Second-order Møller-Plesset theory with linear R12 terms (MP2-R12) revisited: auxiliary basis set method and massively parallel implementation

Ab initio electronic structure approaches in which electron correlation explicitly appears have been the subject of much recent interest. Because these methods accelerate the rate of convergence of the energy and properties with respect to the size of the one-particle basis set, they promise to make accuracies of better than 1 kcal/mol computationally feasible for larger chemical systems than can be treated at present with such accuracy. The linear R12 methods of Kutzelnigg and co-workers are currently the most practical means to include explicit electron correlation. However, the application of such methods to systems of chemical interest faces severe challenges, most importantly, the still steep computational cost of such methods. Here we describe an implementation of the second-order M?ller-Plesset method with terms linear in the interelectronic distances (MP2-R12) which has a reduced computational cost due to the use of two basis sets. The use of two basis sets in MP2-R12 theory was first investigated recently by Klopper and Samson and is known as the auxiliary basis set (ABS) approach. One of the basis sets is used to describe the orbitals and another, the auxiliary basis set, is used for approximating matrix elements occurring in the exact MP2-R12 theory. We further extend the applicability of the approach by parallelizing all steps of the integral-direct MP2-R12 energy algorithm. We discuss several variants of the MP2-R12 method in the context of parallel execution and demonstrate that our implementation runs efficiently on a variety of distributed memory machines. Results of preliminary applications indicate that the two-basis (ABS) MP2-R12 approach cannot be used safely when small basis sets (such as augmented double- and triple-zeta correlation consistent basis sets) are utilized in the orbital expansion. Our results suggest that basis set reoptimization or further modifications of the explicitly correlated ansatz and/or standard approximations for matrix elements are necessary in order to make the MP2-R12 method sufficiently accurate when small orbital basis sets are used. The computer code is a part of the latest public release of Sandia's Massively Parallel Quantum Chemistry program available under GNU General Public License.     

Computational methods for analysis of an unsaturated carbocycle: heptafulvene

With respect to geometric optimizations, harmonic vibrational frequencies and single point conformational energies, various computational methods [HF, MP2, CCSD(T), BD(T), CASSCF, CASPT2, and DFT] were evaluated for their suitability to describe the heptafulvene system. We found that a significant number of basis sets lead to wrong predictions of folded minima, when ab initio methods including dynamic electron correlation are used. Possible explanations for these inconsistencies, such as wave function instabilities, near linear dependences of the basis sets and inadequate inclusion of polarization functions in the basis set, are discussed. Such concerns are likewise important for other classes of π-conjugated compounds, such that the results are expected to be of interest not only for heptafulvenes.     

Property-optimized gaussian basis sets for molecular response calculations

With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H-Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree-Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree-Fock polarizabilities. The mean absolute basis set errors are 3.6%, 1.1%, and 0.3% for property-optimized basis sets of split-valence, triple-zeta, and quadruple-zeta valence quality, respectively. Density functional and second-order M?ller-Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to C(720) using hybrid density functional theory.     

Second row molecular orbital calculations: III. Semi-empirical calculations of geometries

The ability of four semi-empirical methods to predict geometries of molecules containing atoms in the second row of the periodic table is investigated for about 80 molecules. Non-empirical, minimal basis set calculations, with and without optimization of valence orbital exponents, are carried out for a number of diatomic molecules. While none of the methods are capable of predicting geometries with an accuracy comparable to the first row parametrization, the SPD' method of Santry and the related INDO method of Benson and Hudson appear to be the most consistent. The ab initio calculations do not suffer from the drawbacks exhibited by the latter two semi-empirical methods. From this it is concluded that the failure of such methods lies in the parametrization rather than in the use of a minimal basis set.     

Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation

Most modern semiempirical quantum-chemical (SQC) methods are based on the neglect of diatomic differential overlap (NDDO) approximation to ab initio molecular integrals. Here, we check the validity of this approximation by computing all relevant integrals for 32 typical organic molecules using Gaussian-type orbitals and various basis sets (from valence-only minimal to all-electron triple-ζ basis sets) covering in total more than 15.6 million one-electron (1-e) and 10.3 billion two-electron (2-e) integrals. The integrals are calculated in the nonorthogonal atomic basis and then transformed by symmetric orthogonalization to the Löwdin basis. In the case of the 1-e integrals, we find strong orthogonalization effects that need to be included in SQC models, for example, by strategies such as those adopted in the available OMx methods. For the valence-only minimal basis, we confirm that the 2-e Coulomb integrals in the Löwdin basis are quantitatively close to their counterparts in the atomic basis and that the 2-e exchange integrals can be safely neglected in line with the NDDO approximation. For larger all-electron basis sets, there are strong multishell orthogonalization effects that lead to more irregular patterns in the transformed 2-e integrals and thus cast doubt on the validity of the NDDO approximation for extended basis sets. Focusing on the valence-only minimal basis, we find that some of the NDDO-neglected integrals are reduced but remain sizable after the transformation to the Löwdin basis; this is true for the two-center 2-e hybrid integrals, the three-center 1-e nuclear attraction integrals, and the corresponding three-center 2-e hybrid integrals. We consider a scheme with a valence-only minimal basis that includes such terms as a possible strategy to go beyond the NDDO integral approximation in attempts to improve SQC methods. © 2018 Wiley Periodicals, Inc.     

Accuracy of geometries: influence of basis set,exchange–correlation potential,inclusion of core electrons,and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.     

Assessment of theoretical methods for the calculation of methyl cation affinities

The methyl cation affinity (MCA; 298 K) of a variety of neutral and anionic bases has been examined computationally with a wide variety of theoretical methods. These include high-level composite procedures such as W1, G3, G3B3, and G2, conventional ab initio methods such as CCSD(T) and MP2, as well as a selection of density functional theory (DFT) methods. Experimental results for a variety of small model systems are well reproduced with practically all these methods, and the performance of DFT based methods are far superior in comparison to their MP2 analogs for these small models. For larger model, systems including motifs frequently encountered in organocatalysts, the performance deteriorates somewhat for DFT methods, while it improves significantly for MP2, rendering the former methods unreliable for common organic bases. Thus, MP2 calculations performed in combination with basis sets such as 6-31+G(2d, p) or larger, appear to offer a practical and reliable approach to compute MCAs of organic bases.     

Two-photon absorption cross sections: an investigation of the accuracy of calculated absolute and relative values

We have studied the basis set and electron correlation effects on the ab initio calculations of two-photon absorption cross sections of water. Various series of correlation consistent basis sets up to triply augmented basis sets of valence pentuple zeta level as well as the popular 6-31G(d) basis set have been employed in combination with several coupled cluster, configuration interaction, and density functional theory methods. We find that it is very difficult to obtain converged values of the cross sections for even a small molecule such as water. Acknowledging these difficulties in obtaining a fully converged cross section for a given state, we also investigated the possibility of determining relative cross sections for a series of organic molecules. However, we did not find consistency between the relative cross sections calculated at the Hartree-Fock level and several coupled-cluster methods using the 6-31G(d) and aug-cc-pVDZ basis sets. However, we could reproduce the relative ordering of the two-photon absorption cross sections of the molecules studied at the Hartree-Fock level.     

High-order electron-correlation methods with scalar relativistic and spin-orbit corrections

An assortment of computer-generated, parallel-executable programs of ab initio electron-correlation methods has been fitted with the ability to use relativistic reference wave functions. This has been done on the basis of scalar relativistic and spin-orbit effective potentials and by allowing the computer-generated programs to handle complex-valued, spinless orbitals determined by these potentials. The electron-correlation methods that benefit from this extension are high-order coupled-cluster methods (up to quadruple excitation operators) for closed- and open-shell species, coupled-cluster methods for excited and ionized states (up to quadruples), second-order perturbation corrections to coupled-cluster methods (up to triples), high-order perturbation corrections to configuration-interaction singles, and active-space (multireference) coupled-cluster methods for the ground, excited, and ionized states (up to active-space quadruples). A subset of these methods is used jointly such that the dynamical correlation energies and scalar relativistic effects are computed by a lower-order electron-correlation method with more extensive basis sets and all-electron relativistic treatment, whereas the nondynamical correlation energies and spin-orbit effects are treated by a higher-order electron-correlation method with smaller basis sets and relativistic effective potentials. The authors demonstrate the utility and efficiency of this composite scheme in chemical simulation wherein the consideration of spin-orbit effects is essential: ionization energies of rare gases, spectroscopic constants of protonated rare gases, and photoelectron spectra of hydrogen halides.     

Comparison of Density Functional and Correlated Wave Function Methods for the Prediction of Cu(II) Hyperfine Coupling Constants

The reliable prediction of Cu(II) hyperfine coupling constants remains a challenge for quantum chemistry. Until recently only density functional theory (DFT) could target this property for systems of realistic size. However, wave function based methods become increasingly applicable. In the present work, we define a large set of Cu(II) complexes with experimentally known hyperfine coupling constants and use it to investigate the performance of modern quantum chemical methods for the prediction of this challenging spectroscopic parameter. DFT methods are evaluated against orbital-optimized second-order Møller-Plesset (OO-MP2) theory and coupled cluster calculations including singles and doubles excitations, driven by the domain-based local pair natural orbital approach (DLPNO-CCSD). Special attention is paid to the definition of a basis set that converges adequately toward the basis set limit for the given property for all methods considered in this study, and a specifically optimized basis set is proposed for this purpose. The results suggest that wave function based methods can supplant but do not outcompete DFT for the calculation of Cu(II) hyperfine coupling constants. Mainstream hybrid functionals such as B3PW91 remain on average the best choice.     

Feasibility of density functional methods to predict dielectric properties of polymers

Feasibility of density functional theory (DFT) to predict dielectric properties such as polarizability of saturated polymers is investigated. Small saturated molecules, methane and propane, which is a monomer of polypropylene chain, are used in testing the methods. Results for polarizabilities based on several density functionals together with different basis sets are compared and contrasted with each other, with results by Hartree-Fock and second-order Moller-Plesset perturbation theory, as well as experimental data. The generalized gradient approximation PW91 method together with the 6-311++G(**) basis set is found to be the most suitable method, in terms of sufficient accuracy and computational efficiency, to calculate polarizabilities for large oligomers of polypropylene. The dielectric constant is then determined using the calculated polarizabilities and the Clausius-Mossotti equation. The molecular DFT methods at the PW916-311++G(**) level together with the Clausius-Mossotti equation give dielectric constants for saturated polymers such as polypropylene in good accordance with the experimental values.     

Efficient determination and characterization of transition states using ab-initio methods

The gradient of the potential energy with respect to nuclear coordinates has been calculated using ab-initio single determinant molecular orbital methods. The calculated gradient is used together with very efficient minimization methods to locate and characterize transition states on many-dimensional potential energy surfaces. Previously such methods have only been applied to semi-empirical potential functions. Although the calculation of the gradient in addition to the energy increases the computational time by about a factor of four, we have demonstrated the feasibility of these calculations by locating the transition state for the model rearrangement of HNC to HCN using both minimal (STO-3G) and split valence shell (4-31G) basis sets. Further use of such methods in the direct application of ab-initio wavefunctions to dynamical investigations is discussed.     

Detection methods and performance criteria for genetically modified organisms

Detection methods for genetically modified organisms (GMOs) are necessary for many applications, from seed purity assessment to compliance of food labeling in several countries. Numerous analytical methods are currently used or under development to support these needs. The currently used methods are bioassays and protein- and DNA-based detection protocols. To avoid discrepancy of results between such largely different methods and, for instance, the potential resulting legal actions, compatibility of the methods is urgently needed. Performance criteria of methods allow evaluation against a common standard. The more-common performance criteria for detection methods are precision, accuracy, sensitivity, and specificity, which together specifically address other terms used to describe the performance of a method, such as applicability, selectivity, calibration, trueness, precision, recovery, operating range, limit of quantitation, limit of detection, and ruggedness. Performance criteria should provide objective tools to accept or reject specific methods, to validate them, to ensure compatibility between validated methods, and be used on a routine basis to reject data outside an acceptable range of variability. When selecting a method of detection, it is also important to consider its applicability, its field of applications, and its limitations, by including factors such as its ability to detect the target analyte in a given matrix, the duration of the analyses, its cost effectiveness, and the necessary sample sizes for testing. Thus, the current GMO detection methods should be evaluated against a common set of performance criteria.     

Benchmarking NMR indirect nuclear spin-spin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD

Accurate calculations of NMR indirect nuclear spin-spin coupling constants require especially optimized basis sets and correlated wave function methods such as CCSD or SOPPA(CCSD). Both methods scale as N(6), where N is the number of orbitals, which prevents routine applications to molecules with more than 10-15 nonhydrogen atoms. We have therefore developed a modification of the SOPPA(CCSD) method in which the CCSD singles and doubles amplitudes are replaced by CC2 singles and doubles amplitudes. This new method, called SOPPA(CC2), scales only as N(5), like the original SOPPA-method. The performance of the SOPPA(CC2) method for the calculation of indirect nuclear spin-spin coupling constants is compared to SOPPA and SOPPA(CCSD) employing a set of benchmark molecules. We also investigate the basis set dependence by employing three different basis sets optimized for spin-spin coupling constants, namely the HuzIV-su4, ccJ-pVTZ, and ccJ-pVQZ basis sets. The results of the corresponding CCSD calculations are used as a theoretical reference.     

Unambiguous optimization of effective potentials in finite basis sets

The optimization of effective potentials is of interest in density-functional theory (DFT) in two closely related contexts. First, the evaluation of the functional derivative of orbital-dependent exchange-correlation functionals requires the application of optimized effective potential methods. Second, the optimization of the effective local potential that yields a given electron density is important both for the development of improved approximate functionals and for the practical application of embedding schemes based on DFT. However, in all cases this optimization turns into an ill-posed problem if a finite basis set is introduced for the Kohn-Sham orbitals. So far, this problem has not been solved satisfactorily. Here, a new approach to overcome the ill-posed nature of such finite-basis set methods is presented for the optimization of the effective local potential that yields a given electron density. This new scheme can be applied with orbital basis sets of reasonable size and makes it possible to vary the basis sets for the orbitals and for the potential independently, while providing an unambiguous potential that systematically approaches the numerical reference.     

Benchmark calculations of reaction energies, barrier heights, and transition-state geometries for hydrogen abstraction from methanol by a hydrogen atom

We report benchmark calculations of reaction energies, barrier heights, and transition-state geometries for the reaction of CH(3)OH with H to produce CH(2)OH and H(2). Highly accurate composite methods, such as CBS, G2, G3S, G3X, G3SX, and multi-coefficient correlation methods (MCCMs), are used to calibrate lower-cost methods. We also performed single-level CCSD(T) calculations extrapolated to the infinite-basis limit on the basis of aug-cc-pVXZ (X = 3, 4) correlation consistent basis sets. The benchmark high-level calculations give consensus values of the forward reaction barrier height and the reaction energy of 9.7 kcal/mol and - 6.4 kcal/mol, respectively. To evaluate the accuracy of cost-efficient methods that are potentially useful for dynamics studies of the title reaction, we further include the results obtained by hybrid density functional theory methods and hybrid meta density functional theory methods that have recently been designed for chemical kinetics. Results obtained by popular semiempirical methods are also given for comparison. On the basis of the benchmark gas-phase results, we suggest MC-QCISD/3, MC3BB, and BB1K as reasonably accurate and affordable electronic structure methods for calculating dynamics for the title reaction.