Edward F. Valeev

Psi4: an open-source ab initio electronic structure program

The Psi4 program is a new approach to modern quantum chemistry, encompassing Hartree–Fock and density‐functional theory to configuration interaction and coupled cluster. The program is written entirely in C++ and relies on a new infrastructure that has been designed to permit high‐efficiency computations of both standard and emerging electronic structure methods on conventional and high‐performance parallel computer architectures. Psi4 offers flexible user input built on the Python scripting language that enables both new and experienced users to make full use of the programs capabilities, and even to implement new functionality with moderate effort. To maximize its impact and usefulness, Psi4 is available through an open‐source license to the entire scientific community.

HEAT: High accuracy extrapolated ab initio thermochemistry

A theoretical model chemistry designed to achieve high accuracy for enthalpies of formation of atoms and small molecules is described. This approach is entirely independent of experimental data and contains no empirical scaling factors, and includes a treatment of electron correlation up to the full coupled-cluster singles, doubles, triples and quadruples approach. Energies are further augmented by anharmonic zero-point vibrational energies, a scalar relativistic correction, first-order spin-orbit coupling, and the diagonal Born-Oppenheimer correction. The accuracy of the approach is assessed by several means. Enthalpies of formation (at 0 K) calculated for a test suite of 31 atoms and molecules via direct calculation of the corresponding elemental formation reactions are within 1 kJ mol(-1) to experiment in all cases. Given the quite different bonding environments in the product and reactant sides of these reactions, the results strongly indicate that even greater accuracy may be expected in reactions that preserve (either exactly or approximately) the number and types of chemical bonds.

R12 methods in explicitly correlated molecular electronic structure theory

The past few years have seen a particularly rich period in the development of the explicitly correlated R12 theories of electron correlation. These theories bypass the slow convergence of conventional methods, by augmenting the traditional orbital expansions with a small number of terms that depend explicitly on the interelectronic distance r 12. Amongst the very numerous discoveries and developments that we will review here, two stand out as being of particular interest. First, the fundamental numerical approximations of the R12 methods withstand the closest scrutiny: Kutzelniggs use of the resolution of the identity and the generalized Brillouin condition to avoid many-electronic integrals remains sound. Second, it transpires that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear (r 12) to some suitably chosen short-range form (e.g., exp(−αr 12)). Modern R12 (or F12) methods can deliver MP2 energies (and beyond) that are converged to chemical accuracy (1 kcal/mol) in triple- or even double-zeta basis sets. Using a range of approximations, applications to large molecules become possible. Here, the major developments in the field are reviewed, and recommendations for future directions are presented. By comparing with commonly used extrapolation techniques, it is shown that modern R12 methods can deliver high accuracy dramatically faster than by using conventional methods. Contents PAGE 1. Introduction 429  1.1. The origin of the problem 429  1.2. Two-electron systems 430  1.3. Explicitly correlated MP2 methods 430  1.4. Gaussian geminals 431  1.5. Exponentially correlated Gaussians 432  1.6. The transcorrelated method 433 2. R12 wavefunctions 433  2.1. Definition 434  2.2. Correlation factors 435  2.3. Projection operators 437  2.4. Levels of theory 439  2.5. Methods for open shells 440 3. Approximations of many-electron integrals 441  3.1. Exact evaluation 442  3.2. Approximations: GBC, EBC and 443  3.3. Resolution of the identity 445  3.4. Numerical quadrature 447  3.5. Density fitting 449  3.6. DF combined with RI 451 4. Examples from second-order perturbation theory 452  4.1. Technical details 453  4.2. R12 results in comparison with extrapolated values 454  4.3. Comparison between R12 and F12 results 458 5. Perspectives 461  5.1. Higher level methods 461  5.2. Local approximations 461  5.3. Conclusions 462   5.3.1. Correlation factor 462   5.3.2. Projection operator 462   5.3.3. Formulation of intermediate B 463   5.3.4. Approximating integrals 463   5.3.5. Efficiency improvements 463 Acknowledgements 463 References 464

PSI3: An open‐source Ab Initio electronic structure package

PSI3 is a program system and development platform for ab initio molecular electronic structure computations. The package includes mature programming interfaces for parsing user input, accessing commonly used data such as basis‐set information or molecular orbital coefficients, and retrieving and storing binary data (with no software limitations on file sizes or file‐system‐sizes), especially multi‐index quantities such as electron repulsion integrals. This platform is useful for the rapid implementation of both standard quantum chemical methods, as well as the development of new models. Features that have already been implemented include Hartree‐Fock, multiconfigurational self‐consistent‐field, second‐order Møller‐Plesset perturbation theory, coupled cluster, and configuration interaction wave functions. Distinctive capabilities include the ability to employ Gaussian basis functions with arbitrary angular momentum levels; linear R12 second‐order perturbation theory; coupled cluster frequency‐dependent response properties, including dipole polarizabilities and optical rotation; and diagonal Born‐Oppenheimer corrections with correlated wave functions. This article describes the programming infrastructure and main features of the package. PSI3 is available free of charge through the open‐source, GNU General Public License.

Anchoring the water dimer potential energy surface with explicitly correlated computations and focal point analyses

Ten stationary points on the water dimer potential energy surface have been characterized with the coupled-cluster technique which includes all single and double excitations as well as a perturbative approximation of triple excitations [CCSD(T)]. Using a triple-ζ basis set with two sets of polarization functions augmented with higher angular momentum and diffuse functions [TZ2P(f,d)+dif], the fully optimized geometries and harmonic vibrational frequencies of these ten stationary points were determined at the CCSD(T) theoretical level. In agreement with other ab initio investigations, only one of these ten stationary points is a true minimum. Of the other nine structures, three are transition structures, and the remaining are higher order saddle points. These high-level ab initio results indicate that the lowest lying transition state involved in hydrogen interchange is chiral, of C1 symmetry rather than Cs as suggested by recently developed 6D potential energy surfaces. The one- and n-particle limits of t...

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule.

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.

The diagonal Born–Oppenheimer correction beyond the Hartree–Fock approximation

We report on evaluation of the diagonal Born–Oppenheimer correction (DBOC) to the electronic energy with Hartree–Fock (HF) and conventional correlated wave functions for general molecular systems. Convergence of both HF and configuration interaction (CI) DBOC with the one-particle basis seems to be rather fast, with triple-ζ quality correlation consistent sets of Dunning et al. sufficiently complete to approach the respective basis set limits for the DBOC of the ground state of H2 within 0.1 cm−1. Introduction of electron correlation via the CI singles and doubles method has a substantial effect on the absolute value of the DBOC for H2, H2O, and BH in their ground states (ca. +13 cm−1 out of 115 cm−1, +22 cm−1 out of 622 cm−1, and +11 cm−1 out of 370 cm−1, respectively). The effect of the correlation correction to the DBOC on relative energies is small, e.g., the barrier to linearity of water changes by ca. 1 cm−1; however, the value is difficult to converge to the ab initio limit. Based on recent results...

Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations.

The explicitly correlated coupled-cluster singles and doubles (CCSD-R12) and related methods-its linearized approximation CCSD(R12) and explicitly correlated second-order Moller-Plesset perturbation method-have been implemented into efficient computer codes that take into account point-group symmetry. The implementation has been largely automated by the computerized symbolic algebra SMITH that can handle complex index permutation symmetry of intermediate tensors that occur in the explicitly correlated methods. Unlike prior implementations that invoke the standard approximation or the generalized or extended Brillouin condition, our CCSD-R12 implementation is based on the nontruncated formalisms [T. Shiozaki et al., Phys. Chem. Chem. Phys. 10, 3358 (2008)] in which every diagrammatic term that arises from the modified Ansatz 2 is evaluated either analytically or by the resolution-of-the-identity insertion with the complementary auxiliary basis set. The CCSD-R12 correlation energies presented here for selected systems using the Slater-type correlation function can, therefore, serve as benchmarks for rigorous assessment of other approximate CC-R12 methods. Two recently introduced methods, CCSD(R12) and CCSD(2)(R12), are shown to be remarkably accurate approximations to CCSD-R12.

THE PROTONATED WATER DIMER : BRUECKNER METHODS REMOVE THE SPURIOUS C1 SYMMETRY MINIMUM

The H5O2+ system has been studied using a variety of coupled cluster methods based on a Brueckner reference determinant with levels of correlation up to double and perturbatively treated connected triple excitations [B–CCD(T)]. Basis sets as large as the triple-ζ plus double polarization basis augmented with f functions on oxygen and d functions on hydrogen [TZ2P(f,d)] were used. Harmonic vibrational frequencies were also predicted. In contrast with previous high-level ab initio studies, a stationary point of C1 symmetry was not found. An absence of imaginary vibrational frequencies at all levels of theory for the stationary point of C2 symmetry proves it to be the global minimum, lying only ∼0.4 kcal/mol lower in energy than the transition state of Cs symmetry.