state. Absorption and fluorescence energies were calculated using TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods. Vertical excitation energies and fluorescence energies were obtained by extrapolating these values to infinite chain length, resulting in extrapolated values for vertical excitation energy of 2.89 and 2.87 eV, respectively. The S₁ ← S₀ electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is distinguishing in terms of oscillator strength. Fluorescence energies of (FP)_n calculated from TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods are 2.27 and 2.26 eV, respectively. Radiative lifetimes are predicted to be 0.55 and 0.51 ns for TD‐B3LYP/SVP and TD‐B3LYP/SVP+ calculations, respectively. These fundamental information are valuable data in designing and making of promising materials for LED materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

Massively parallel algorithm and implementation of RI‐MP2 energy calculation for peta‐scale many‐core supercomputers

A new parallel algorithm and its implementation for the RI‐MP2 energy calculation utilizing peta‐flop‐class many‐core supercomputers are presented. Some improvements from the previous algorithm (J. Chem. Theory Comput. 2013, 9, 5373) have been performed: (1) a dual‐level hierarchical parallelization scheme that enables the use of more than 10,000 Message Passing Interface (MPI) processes and (2) a new data communication scheme that reduces network communication overhead. A multi‐node and multi‐GPU implementation of the present algorithm is presented for calculations on a central processing unit (CPU)/graphics processing unit (GPU) hybrid supercomputer. Benchmark results of the new algorithm and its implementation using the K computer (CPU clustering system) and TSUBAME 2.5 (CPU/GPU hybrid system) demonstrate high efficiency. The peak performance of 3.1 PFLOPS is attained using 80,199 nodes of the K computer. The peak performance of the multi‐node and multi‐GPU implementation is 514 TFLOPS using 1349 nodes and 4047 GPUs of TSUBAME 2.5. © 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     

An ab initio study of the structures and energetics of the planar ground and 90°‐twisted excited states of substituted ethylenes

Ab initio molecular orbital calculations are performed on the planar ground states (S₀), the 90°‐twisted triplet (T₁), and pyramidalized singlet (S₁) excited states of ethylene, methaniminium cation (MC), monocyano‐ (MCE), 1,1‐dicyano‐ (DCE), 1,1‐dihydroxy‐ (DHE), and 1,1‐dicyano‐2,2‐dihydroxy (DCHE) ethylenes. Equilibrium geometries are optimized at the Hartree–Fock (HF) level with the 6‐31G* basis set. Electron correlation corrections are estimated by optimizing the HF/6‐31G* geometries at the (U)MP2/6‐31G* level and then by carrying out single‐point calculations at the fourth‐order Møller–Plesset perturbation theory ((U)MP4/6‐311G**//MP2/6‐31G*). The effects of various types of perturbations on the structures, energetics, dipole moments, and state ordering of S₀, S₁, and T₁ are carefully investigated. “Positive” S₁–T₁ splittings are estimated at the HF level for all studied molecules, while “negative” S₁–T₁ splittings are obtained at the MP2 level for MC, DHE, and DCHE. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 242–254, 2001     

Quantum chemistry in parallel with PQS

This article describes the capabilities and performance of the latest release (version 4.0) of the Parallel Quantum Solutions (PQS) ab initio program package. The program was first released in 1998 and evolved from the TEXAS program package developed by Pulay and coworkers in the late 1970s. PQS was designed from the start to run on Linux‐based clusters (which at the time were just becoming popular) with all major functionality being (a) fully parallel; and (b) capable of carrying out calculations on large—by ab initio standards—molecules, our initial aim being at least 100 atoms and 1000 basis functions with only modest memory requirements. With modern hardware and recent algorithmic developments, full accuracy, high‐level calculations (DFT, MP2, CI, and Coupled‐Cluster) can be performed on systems with up to several thousand basis functions on small (4‐32 node) Linux clusters. We have also developed a graphical user interface with a model builder, job input preparation, parallel job submission, and post‐job visualization and display. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Ab initio investigation of water clusters (H2O)n (n = 2–34)

Various properties of typical structures of water clusters in the n = 2–34 size regime with the change of cluster size have been systematically explored. Full optimizations are carried out for the structures presented in this article at the Hartree–Fock (HF) level using the 6‐31G(d) basis set by taking into account the positions of all atoms within the cluster. The influence of the HF level on the results has been reflected by the comparison between the binding energies of (H₂O)_n (n = 2–6, 8, 11, 13, 20) calculated at the HF level and those obtained from high‐level ab initio calculations at the second‐order Møller–Plesset (MP2) perturbation theory and the coupled cluster method including singles and doubles with perturbative triples (CCSD(T)) levels. HF is inaccurate when compared with MP2 and CCSD(T), but it is more practical and allows us to study larger systems. The computed properties characterizing water clusters (H₂O)_n (n = 2–34) include optimal structures, structural parameters, binding energies, hydrogen bonds, charge distributions, dipole moments, and so on. When the cluster size increases, trends of the above various properties have been presented to provide important reference for understanding and describing the nature of the hydrogen bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Analysis of Why Boron Avoids sp2 Hybridization and Classical Structures in the BnHn+2 Series

We performed global minimum searches for the B_nH_n+2 (n=2‐5) series and found that classical structures composed of 2c–2e B? H and B? B bonds become progressively less stable along the series. Relative energies increase from 2.9 kcal mol^?1 in B₂H₄ to 62.3 kcal mol^?1 in B₅H₇. We believe this occurs because boron atoms in the studied molecules are trying to avoid sp² hybridization and trigonal structure at the boron atoms, as in that case one 2p‐AO is empty, which is highly unfavorable. This affinity of boron to have some electron density on all 2p‐AOs and avoiding having one 2p‐AO empty is a main reason why classical structures are not the most stable configurations and why multicenter bonding is so important for the studied boron–hydride clusters as well as for pure boron clusters and boron compounds in general.     

Small Cycloalkane (CN)2CC(CN)2 Structures Are Highly Directional Non‐covalent Carbon‐Bond Donors

High‐level calculations (RI‐MP2/def2‐TZVP) disclosed that the σ‐hole in between two C atoms of cycloalkane X₂C?CX₂ structures (X=F, CN) is increasingly exposed with decreasing ring size. The interacting energy of complexes of F^?, HO^?, N≡C^?, and H₂CO with cyclopropane and cyclobutane X₂C?CX₂ derivatives was calculated. For X=F, these energies are small to positive, while for X=CN they are all negative, ranging from ?6.8 to ?42.3 kcal mol^?1. These finding are corroborated by a thorough statistical survey of the Cambridge Structural Database (CSD). No clear evidence could be found in support of non‐covalent carbon bonding between electron‐rich atoms (El.R.) and F₂C?CF₂ structures. In marked contrast, El.R.???(CN)₂C?C(CN)₂ interactions are abundant and highly directional. Based on these findings, the hydrophobic electrophilic bowl formed by 1,1′,2,2′‐tetracyano cyclopropane or cyclobutane derivatives is proposed as a new and synthetically accessible supramolecular synthon.     

MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations

We present the software package MO VI PAC for calculations of vibrational spectra, namely infrared, Raman, and Raman Optical Activity (ROA) spectra, in a massively parallelized fashion. MO VI PAC unites the latest versions of the programs SNF and AKIRA alongside with a range of helpful add‐ons to analyze and interpret the data obtained in the calculations. With its efficient parallelization and meta‐program design, MO VI PAC focuses in particular on the calculation of vibrational spectra of very large molecules containing on the order of a hundred atoms. For this purpose, it also offers different subsystem approaches such as Mode‐ and Intensity‐Tracking to selectively calculate specific features of the full spectrum. Furthermore, an approximation to the entire spectrum can be obtained using the Cartesian Tensor Transfer Method. We illustrate these capabilities using the example of a large π‐helix consisting of 20 (S)‐alanine residues. In particular, we investigate the ROA spectrum of this structure and compare it to the spectra of α‐ and 3₁₀‐helical analogs. © 2012 Wiley Periodicals, Inc.     

Engineering the Atomic Interface with Single Platinum Atoms for Enhanced Photocatalytic Hydrogen Production

It is highly desirable but challenging to optimize the structure of photocatalysts at the atomic scale to facilitate the separation of electron–hole pairs for enhanced performance. Now, a highly efficient photocatalyst is formed by assembling single Pt atoms on a defective TiO₂ support (Pt₁/def‐TiO₂). Apart from being proton reduction sites, single Pt atoms promote the neighboring TiO₂ units to generate surface oxygen vacancies and form a Pt‐O‐Ti³⁺ atomic interface. Experimental results and density functional theory calculations demonstrate that the Pt‐O‐Ti³⁺ atomic interface effectively facilitates photogenerated electrons to transfer from Ti³⁺ defective sites to single Pt atoms, thereby enhancing the separation of electron–hole pairs. This unique structure makes Pt₁/def‐TiO₂ exhibit a record‐level photocatalytic hydrogen production performance with an unexpectedly high turnover frequency of 51423 h^?1, exceeding the Pt nanoparticle supported TiO₂ catalyst by a factor of 591.     

CPMD/GULP QM/MM interface for modeling periodic solids: Implementation and its application in the study of Y‐zeolite supported Rhn clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane‐wave density functional theory based CPMD code and the empirical force‐field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born–Oppenheimer and Car–Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in α‐cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh_n; n = 2 to 6) formed from Rh(C₂H₄)₂ complex adsorbed within a cavity of Y‐zeolite in a reducible atmosphere of H₂ gas. © 2016 Wiley Periodicals, Inc.     

An integral direct, distributed-data, parallel MP2 algorithm

Summary A scalable integral direct, distributed-data parallel algorithm for four-index transformation is presented. The algorithm was implemented in the context of the second-order M?ller-Plesset (MP2) energy evaluation, yet it is easily adopted for other electron correlation methods, where only MO integrals with two indices in the virtual orbitals space are required. The major computational steps of the MP2 energy are the two-electron integral evaluationO(N ⁴) and transformation into the MO basisO(ON ⁴), whereN is the number of basis functions, andO the number of occupied orbitals, respectively. The associated maximal communication costs scale asO(n _Σ O ² V N), whereV andn _Σ denote the number of virtual orbitals, and the number of symmetry-unique shells. The largest local and global memory requirements areO(N ²) for the MO coefficients andO(OV N) for the three-quarter transformed integrals, respectively. Several aspects of the implementation such as symmetry-treatment, integral prescreening, and the distribution of data and computational tasks are discussed. The parallel efficiency of the algorithm is demonstrated by calculations on the phenanthrene molecule, with 762 primitive Gaussians, contracted to 412 basis functions. The calculations were performed on an IBM SP2 with 48 nodes. The measured wall clock time on 48 nodes is less than 15 min for this calculation, and the speedup relative to single-node execution is estimated to 527. This superlinear speedup is a result of exploiting both the compute power and the aggregate memory of the parallel computer. The latter reduces the number of passes through the AO integral list, and hence the operation count of the calculation. The test calculations also show that the evaluation of the two-electron integrals dominates the calculation, despite the higher scaling of the transformation step.     

An unusual polycatenating network self‐assembled by the 2D → 2D parallel → 3D parallel interpenetration of coordinative and hydrogen‐bonded (6,3) motifs

In the title coordination compound, catena‐poly[[[bis[diaquacadmium(II)]‐μ₂‐trans‐1,2‐bis(4‐pyridyl)ethene]bis{μ₂‐2,2′‐[(5‐carboxymethoxy‐m‐phenylene)dioxy]diacetato}] trans‐1,2‐bis(4‐pyridyl)ethene solvate dihydrate], {[Cd₂(C₁₂H₁₀O₉)₂(C₁₂H₁₀N₂)(H₂O)₄]·C₁₂H₁₀N₂·2H₂O}_n, (I), each Cd^II centre adopts a pentagonal–bipyramidal coordination geometry. The incompletely deprotonated 2,2′‐[(5‐carboxymethoxy‐m‐phenylene)dioxy]diacetate (TCMB) ligands and trans‐1,2‐bis(4‐pyridyl)ethene (bpe) ligands both act as bidentate bridges, linking the Cd^II centres into one‐dimensional ladders, which are connected into an undulating two‐dimensional (6,3) layer through O—H...N hydrogen bonds between the carboxylate groups of the TCMB ligands and the N atoms of the uncoordinated bpe ligands. Each undulating layer polycatenates two other identical layers, exhibiting the unusual combination of both 2D → 2D parallel and 2D → 3D parallel interpenetration (2D and 3D are two‐ and three‐dimensional, respectively).     

Univalent Gallium and Indium Phosphane Complexes: From Pyramidal M(PPh3)3+ to Carbene‐Analogous Bent M(PtBu3)2+ (M=Ga,In) Complexes

In a new oxidative route, Ag⁺[Al(OR^F)₄]^? (R^F=C(CF₃)₃) and metallic indium were sonicated in aromatic solvents, such as fluorobenzene (PhF), to give a precipitate of silver metal and highly soluble [In(PhF)_n]⁺ salts (n=2, 3) with the weakly coordinating [Al(OR^F)₄]^? anion in quantitative yield. The In⁺ salt and the known analogous Ga⁺[Al(OR^F)₄]^? were used to synthesize a series of homoleptic PR₃ phosphane complexes [M(PR₃)_n]⁺, that is, the weakly PPh₃‐bridged [(Ph₃P)₃In–(PPh₃)–In(PPh₃)₃]²⁺ that essentially contains two independent [In(PPh₃)₃]⁺ cations or, with increasing bulk of the phosphane, the carbene‐analogous [M(PtBu₃)₂]⁺ (M=Ga, In) cations. The M^I? P distances are 27 to 29 pm longer for indium, and thus considerably longer than the difference between their tabulated radii (18 pm). The structure, formation, and frontier orbitals of these complexes were investigated by calculations at the BP86/SV(P), B3LYP/def2‐TZVPP, MP2/def2‐TZVPP, and SCS‐MP2/def2‐TZVPP levels.