A comparative study of single reference correlation methods of the coupled-pair type

Several variants of coupled electron pair type approximations are compared with respect to their accuracy in the prediction of bond distances, harmonic vibrational frequencies and anharmonic corrections for a range of closed-shell diatomic molecules. In the first part of the paper the coupled-electron pair (CEPA) methods (CEPA/1,2,3) are discussed. Extensions of these methods allow the derivation of the correlation energy from the stationarization of a correlation energy functional (CPF/1,2,3 methods). All methods are formulated as diagonally dressed configuration–interaction with single- and double-excitations (CISD) eigenvalue problems. Averaging the diagonal shifts of the CPF methods in various ways lead to the ACPF and AQCC methods. Several small modifications of the shifts for the single excitations are proposed that enhance the stability of the methods (NCPF/1,2,3, NCEPA/1,2,3, NACPF). The reduced shifts are justified by linear response arguments. The implementation of the methods for a closed-shell ground state is described. In the application part, we first tested the size-consistency, exactness for two-electron systems and unitary invariance of the methods. Extensive numerical studies with polarized quadruple-ζ basis sets are employed to test the accuracy of the coupled pair approaches relative to the more elaborate quadratic CI (QCISD) and coupled-cluster (CCSD and CCSD(T)) approaches. Not surprisingly, the CCSD(T) method is the most accurate approach on average. However, the proposed NCPF/1 variant led to even smaller average errors for bond distances (∼0.2 pm relative to ∼0.3 pm for CCSD(T)) while predicting still accurate harmonic frequencies (av. Error ∼25 cm−1 for NCPF/1, ∼8 cm−1 for CCSD(T) and ∼45 cm−1 for CCSD). All coupled pair methods are more accurate than present day DFT approaches (BP86, B3LYP). The exception is the recently proposed double-hybrid B2PLYP functional that approaches the coupled pair performance. Some more difficult copper containing diatomics are treated as well (CuH, CuF, CuCl and Cu2). We discuss why we believe that the coupled-pair approaches (and in particular the proposed NCPF/1 variant) are attractive for large-scale chemical applications

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method

Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller–Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50–100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol−1. Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chemical applications

Arbitrary Angular Momentum Electron Repulsion Integrals with Graphical Processing Units: Application to the Resolution of Identity Hartree-Fock Method.

A resolution of identity based implementation of the Hartree-Fock method on graphical processing units (GPUs) is presented that is capable of handling basis functions with arbitrary angular momentum. For practical reasons, only functions up to (ff|f) angular momentum are presently calculated on the GPU, thus leaving the calculation of higher angular momenta integrals on the CPU of the hybrid CPU-GPU environment. Speedups of up to a factor of 30 are demonstrated relative to state-of-the-art serial and parallel CPU implementations. Benchmark calculations with over 3500 contracted basis functions (def2-SVP or def2-TZVP basis sets) are reported. The presented implementation supports all devices with OpenCL support and is capable of utilizing multiple GPU cards over either MPI or OpenCL itself

Accurate Theoretical Chemistry with Coupled Pair Models

Quantum chemistry has found its way into the everyday work of many experimental chemists. Calculations can predict the outcome of chemical reactions, afford insight into reaction mechanisms, and be used to interpret structure and bonding in molecules. Thus, contemporary theory offers tremendous opportunities in experimental chemical research. However, even with present-day computers and algorithms, we cannot solve the many particle Schrödinger equation exactly; inevitably some error is introduced in approximating the solutions of this equation. Thus, the accuracy of quantum chemical calculations is of critical importance. The affordable accuracy depends on molecular size and particularly on the total number of atoms: for orientation, ethanol has 9 atoms, aspirin 21 atoms, morphine 40 atoms, sildenafil 63 atoms, paclitaxel 113 atoms, insulin nearly 800 atoms, and quaternary hemoglobin almost 12,000 atoms. Currently, molecules with up to ∼10 atoms can be very accurately studied by coupled cluster (CC) theory, ∼100 atoms with second-order Møller−Plesset perturbation theory (MP2), ∼1000 atoms with density functional theory (DFT), and beyond that number with semiempirical quantum chemistry and force-field methods. The overwhelming majority of present-day calculations in the 100-atom range use DFT. Although these methods have been very successful in quantum chemistry, they do not offer a well-defined hierarchy of calculations that allows one to systematically converge to the correct answer. Recently a number of rather spectacular failures of DFT methods have been found-even for seemingly simple systems such as hydrocarbons, fueling renewed interest in wave function-based methods that incorporate the relevant physics of electron correlation in a more systematic way. Thus, it would be highly desirable to fill the gap between 10 and 100 atoms with highly correlated ab initio methods. We have found that one of the earliest (and now almost forgotten) of this class of methods, the coupled-electron pair approximation (CEPA), performs exceedingly well in chemical applications. In this Account, we examine the performance of CEPA in chemical applications. One attractive feature of CEPA, in addition to its surprising accuracy that surpasses that of DFT and MP2 theory, is a simplicity that allows for straightforward and very efficient approximations and extensions to be developed; these are much more difficult or even impossible with the more rigorous CC theory. Thus, approximate CEPA methods can be implemented efficiently enough to allow for calculations on molecules of 50−100 atoms, perhaps the most common range in contemporary chemical research

Theoretical bioinorganic chemistry: the electronic structure makes a difference

Theoretical bioinorganic and biomimetic chemistry involves the careful description of the electronic structure: for example, ‘valence bond reading’ of broken-symmetry density functional theory computations gives insight into the structure and bonding of metal–radical systems with complex electronic structures. Exploring the reactivities of such systems leads to the design of novel compounds with better reactivities. Combined quantum-mechanics/molecular-mechanics (QM/MM), where the QM part is a sophisticated ab initio method, aids in understanding nature's most complicated reaction mechanisms in atomic detail. First principles molecular dynamics simulations (Car–Parrinello simulations) open up exciting new avenues for studying transition metal centers and enable several questions to be addressed that cannot be resolved with either standard quantum chemical or traditional force-field methods

Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange

In this paper, the possibility is explored to speed up Hartree–Fock and hybrid density functional calculations by forming the Coulomb and exchange parts of the Fock matrix by different approximations. For the Coulomb part the previously introduced Split-RI-J variant (F. Neese, J. Comput. Chem. 24 (2003) 1740) of the well-known ‘density fitting’ approximation is used. The exchange part is formed by semi-numerical integration techniques that are closely related to Friesner’s pioneering pseudo-spectral approach. Our potentially linear scaling realization of this algorithm is called the ‘chain-of-spheres exchange’ (COSX). A combination of semi-numerical integration and density fitting is also proposed. Both Split-RI-J and COSX scale very well with the highest angular momentum in the basis sets. It is shown that for extended basis sets speed-ups of up to two orders of magnitude compared to traditional implementations can be obtained in this way. Total energies are reproduced with an average error of <0.3 kcal/mol as determined from extended test calculations with various basis sets on a set of 26 molecules with 20–200 atoms and up to 2000 basis functions. Reaction energies agree to within 0.2 kcal/mol (Hartree–Fock) or 0.05 kcal/mol (hybrid DFT) with the canonical values. The COSX algorithm parallelizes with a speedup of 8.6 observed for 10 processes. Minimum energy geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angels from their canonical values. These developments enable highly efficient and accurate self-consistent field calculations including nonlocal Hartree–Fock exchange for large molecules. In combination with the RI-MP2 method and large basis sets, second-order many body perturbation energies can be obtained for medium sized molecules with unprecedented efficiency. The algorithms are implemented into the ORCA electronic structure system

The ORCA quantum chemistry program package

In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theoretical research in all areas of chemistry and many neighboring disciplines such as materials sciences and biochemistry. ORCA features density functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/molecular mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to “real-life” chemical applications involving systems with a few hundred atoms. In addition to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a number of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-reference local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chemistry and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry

Structure-Activity Relationships of a Caged Thrombin-Binding DNA Aptamer: Insight gained from molecular dynamics simulation studies

15-mer ssDNA aptamers play a vital role in the inhibition of alpha-thrombin in the blood clotting mechanism. It is of high importance to explore the structural factors controlling the inhibitory nature of the aptamer. Here we investigated the structure-function relationship of the anti-thrombin aptamer, as well as its 'caged' variant (2-(2-nitrophenyl)-propyl group (NPP)) by molecular dynamics simulations. The stability of the unmodified aptamer at different temperatures is examined in 2ns all-atom simulations and compared to experiment. The change in structure when introducing the photo-labile caged compound is analyzed, and the regiospecificity of this modification explained on atomic level. Removal of the photo-labile group leads to the reformation of the active aptamer structure from its inactive state. The mechanism for this formation process is a concerted movement of the aptamer backbone and some highly important bases. The binding of the aptamer to thrombin with regard to the 'caged' group is studied in an explicit simulation with the aptamer-thrombin complex and the reason for the binding/unbinding nature of the aptamer shown

Spectroscopic Properties of Protein‐Bound Cofactors: Calculation by Combined Quantum Mechanical/Molecular Mechanical (QM/MM) Approaches

In this article, we discuss some aspects of the combined quantum mechanics/molecular mechanics (QM/MM) method for the calculation of energetics and spectroscopic parameters of protein‐bound cofactors. Following a brief introduction to the theory of the QM/MM approach, some selected examples are discussed that illustrate the use of this methodology in theoretical spectroscopic studies. The examples cover the following: (i) excitation energies for the S0 → S1 transition in bacteriorhodopsin; (ii) electron paramagnetic resonance (EPR) and absorption spectra of plastocyanin; and (iii) the spin Hamiltonian parameters of compound I in cytochrome P450cam

Spectroscopic Properties of Protein‐Bound Cofactors: Calculation by Combined Quantum Mechanical/Molecular Mechanical (QM/MM) Approaches

In this article, we discuss some aspects of the combined quantum mechanics/molecular mechanics (QM/MM) method for the calculation of energetics and spectroscopic parameters of protein‐bound cofactors. Following a brief introduction to the theory of the QM/MM approach, some selected examples are discussed that illustrate the use of this methodology in theoretical spectroscopic studies. The examples cover the following: (i) excitation energies for the S0 → S1 transition in bacteriorhodopsin; (ii) electron paramagnetic resonance (EPR) and absorption spectra of plastocyanin; and (iii) the spin Hamiltonian parameters of compound I in cytochrome P450cam