Natural bond orbital‐based energy density analysis for correlated methods: Second‐order Møller–Plesset perturbation and coupled‐cluster singles and doubles

Natural bond orbital‐based energy density analysis (NBO‐EDA), which split energies into atomic and bonding contributions, is proposed for correlated methods such as coupled‐cluster singles and doubles (CCSD) and second‐order Møller–Plesset (MP2) perturbation. Applying NBO‐EDA for CCSD and MP2 to ethylene and the Diels–Alder reaction, we are successful in obtaining useful knowledge regarding electron correlation of π‐ and σ‐type orbitals, and clarifying the difference of the reaction barriers and heat of reaction calculated by CCSD and MP2. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Multi‐state multi‐reference Møller–Plesset second‐order perturbation theory for molecular calculations

This work presents multi‐state multi‐reference Møller–Plesset second‐order perturbation theory as a variant of multi‐reference perturbation theory to treat electron correlation in molecules. An effective Hamiltonian is constructed from the first‐order wave operator to treat several strongly interacting electronic states simultaneously. The wave operator is obtained by solving the generalized Bloch equation within the first‐order interaction space using a multi‐partitioning of the Hamiltonian based on multi‐reference Møller–Plesset second‐order perturbation theory. The corresponding zeroth‐order Hamiltonians are nondiagonal. To reduce the computational effort that arises from the nondiagonal generalized Fock operator, a selection procedure is used that divides the configurations of the first‐order interaction space into two sets based on the strength of the interaction with the reference space. In the weaker interacting set, only the projected diagonal part of the zeroth‐order Hamiltonian is taken into account. The justification of the approach is demonstrated in two examples: the mixing of valence Rydberg states in ethylene, and the avoided crossing of neutral and ionic potential curves in LiF. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Can periodane accommodate neon?

Periodane is a molecule in which each of the atoms from the second period other than neon occur exactly once. The isomers of a neon analogue of periodane are studied computationally using density functional theory and Møller–Plesset perturbation theory. We were unable to find stable structures in which neon was tightly bound; all the minima are found to be weakly bound NCB(F)OLi  Ne complexes. However, the novel NCB(F)OLi and NCBF molecules were found during the search.     

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.     

Exact size consistency of multireference Møller–Plesset perturbation theory

Single‐reference closed‐shell Møller–Plesset perturbation theory is well known for its size consistency, a quality that is essential for consistent comparisons of calculations on molecules of different size. However, it is far from obvious whether this quality can be retained in the multireference case. In this work it is shown that an exactly size consistently generalization to multireference perturbation theory can be constructed. The central result is that the zeroth‐order Hamiltonian should be constructed using separate projection operators for each excitation level, i.e., it should contain no couplings between different excitation levels. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 549–558, 1999     

Dynamic hyperpolarizabilities in Møller–Plesset perturbation theory

As a formulation for calculating the dynamic polarizabilities and hyperpolarizabilities, two different types of the time‐dependent Møller–Plesset perturbation theory (MPPT) are presented: the MPPT in the quasienergy derivative method (QED–MPPT) and the MPPT in the energylike derivative method (ELD–MPPT). The explicit expressions for the response properties in each of these MPPT up to the quadratic response [μ, α(−ω₁, ω₁), β(−ω_σ, ω₁, ω₂)] at an arbitrary correlated order are given. Calculations of the dynamic polarizabilities and hyperpolarizabilities dependent on one frequency at the second‐order MPPT (MP2), in the QED method (QED–MP2) and in the ELD method (ELD–MP2), are examined for 10‐electron systems: hydrogen fluoride and neon. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 251–271, 1999     

<Emphasis Type="Italic">Ab initio</Emphasis> study of small coinage metal telluride clusters Au<Subscript>n</Subscript>Te<Subscript>m</Subscript> (<Emphasis Type="Italic">n,m</Emphasis> = 1, 2)

The geometries of the most stable isomers of gold telluride systems AuTe, Au₂Te, and AuTe₂ are determined using the MP2 method. The aspect of gold—telluride interaction, the electron correlation, and relativistic effects on geometry and stability are investigated at the MP2 and CCSD(T) theoretical levels. The results show that the electron correlation and relativistic effects are responsible not only for gold—gold attraction but also for additional gold—telluride interaction. The gold—telluride interaction is strong enough to modify the known pattern of bare gold clusters. Both effects are essential for determining the geometry and relative stability of this type of systems.     

Catalytic Activities of Au6, , and Clusters for CO oxidation: A density functional study

We have studied the CO oxidation over neutral, anionic, and cationic gold hexamer clusters using density functional theory which elucidates the effect of cluster charge state on the catalytic activity. Herein, we have considered the conventional bimolecular Langmuir–Hinshelwood mechanism with coadsorbed CO and O₂ at the neighboring sites in all the clusters. Among the three clusters, entails lower barriers during the various steps of the oxidation mechanism. The stability of all the species including the transition states with respect to the interacting species in indicates no thermal activation. Our study suggests better catalytic activity of as compared to the neutral and cationic counterparts. © 2014 Wiley Periodicals, Inc.     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.     

The intermolecular interaction in the charge-transfer complexes between amines and halogens: A theoretical characterization of the trends in halogen bonding

The trends in the properties of prereactive or charge-transfer complexes formed between the simple amines NH₃, CH₃NH₂, (CH₃)₂NH, and (CH₃)₃N and the halogens F₂, ClF, Cl₂, BrF, BrCl, and Br₂ were investigated by the ab initio restricted Hartree–Fock approach, the Møller–Plesset second-order method, and with several density functional theory variants using extended polarized basis sets. The most important structural parameters, the stabilization energies, the dipole moments, and other quantities characterizing the intermolecular halogen bond in these complexes are monitored, discussed, and compared. A wide range of interaction strengths is spanned in these series. Successive methyl substitution of the amine as well as increasing polarities and polarizabilities of the halogen molecules both systematically enhance the signature of charge-transfer interaction. These trends in halogen bonds of varying strength, in many aspects, parallel the features of hydrogen bonding.     

The performance of density functional theory for LnF (Ln=Nd,Eu, Gd,Yb) and YbH

Different density functional theory (DFT) functionals have been evaluated by studying geometries and bond strengths of YbH, YbF, EuF, GdF, and NdF and compared with accurate CCSD(T) results and, when available, experiment. The agreement between the CCSD(T) results and experiment, when available, is good. The agreement is also good between bond strengths calculated at the DFT level using relativistic effective core potentials and the CCSD(T) results. However, the all-electron ADF calculations systematically overestimate binding energies. The geometries obtained by both the all-electron and the effective-core-potential-based DFT calculations are generally in good agreement with the CCSD(T) results.Contribution to the Björn Roos Honorary Issue     

Theoretical analysis of correlation between ionization threshold fluence in IR‐MALDI and IR absorption spectrum of matrix molecules

To investigate the correlation between the wavelength dependence of ionization threshold fluence of target molecule in matrix‐assisted laser desorption/ionization by infrared (IR) laser and the IR absorption spectrum of matrix molecule, we have analyzed the IR absorption spectra of four matrix molecules using density functional theory and correlated ab initio molecular orbital method. The calculated IR absorption spectra of the isolated molecules showed more qualitative correlation with the wavelength dependence of ionization threshold fluence than those of the solid state structures. We can consider that a portion of matrix molecules lost the ordered crystal structure and that the transition to the diluted or isolated state occurred at the early process of IR laser irradiation. © 2012 Wiley Periodicals, Inc.     

Study of the formamide–methanol dimer with ab initio and density functional theory methods

For the first time, the structures and energies for the hydrogen bonding of a 1:1 complex formed between formamide and methanol molecules have been computed with various pure and hybrid density functional theory (DFT) and ab initio methods at varied basis set levels from 6‐31g to 6‐31+g(d,p). Five reasonable geometries on the potential energy surface of methanol and formamide system are considered and their relative stability is discussed. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. From the systematic studies, it is found that all the DFT methods selected here correctly compute the dimerization energies and geometries, with the B3P86 method predicting the hydrogen bond lengths relatively shorter and BPW91 yielding the interaction energies relatively lower. Finally, the solvent effects on the geometries of the formamide–methanol complexes have also been investigated using self‐consistent reaction field (SCRF) calculations with five different DFT methods at the 6‐31+g(d,p) basis set level. The results indicate that the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers. Moreover, the basis set superposition error correction is critical to the interaction energies in the polar solvents. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Theoretical study of structure and vibrational properties of MgnOn (n = 3–10) clusters

The structure and harmonic vibrations of Mg_nO_n (n = 3–10) clusters have been investigated using density functional theory. All structures are found to be cumulenic D_nh rings (equal bonds, alternating angles), with one intense out‐of‐plane mode and three infrared (IR)‐active degenerate modes, of which the highest one is extremely intense and increases asymptotically to 1000 cm^?1 for n = 10 at the B3LYP/6‐311++G(2d,2p) level. Comparisons with C_2n clusters show that B_nN_n and Be_nO_n clusters, the structure and bonding type for the Mg_nO_n clusters are consistent with those of the C_2n (n = 3, 5, 7,…) clusters B_nN_n(n = 3–10) and Be_nO_n(n = 3–10) clusters. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Noncollinear spin density functional theory for spin‐frustrated and spin‐degenerate systems

We have implemented ab initio linear combinations of Gaussian‐type orbital calculations with generalized localized spin density approximation (GLSDA) for a dimer of equilateral H₃ as a model of the noncollinear magnetic clusters. It has been found that the GLSDA solution with the three‐dimensional noncollinear spin structure is, contrary to prior band calculations by other groups, the ground state near the O_h conformation. Further computational results are compared to that of ab initio generalized Hartree–Fock. The difference between them and the influence of the correlation correction were discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The ene reaction: Comparison of results of Hartree-Fock,Møller-Plesset,CASSCF, and DFT calculations

Structural and energetic aspects of the ene reaction were investigated using a variety of computational methods incorporating different ways of accounting for electron correlation. Compared to the noncorrelated Hartree-Fock method, opposing trends were observed in the geometry of the transition state when using the Complete Active Space-Self Consistent Field (CASSCF) method versus Møller-Plesset and density functional theory (DFT) methods. For reproducing experimental results, both Møller-Plesset and DFT methods appear to be successful, while the CASSCF method failed to reproduce the experimental energy changes. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 509–514, 1997     

Density functional theory study of geometry and stability of small Zrn (n = 2–10) clusters

Geometric structures, electronic properties, and stabilities of small Zr_n and Zr (n = 2–10) clusters have been investigated using density functional theory with effective core potential LanL2DZ basis set. For both neutral and charged systems, several isomers and different multiplicities were studied to determine the lowest energy structures. Many most stable states with high symmetry were found for small Zr_n clusters. The most stable structures and symmetries of Zr clusters are the same as the neutral ones except n = 4 and 7. We found that the clusters with n > 3 possess highly compact structures. The clusters are inclined to form the caged‐liked geometry containing pentagonal structures for n > 8, which is in favor of energy. From the formation energy and second‐order energy difference, we obtained that 2‐, 5‐, 7‐atoms of neutral and 4‐, 7‐atoms cationic clusters are the magic numbers. Furthermore, the highest occupied molecular orbital‐lowest unoccupied molecular orbital gaps display that the Zr₃, Zr₆, Zr, and Zr are more stable in chemical stability. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Analytic derivatives for the XYG3 type of doubly hybrid density functionals: Theory,implementation, and assessment

We present a theoretical development of the equations required to perform an analytic geometry optimization of a molecular system using the XYG3 type of doubly hybrid (xDH) functionals. In contrast to the well‐established B2PLYP type of DH functionals, the energy expressions in the xDH functionals are constructed by using density and orbital information from another standard Kohn–Sham (KS) functional (e.g., B3LYP) for doing the self‐consistent field calculations. Thus, the xDH functionals are nonvariational in both the hybrid density functional part and the second‐order perturbation part, each of which requires formally to solve a coupled‐perturbed KS equation. An implementation is reported here which combines the two parts by defining a total Lagrangian such that only a single set of the Z‐vector equations need to be solved. The computational cost with our implementation is of the same order as those for the conventional Møller–Plesset theory to the second order (MP2) and B2PLYP. Systematic test calculations are provided for covalently bonded molecules as well as compounds involving the intramolecular nonbonded interactions for the main group elements. Satisfactory performance of the xDH functionals demonstrates that the extra computer time on top of the conventional KS procedure is well‐invested, in particular, when the standard KS functionals and MP2 as well, are problematic. © 2013 Wiley Periodicals, Inc.