Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation

An efficient implementation of the orbital-optimized second-order perturbation theory with the density-fitting (DF-OMP2) and Cholesky decomposition (CD-OMP2) approaches is presented. The DF-OMP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost with the conventional orbital-optimized MP2 (OMP2) [Bozkaya, U.; Turney, J. M.; Yamaguchi, Y.; Schaefer, H. F.; Sherrill, C. D. <i>J. Chem. Phys.</i> <b>2011</b>, <i>135</i>, 104103] and the orbital-optimized MP2 with the resolution of the identity approach (OO-RI-MP2) [Neese, F.; Schwabe, T.; Kossmann, S.; Schirmer, B.; Grimme, S. <i>J. Chem. Theory Comput.</i> <b>2009</b>, <i>5</i>, 3060–3073]. Our results demonstrate that the DF-OMP2 method provides substantially lower computational costs than OMP2 and OO-RI-MP2. Further application results show that the orbital-optimized methods are very beneficial for the computation of open-shell noncovalent interactions. Considering both computational efficiency and the accuracy of the DF-OMP2 method, we conclude that DF-OMP2 is very promising for the study of weak interactions in open-shell molecular systems

Orbital-Optimized MP3 and MP2.5 with Density-Fitting and Cholesky Decomposition Approximations

Efficient implementations of the orbital-optimized MP3 and MP2.5 methods with the density-fitting (DF-OMP3 and DF-OMP2.5) and Cholesky decomposition (CD-OMP3 and CD-OMP2.5) approaches are presented. The DF/CD-OMP3 and DF/CD-OMP2.5 methods are applied to a set of alkanes to compare the computational cost with the conventional orbital-optimized MP3 (OMP3) [Bozkaya <i>J. Chem. Phys.</i> <b>2011</b>, <i>135</i>, 224103] and the orbital-optimized MP2.5 (OMP2.5) [Bozkaya and Sherrill <i>J. Chem. Phys.</i> <b>2014</b>, <i>141</i>, 204105]. Our results demonstrate that the DF-OMP3 and DF-OMP2.5 methods provide considerably lower computational costs than OMP3 and OMP2.5. Further application results show that the orbital-optimized methods are very helpful for the study of open-shell noncovalent interactions, aromatic bond dissociation energies, and hydrogen transfer reactions. We conclude that the DF-OMP3 and DF-OMP2.5 methods are very promising for molecular systems with challenging electronic structures

Analytic Energy Gradients and Spin Multiplicities for Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting Approximation: An Efficient Implementation

An efficient implementation of analytic energy gradients and spin multiplicities for the density-fitted orbital-optimized second-order perturbation theory (DF-OMP2) [Bozkaya, U. <i>J. Chem. Theory Comput.</i> <b>2014</b>, <i>10</i>, 2371–2378] is presented. The DF-OMP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the cost of single point analytic gradient computations with the orbital-optimized MP2 with the resolution of the identity approach (OO-RI-MP2) [Neese, F.; Schwabe, T.; Kossmann, S.; Schirmer, B.; Grimme, S. <i>J. Chem. Theory Comput.</i> <b>2009</b>, <i>5</i>, 3060–3073]. Our results demonstrate that the DF-OMP2 method provides substantially lower computational costs for analytic gradients than OO-RI-MP2. On average, the cost of DF-OMP2 analytic gradients is 9–11 times lower than that of OO-RI-MP2 for systems considered. We also consider aromatic bond dissociation energies, for which MP2 provides poor reaction energies. The DF-OMP2 method exhibits a substantially better performance than MP2, providing a mean absolute error of 2.5 kcal mol^–1, which is more than 9 times lower than that of MP2 (22.6 kcal mol^–1). Overall, the DF-OMP2 method appears very helpful for electronically challenging chemical systems such as free radicals or other cases where standard MP2 proves unreliable. For such problematic systems, we recommend using DF-OMP2 instead of the canonical MP2 as a more robust method with the same computational scaling

Assessment of Orbital-Optimized MP2.5 for Thermochemistry and Kinetics: Dramatic Failures of Standard Perturbation Theory Approaches for Aromatic Bond Dissociation Energies and Barrier Heights of Radical Reactions

An assessment of orbital-optimized MP2.5 (OMP2.5) [Bozkaya, U.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 204105] for thermochemistry and kinetics is presented. The OMP2.5 method is applied to closed- and open-shell reaction energies, barrier heights, and aromatic bond dissociation energies. The performance of OMP2.5 is compared with that of the MP2, OMP2, MP2.5, MP3, OMP3, CCSD, and CCSD­(T) methods. For most of the test sets, the OMP2.5 method performs better than MP2.5 and CCSD, and provides accurate results. For barrier heights of radical reactions and aromatic bond dissociation energies OMP2.5–MP2.5, OMP2–MP2, and OMP3–MP3 differences become obvious. Especially, for aromatic bond dissociation energies, standard perturbation theory (MP) approaches dramatically fail, providing mean absolute errors (MAEs) of 22.5 (MP2), 17.7 (MP2.5), and 12.8 (MP3) kcal mol^–1, while the MAE values of the orbital-optimized counterparts are 2.7, 2.4, and 2.4 kcal mol^–1, respectively. Hence, there are 5–8-folds reductions in errors when optimized orbitals are employed. Our results demonstrate that standard MP approaches dramatically fail when the reference wave function suffers from the spin-contamination problem. On the other hand, the OMP2.5 method can reduce spin-contamination in the unrestricted Hartree–Fock (UHF) initial guess orbitals. For overall evaluation, we conclude that the OMP2.5 method is very helpful not only for challenging open-shell systems and transition-states but also for closed-shell molecules. Hence, one may prefer OMP2.5 over MP2.5 and CCSD as an <i>O</i>(<i>N</i>⁶) method, where <i>N</i> is the number of basis functions, for thermochemistry and kinetics. The cost of the OMP2.5 method is comparable with that of CCSD for energy computations. However, for analytic gradient computations, the OMP2.5 method is only half as expensive as CCSD

Theoretical Study of Thermal Rearrangements of 1-Hexen-5-yne, 1,2,5-Hexatriene, and 2-Methylenebicyclo[2.1.0]pentane

In this research, a comprehensive theoretical investigation of the thermal rearrangements of 1-hexen-5-yne, 1,2,5-hexatriene, and 2-methylenebicyclo[2.1.0]­pentane is carried out employing density functional theory (DFT) and high level <i>ab initio</i> methods, such as the complete active space self-consistent field (CASSCF), multireference second-order Møller–Plesset perturbation theory (MRMP2), and coupled-cluster singles and doubles with perturbative triples [CCSD­(T)]. The potential energy surface (PES) for the relevant system is explored to provide a theoretical account of pyrolysis experiments by Huntsman, Baldwin, and Roth on the target system. The rate constants and product distributions are calculated using theoretical kinetic modelings. The rate constant for each isomerization reaction is computed using the transition state theory (TST). The simultaneous first-order ordinary-differential equations are solved numerically for the relevant system to obtain time-dependent concentrations, hence the product distributions at a given temperature. Our computed energy values (reaction energies and activation parameters) are in agreement with Roth’s experiments and the product distributions of Huntsman’s experiments at 340 and 385 °C with various reaction times, while simulated product fractions are in qualitative accordance with Baldwin’s experiment

Assessment of Orbital-Optimized MP2.5 for Thermochemistry and Kinetics: Dramatic Failures of Standard Perturbation Theory Approaches for Aromatic Bond Dissociation Energies and Barrier Heights of Radical Reactions

An assessment of orbital-optimized MP2.5 (OMP2.5) [Bozkaya, U.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 204105] for thermochemistry and kinetics is presented. The OMP2.5 method is applied to closed- and open-shell reaction energies, barrier heights, and aromatic bond dissociation energies. The performance of OMP2.5 is compared with that of the MP2, OMP2, MP2.5, MP3, OMP3, CCSD, and CCSD­(T) methods. For most of the test sets, the OMP2.5 method performs better than MP2.5 and CCSD, and provides accurate results. For barrier heights of radical reactions and aromatic bond dissociation energies OMP2.5–MP2.5, OMP2–MP2, and OMP3–MP3 differences become obvious. Especially, for aromatic bond dissociation energies, standard perturbation theory (MP) approaches dramatically fail, providing mean absolute errors (MAEs) of 22.5 (MP2), 17.7 (MP2.5), and 12.8 (MP3) kcal mol^–1, while the MAE values of the orbital-optimized counterparts are 2.7, 2.4, and 2.4 kcal mol^–1, respectively. Hence, there are 5–8-folds reductions in errors when optimized orbitals are employed. Our results demonstrate that standard MP approaches dramatically fail when the reference wave function suffers from the spin-contamination problem. On the other hand, the OMP2.5 method can reduce spin-contamination in the unrestricted Hartree–Fock (UHF) initial guess orbitals. For overall evaluation, we conclude that the OMP2.5 method is very helpful not only for challenging open-shell systems and transition-states but also for closed-shell molecules. Hence, one may prefer OMP2.5 over MP2.5 and CCSD as an <i>O</i>(<i>N</i>⁶) method, where <i>N</i> is the number of basis functions, for thermochemistry and kinetics. The cost of the OMP2.5 method is comparable with that of CCSD for energy computations. However, for analytic gradient computations, the OMP2.5 method is only half as expensive as CCSD

Transition Metal Cation−π Interactions: Complexes Formed by Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ Binding with Benzene Molecules

A computational investigation of the structures and interaction energies of complexes formed by Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ binding with benzene (Bz) molecules is performed employing high level <i>ab initio</i> quantum chemical methods, such as the second-order perturbation theory (MP2), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD­(T)] methods, along with the 6-311++G­(2d,2p) and 6-311++G­(d,p) basis sets. As far as we know, the present work is the first to study the structures and energetics of Bz–M²⁺ and Bz–M²⁺–Bz type complexes (M = Co, Ni, Cu, and Zn). Relativistic effects are also investigated via Douglas–Kroll–Hess second-order scalar relativistic computations for the complexes considered. Our results demonstrate that there are strong bindings between transition metal cations and benzene molecules. The computed interaction energies, including relativistic energy corrections, for the Bz–M²⁺ type complexes at the CCSD­(T)/6-311++G­(2d,2p) level are −131.9 (Bz–Fe²⁺), −172.6 (Bz–Co²⁺), −189.8 (Bz–Ni²⁺), −181.1 (Bz–Cu²⁺), and −158.2 (Bz–Zn²⁺) kcal mol^–1. Similarly, interaction energies for the Bz–M²⁺–Bz type complexes at the CCSD­(T)/6-311++G­(d,p) level are −206.4 (Bz–Fe²⁺–Bz), −213.4 (Bz–Co²⁺–Bz), −249.7 (Bz–Ni²⁺–Bz), −258.6 (Bz–Cu²⁺–Bz), and −235.2 (Bz–Zn²⁺–Bz) kcal mol^–1. Further, our results also demonstrate that the relativistic effects are very important in accurate computations of interaction energies. The predicted relativistic energy corrections to interaction energies, using the ωB97X-D functional, are between −1.9 and −7.7 kcal mol^–1. The transition metal cation−π interactions investigated in this study prove significantly larger binding energies compared to arbitrary π–π interactions and main group cation−π interactions. We believe that the present study may open new avenues in cation−π interactions

Thermal Aromatizations of 2-Vinylmethylenecyclopropane and 3-Vinylcyclobutene

A comprehensive theoretical investigation of thermal rearrangements of 2-vinylmethylenecyclopropane and 3-vinylcyclobutene is carried out employing density functional theory and high level ab initio methods, such as the complete active space self-consistent field, multi-reference second-order Møller–Plesset perturbation theory, and coupled-cluster singles and doubles with perturbative triples. In all computations, Pople’s polarized triple-ζ split valence basis set, 6-311G­(d,p), is utilized. The potential energy surface for the relevant system is explored to provide theoretical insights for the thermal aromatizations of 2-vinylmethylenecyclopropane and 3-vinylcyclobutene. The rate constant for each isomerization reaction is computed using the transition state theory. The simultaneous first-order ordinary-differential equations are solved numerically for the considered system to obtain time-dependent concentrations, hence the product distributions at a given temperature. Our results demonstrate that at high temperatures thermal aromatizations of 2-vinylmethylenecyclopropane (at 700 °C and higher) and 3-vinylcyclobutene (at 500 °C and higher) are feasible under appropriate experimental conditions. However, at low temperatures (at 500 °C and lower), 2-vinylmethylenecyclopropane yields 3-methylenecyclopentene as a unique product, kinetically, and the formation of benzene is not favorable. Similarly, at 300 °C and lower temperatures, 3-vinylcyclobutene can only yield <i>trans</i>-1,3,5-hexatriene (major) and <i>cis</i>-1,3,5-hexatriene (minor). At 300 < <i>T</i> < 500 °C, 3-vinylcyclobutene almost completely yields 1,3-cyclohexadiene. Hence, our computations provide a useful insight for the synthesis of substituted aromatic compounds. Further, calculated energy values (reaction energies and activation parameters) are in satisfactory agreement with the available experimental results