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Second-order perturbation theory using explicitly correlated wave functions has been introduced into a quasirelativistic two-component formalism. The convergence of the correlation energy is as much improved as for the nonrelativistic Hamiltonian, achieving basis-set-limit results in a moderate-size basis set. Equilibrium distances and vibrational frequencies of small molecules of the 6th period of the periodic system of the elements have been calculated, demonstrating the improved behavior of the explicitly correlated wave functions. Taking advantage of density-fitting techniques, the explicitly correlated approach is an economical and appealing alternative to conventional two-component second-order perturbation theory in a large one-particle basis. [ABSTRACT FROM AUTHOR]

To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning’s hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to improvements comparable to or even better than those obtained by increasing the cardinal number in the used basis set by one. However, BSE alone is insufficient to improve agreement with experiment, even after additional consideration of inner-shell correlation and quadruple-excitation effects (mean error and standard deviation with extrapolation are -0.014 and 0.047 pm in comparison with mean error and standard deviation of -0.002 and 0.036 pm without extrapolation). Improvement is obtained only when other contributions of similar magnitude as the BSE contributions (e.g., pentuple-excitation effects and relativistic effects) are also considered. A rather large discrepancy (of the order of a few tenths of a picometer) is observed for the F2 molecule indicating an enhanced basis-set requirement for the various contributions in this case. [ABSTRACT FROM AUTHOR]

Coupled-cluster response theory for vertical excitation energies within the second-order approximate coupled-cluster singles-and-doubles model CC2, including linear-r12 corrections, is derived and implemented for Ansätze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation in order to calculate the three- and four-electron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground- and excited-state wave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory. [ABSTRACT FROM AUTHOR]

The analytic calculation of first-order properties has been implemented in the DALTON program at the level of explicitly correlated second-order Mo\ller-Plesset perturbation theory (MP2-R12). The implementation has been accomplished for MP2-R12 theory based on standard approximations A, A′, and B, using an auxiliary basis for the resolution-of-the-identity approximation, with and without a frozen core. MP2-R12 first-order molecular properties have been calculated analytically for a few small test molecules. For BH and HF, the MP2-R12 results were supplemented with explicitly correlated coupled-cluster calculations (but at this level from numerical derivatives) including vibrational and relativistic corrections. [ABSTRACT FROM AUTHOR]

In the framework of second-order Møller—Plesset linear-r12 MP2-R12 perturbation theory, a method is developed and implemented that uses an auxiliary basis set for the resolution-of-the-identity RI approximation for the three- and four-electron integrals. In contrast to previous work, the two-electron integrals that must be evaluated never involve more than one auxiliary basis function. The new method therefore scales linearly with the number of auxiliary basis functions and is much more efficient than the previous one, which scaled quadratically. A general formulation of MP2-R12 theory is presented for various ansätze, approximations, and orbitals (canonical or localized). The new method is assessed by computations of the valence-shell second-order Møller—Plesset correlation energy of a few small closed-shell systems. The preliminary calculations indicate that the difference between the new and previous methods is about one order of magnitude smaller than the errors that occur due to basis-set truncations and RI approximations and under the assumptions of generalized and extended Brillouin conditions. [ABSTRACT FROM AUTHOR]

In explicitly correlated Møller–Plesset (MP2-R12) methods, the first-order wave function is expanded not only in terms of products of one-electron functions—that is, orbitals—but also in terms of two-electron functions that depend linearly on the interelectronic coordinates r[sub ij]. With these functions, three- and four-electron integrals occur, but these integrals can be avoided by inserting a resolution of the identity (RI) in terms of the one-electron basis. In previous work, only one single basis was used for both the electronic wave function and the RI approximation. In the present work, a new computational approach is developed that uses an auxiliary basis set to represent the RI. This auxiliary basis makes it possible to employ standard basis sets in explicitly correlated MP2-R12 calculations.© 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Investigates the basic-set convergence of the electronic correlation energy in the water molecule. Results of the investigation at the Moller-Plesset level; Basis-set limits of the correlation energy; Extrapolation from sequences of calculations using correlation-consistent basis sets.

The MP2-R12 method (Mo\ller–Plesset second-order perturbation theory with terms linear in the interelectronic coordinate r12) in the approximations A and B as outlined in paper I of this series is applied to the ground states of the molecules H2, LiH, HF, H2O, NH3, CH4, Be2, N2, F2, C2H2, and CuH in their experimental equilibrium geometry, and to the van der Waals interaction between two He atoms. In all cases MP2 correlation energies are obtained that are supposed to differ by at most a few percent from the basis set limit. For CH4 the dependence of the energy on the symmetric stretching coordinate is studied, which together with other information leads to a recommended bond length of 1.086 Å for the CH bond length. For He2 and F2 the canonical and localized descriptions are compared. The latter is superior for the K-shell contributions, otherwise there is a little difference. For He2 in the localized representation rather good results for the dispersion interaction are obtained. The potential curve of Be2 is significantly improved in MP2-R12 as compared to conventional MP2. The examples C2H2 and CuH show that the method is not limited to very small systems. [ABSTRACT FROM AUTHOR]

Oriented circular dichroism (OCD) is explored and successfully applied to investigate chiral surface-anchored metal-organic frameworks (SURMOFs) based on camphoric acid (D- and Lcam) with the composition [Cu2(Dcam)2 x(Lcam)2−2 x(dabco)] n (dabco=1,4-diazabicyclo-[2.2.2]-octane). The three-dimensional chiral SURMOFs with high-quality orientation were grown on quartz glass plates by using a layer-by-layer liquid-phase epitaxy method. The growth orientation, as determined by X-ray diffraction (XRD), could be switched between the [001] and [110] direction by using either OH- or COOH-terminated substrates. These SURMOFs were characterized by using OCD, which confirmed the ratio as well as the orientation of the enantiomeric linker molecules. Theoretical computations demonstrate that the OCD band intensities of the enantiopure [Cu2(Dcam)2(dabco)] n grown in different orientations are a direct result of the anisotropic nature of the chiral SURMOFs. Finally, the enantiopure [Cu2(Dcam)2(dabco)] n and [Cu2(Lcam)2(dabco)] n SURMOFs were loaded with the two chiral forms of ethyl lactate [(+)-ethyl- D-lactate and (−)-ethyl- L-lactate)]. An enantioselective enrichment of >60 % was observed by OCD when the chiral host scaffold was loaded from the racemic mixture. [ABSTRACT FROM AUTHOR]

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller-Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree-Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller-Plesset theory outperforms conventional second-order Møller-Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level. [ABSTRACT FROM AUTHOR]

We review the current status of quantum chemistry as a predictive tool of chemistry and molecular physics, capable of providing highly accurate, quantitative data about molecular systems. We begin by reviewing wave-function based electronic-structure theory, emphasizing the N-electron hierarchy of coupled-cluster theory and the one-electron hierarchy of correlation-consistent basis sets. Following a discussion of the slow basis-set convergence of dynamical correlation and basis-set extrapolations, we consider the methods of explicit correlation, from the early work of Hylleraas in the 1920s to the latest developments in such methods, capable of yielding high-accuracy results in medium-sized basis sets. Next, we consider the small corrections to the electronic energy (high-order virtual excitations, vibrational, relativistic, and diagonal Born-Oppenheimer corrections) needed for high accuracy and conclude with a review of the composite methods and computational protocols of electronic-structure theory. [ABSTRACT FROM AUTHOR]

Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of $${\gamma = 1.4 a_{0}^{-1}}$$ can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated. [ABSTRACT FROM AUTHOR]

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: Kutzelnigg's 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(-α r 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. [ABSTRACT FROM AUTHOR]