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Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.

Optimizing orbitals in the presence of electron correlation, as in orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2), can remove artifacts associated with mean-field orbitals such as spin contamination and artificial symmetry-breaking. However, OOMP2 is known to suffer from divergent correlation energies in regimes of small orbital energy gaps. To address this issue, several approaches to amplitude regularization have been explored, with those featuring energy-gap-dependent regularizers appearing to be most transferable and physically justifiable. For instance, κ-OOMP2 was shown to address the energy divergence issue in, for example, bond-breaking processes while offering a significant improvement in accuracy for the W4-11 thermochemistry data set, and a parameter of κ = 1.45 was recommended. A more recent investigation of regularized MP2 with Hartree-Fock orbitals revealed that stronger regularization (i.e., smaller values of κ) than what had previously been recommended for κ-OOMP2 may offer huge improvements in certain cases such as noncovalent interactions while retaining a high level of accuracy for main-group thermochemistry data sets. In this study, we investigate the transferability of those findings to κ-OOMP2 and assess the implications of stronger regularization on the ability of κ-OOMP2 to diagnose strong static correlation. We found similar results using κ-OOMP2 for several main-group thermochemistry, barrier height, and noncovalent interaction data sets including both closed shell and open shell species. However, stronger regularization yielded substantially higher accuracy for open-shell transition-metal (TM) thermochemistry and is necessary to provide qualitatively correct spin symmetry breaking behavior for several large and electrochemically relevant TM systems. We therefore find a single κ value insufficient to treat all systems using κ-OOMP2.

Second-order Møller-Plesset theory (MP2) notoriously breaks down for π-driven dispersion interactions and dative bonds in transition metal complexes. Herein, we investigate three physically justified forms of single-parameter, energy-gap dependent regularization which can yield high and transferable accuracy for a variety of noncovalent interactions (including S22, S66, and L7 test sets) and (mostly closed shell) transition metal thermochemistry. Regularization serves to damp overestimated pairwise additive contributions, renormalizing first-order amplitudes such that the effects of higher-order correlations are incorporated. The optimal parameter values for the noncovalent and transition metal sets are 1.1, 0.7, and 0.4 for κ, σ, and σ2 regularizers, respectively. However, such regularization slightly degrades the accuracy of conventional MP2 for some small-molecule test sets, most of which have relatively large average frontier energy gaps. Our results suggest that appropriately regularized MP2 models may improve double hybrid density functionals, at no additional cost over conventional MP2.

Magnetic properties of molecules such as magnetizabilities represent second order derivatives of the energy with respect to external perturbations. To avoid the need for analytic second derivatives and thereby permit evaluation of the performance of methods where they are not available, a new implementation of quantum chemistry calculations in finite applied magnetic fields is reported. This implementation is employed for a collection of small molecules with the aug-cc-pVTZ basis set to assess orbital optimized (OO) MP2 and a recently proposed regularized variant of OOMP2, called κ-OOMP2. κ-OOMP2 performs significantly better than conventional second order Møller-Plesset (MP2) theory, by reducing MP2's exaggeration of electron correlation effects. As a chemical application, we revisit an old aromaticity criterion called magnetizability exaltation. In lieu of empirical tables or increment systems to generate references, we instead use straight chain molecules with the same formal bond structure as the target cyclic planar conjugated molecules. This procedure is found to be useful for qualitative analysis, yielding exaltations that are typically negative for aromatic species and positive for antiaromatic molecules. One interesting species, N2S2, shows a positive exaltation despite having aromatic characteristics.

Ethynylsilylene (HCCSiH; X1A') has been prepared in the gas phase through the elementary reaction of singlet dicarbon (C2) with silane (SiH4) under single-collision conditions. Electronic structure calculations reveal a barrierless reaction pathway involving 1,1-insertion of dicarbon into one of the silicon-hydrogen bonds followed by hydrogen migration to form the 3-sila-methylacetylene (HCCSiH3) intermediate. The intermediate undergoes unimolecular decomposition through molecular hydrogen loss to ethynylsilylene (HCCSiH; Cs; X1A'). The dicarbon-silane system defines a benchmark to explore the consequence of a single collision between the simplest "only carbon" molecule (dicarbon) with the prototype of a closed-shell silicon hydride (silane) yielding a nonclassical silacarbene, whose molecular geometry and electronic structure are quite distinct from the isovalent triplet propargylene (HCCCH; C2; 3B) carbon-counterpart. These organosilicon transients cannot be prepared through traditional organic, synthetic methods, thus opening up a versatile path to access the previously largely elusive class of silacarbenes.

Unrestricted density functional theory (DFT) methods are typically expected to describe the homolytic dissociation of nonpolar single bonds in neutral species with qualitative accuracy, due to the lack of significant delocalization error. We however find that many widely used density functional approximations fail to describe features along the dissociation curve of the simple H2 molecule. This is not a universal failure of DFT in the sense that many classic functionals like PBE and B3LYP give very reasonable results, as do some more modern methods like MS2. However, some other widely used functionals like B97-D (empirically fitted) and TPSS (non-empirically constrained) predict qualitatively wrong static polarizabilities, force constants, and some even introduce an artificial barrier against association of independent H atoms to form H2. The polarizability and force constant prediction failures appear to stem from incomplete spin localization into individual H atoms beyond the Coulson-Fischer point, resulting in "fractionally bonded" species where the ionic contributions to the Slater determinant are not completely eliminated, unlike the case of unrestricted Hartree-Fock. These errors therefore appear to be a consequence of poor self-consistent density prediction by the problematic functional. The same reasons could potentially lead to spurious barriers toward H atom association, indirectly also leading to incorrect forces. These unphysicalities suggest that the use of problematic functionals is probably unwise in ab initio dynamics calculations, especially if strong electrostatic interactions are possible.

Unrestricted density functional theory (DFT) methods are typically expected to describe the homolytic dissociation of nonpolar single bonds in neutral species with qualitative accuracy, due to the lack of significant delocalization error. We however find that many widely used density functional approximations fail to describe features along the dissociation curve of the simple H2 molecule. This is not a universal failure of DFT in the sense that many classic functionals like PBE and B3LYP give very reasonable results, as do some more modern methods like MS2. However, some other widely used functionals like B97-D (empirically fitted) and TPSS (non-empirically constrained) predict qualitatively wrong static polarizabilities, force constants, and some even introduce an artificial barrier against association of independent H atoms to form H2. The polarizability and force constant prediction failures appear to stem from incomplete spin localization into individual H atoms beyond the Coulson-Fischer point, resulting in "fractionally bonded" species where the ionic contributions to the Slater determinant are not completely eliminated, unlike the case of unrestricted Hartree-Fock. These errors therefore appear to be a consequence of poor self-consistent density prediction by the problematic functional. The same reasons could potentially lead to spurious barriers toward H atom association, indirectly also leading to incorrect forces. These unphysicalities suggest that the use of problematic functionals is probably unwise in ab initio dynamics calculations, especially if strong electrostatic interactions are possible. [ABSTRACT FROM AUTHOR]

Unrestricted density functional theory (DFT) methods are typically expected to describe the homolytic dissociation of nonpolar single bonds in neutral species with qualitative accuracy, due to the lack of significant delocalization error. We however find that many widely used density functional approximations fail to describe features along the dissociation curve of the simple H2 molecule. This is not a universal failure of DFT in the sense that many classic functionals like PBE and B3LYP give very reasonable results, as do some more modern methods like MS2. However, some other widely used functionals like B97-D (empirically fitted) and TPSS (non-empirically constrained) predict qualitatively wrong static polarizabilities, force constants, and some even introduce an artificial barrier against association of independent H atoms to form H2. The polarizability and force constant prediction failures appear to stem from incomplete spin localization into individual H atoms beyond the Coulson-Fischer point, resulting in "fractionally bonded" species where the ionic contributions to the Slater determinant are not completely eliminated, unlike the case of unrestricted Hartree-Fock. These errors therefore appear to be a consequence of poor self-consistent density prediction by the problematic functional. The same reasons could potentially lead to spurious barriers toward H atom association, indirectly also leading to incorrect forces. These unphysicalities suggest that the use of problematic functionals is probably unwise in ab initio dynamics calculations, especially if strong electrostatic interactions are possible. [ABSTRACT FROM AUTHOR]

Ethynylsilylene (HCCSiH; X 1 A') has been prepared in the gas phase through the elementary reaction of singlet dicarbon (C 2 ) with silane (SiH 4 ) under single-collision conditions. Electronic structure calculations reveal a barrierless reaction pathway involving 1,1-insertion of dicarbon into one of the silicon-hydrogen bonds followed by hydrogen migration to form the 3-sila-methylacetylene (HCCSiH 3 ) intermediate. The intermediate undergoes unimolecular decomposition through molecular hydrogen loss to ethynylsilylene (HCCSiH; C s ; X 1 A'). The dicarbon-silane system defines a benchmark to explore the consequence of a single collision between the simplest "only carbon" molecule (dicarbon) with the prototype of a closed-shell silicon hydride (silane) yielding a nonclassical silacarbene, whose molecular geometry and electronic structure are quite distinct from the isovalent triplet propargylene (HCCCH; C 2 ; 3 B) carbon-counterpart. These organosilicon transients cannot be prepared through traditional organic, synthetic methods, thus opening up a versatile path to access the previously largely elusive class of silacarbenes.