Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry (original) (raw)
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Auxiliary Basis Sets for Density Fitting in Explicitly Correlated Calculations: The Atoms H-Ar
Journal of chemical theory and computation, 2015
Auxiliary basis sets specifically matched to the correlation consistent cc-pVnZ-F12 and cc-pCVnZ-F12 orbital basis sets for the elements H-Ar have been optimized at the density-fitted second-order Møller-Plesset perturbation theory level of theory for use in explicitly correlated (F12) methods, which utilize density fitting for the evaluation of two-electron integrals. Calculations of the correlation energy for a test set of small to medium sized molecules indicate that the density fitting error when using these auxiliary sets is 2 to 3 orders of magnitude smaller than the F12 orbital basis set incompleteness error. The error introduced by the use of these fitting sets within the resolution-of-the-identity approximation of the many-electron integrals arising in F12 theory has also been assessed and is demonstrated to be negligible and well-controlled. General guidelines are proposed for the optimization of density fitting auxiliary basis sets for use with F12 methods for other eleme...
Multi-Coefficient Correlation Method for Quantum Chemistry
The Journal of Physical Chemistry A, 1999
We present a new method for extrapolating correlated electronic structure calculations based on correlationconsistent polarized double-and triple-basis sets for calculation of molecular energies (atomization energies).
Theoretica Chimica Acta, 1990
Generally contracted basis sets for first row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations.
The Journal of Chemical Physics, 2002
The nuclear-electronic orbital ͑NEO͒ method for the calculation of mixed nuclear-electronic wave functions is presented. Both electronic and nuclear molecular orbitals are expressed as linear combinations of Gaussian basis functions. In the NEO-HF ͑Hartree-Fock͒ method, the energy corresponding to the single-configurational mixed nuclear-electronic wave function is minimized with respect to the molecular orbitals. Multiconfigurational approaches are implemented to include significant correlation effects. In the NEO-CI ͑configuration interaction͒ method, the energy corresponding to the multiconfigurational mixed nuclear-electronic wave function is minimized with respect to the CI coefficients. In the NEO-MCSCF ͑multiconfigurational self-consistent-field͒ method, the energy is minimized with respect to the molecular orbitals as well as the CI coefficients. Analytic gradient expressions are presented for NEO-HF and NEO-MCSCF. These analytic gradients allow the variational optimization of the centers of the nuclear basis functions. They also enable the location and characterization of geometry stationary points and the generation of minimum energy paths and dynamic reaction paths. The advantages of the NEO approach are that nuclear quantum effects are incorporated during the electronic structure calculation, the Born-Oppenheimer separation of electrons and nuclei is avoided, excited vibrational-electronic states may be calculated, and its accuracy may be improved systematically. Initial applications are presented to illustrate the computational feasibility and accuracy of this approach.
The Journal of Chemical Physics, 2002
Correlation consistent basis sets for accurately describing core-core and core-valence correlation effects in atoms and molecules have been developed for the second row atoms Al-Ar. Two different optimization strategies were investigated, which led to two families of core-valence basis sets when the optimized functions were added to the standard correlation consistent basis sets (cc-pVnZ). In the first case, the exponents of the augmenting primitive Gaussian functions were optimized with respect to the difference between all-electron and valence-electron correlated calculations, i.e., for the core-core plus core-valence correlation energy. This yielded the cc-pCVnZ family of basis sets, which are analogous to the sets developed previously for the first row atoms ͓D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 103, 4572 ͑1995͔͒. Although the cc-pCVnZ sets exhibit systematic convergence to the all-electron correlation energy at the complete basis set limit, the intershell ͑core-valence͒ correlation energy converges more slowly than the intrashell ͑core-core͒ correlation energy. Since the effect of including the core electrons on the calculation of molecular properties tends to be dominated by core-valence correlation effects, a second scheme for determining the augmenting functions was investigated. In this approach, the exponents of the functions to be added to the cc-pVnZ sets were optimized with respect to just the core-valence ͑intershell͒ correlation energy, except that a small amount of core-core correlation energy was included in order to ensure systematic convergence to the complete basis set limit. These new sets, denoted weighted corevalence basis sets (cc-pwCVnZ), significantly improve the convergence of many molecular properties with n. Optimum cc-pwCVnZ sets for the first-row atoms were also developed and show similar advantages. Both the cc-pCVnZ and cc-pwCVnZ basis sets were benchmarked in coupled cluster ͓CCSD͑T͔͒ calculations on a series of second row homonuclear diatomic molecules (Al 2 , Si 2 , P 2 , S 2 , and Cl 2 ), as well as on selected diatomic molecules involving first row atoms ͑CO, SiO, PN, and BCl͒. For the calculation of core correlation effects on energetic and spectroscopic properties, the cc-pwCVnZ basis sets are recommended over the cc-pCVnZ ones.
We have developed and benchmarked a new extended basis set for explicitly correlated calculations, namely cc-pV5Z-F12. It is offered in two variants, cc-pV5Z-F12 and cc-pV5Z-F12(rev2), the latter of which has additional basis functions on hydrogen not present in the cc-pVnZ-F12 (n = D,T,Q) sequence. A large uncontracted 'reference' basis set is used for benchmarking. cc-pVnZ-F12 (n = D-5) is shown to be a convergent hierarchy. Especially the cc-pV5Z-F12(rev2) basis set can yield the valence CCSD (coupled cluster with all single and double substitutions) component of total atomisation energies, without any extrapolation, to an accuracy normally associated with aug-cc-pV{5,6}Z extrapolations. Hartree-Fock self-consistent field (SCF) components are functionally at the basis set limit, while the MP2 limit can be approached to as little as 0.01 kcal/mol without extrapolation. The determination of (T) appears to be the most difficult of the three components and cannot presently be accomplished without extrapolation or scaling. (T) extrapolation from cc-pV{T,Q}Z-F12 basis sets, combined with CCSD-F12b/cc-pV5Z-F12 calculations, appears to be an accurate combination for explicitly correlated thermochemistry. For accurate work on noncovalent interactions, the basis set superposition error with the cc-pV5Z-F12 basis set is shown to be so small that counterpoise corrections can be neglected for all but the most exacting purposes.
The Journal of Chemical Physics, 2010
Correlation consistent basis sets have been optimized for accurately describing core-core and core-valence correlation effects with explicitly correlated F12 methods. The new sets, denoted cc-pCVnZ-F12 ͑n =D, T, Q͒ and aug-cc-pC F12 VnZ ͑n =D, T, Q, 5͒, were developed by augmenting the cc-pVnZ-F12 and aug-cc-pVnZ families of basis sets with additional functions whose exponents were optimized based on the difference between all-electron and valence-electron correlation energies. The number of augmented functions added is fewer, in general, than in the standard cc-pCVnZ and cc-pwCVnZ families of basis sets. Optimal values of the geminal Slater exponent for use with these basis sets in MP2-F12 calculations are presented and are also recommended for CCSD-F12b calculations. Auxiliary basis sets for use in the resolution of the identity approximation in explicitly correlated calculations have also been optimized and matched to the new cc-pCVnZ-F12 series of orbital basis sets. The cc-pCVnZ-F12 basis sets, along with the new auxiliary sets, were benchmarked in CCSD͑T͒-F12b calculations of spectroscopic properties on a series of homo-and heteronuclear first and second row diatomic molecules. Comparing the effects of correlating the outer core electrons in these molecules with those from conventional CCSD͑T͒ at the complete basis set limit, which involved calculations with new cc-pCV6Z basis sets for the second row elements that were also developed in the course of this work, it is observed that the F12 values are reasonably well converged already at just the triple-level. Physics 132, 054108-1 054108-2 Hill, Mazumder, and Peterson J. Chem. Phys. 132, 054108 ͑2010͒ 054108-3 F12 basis sets for core correlation effects J. Chem. Phys. 132, 054108 ͑2010͒ 054108-8 Hill, Mazumder, and Peterson J. Chem. Phys. 132, 054108 ͑2010͒ 054108-10 Hill, Mazumder, and Peterson J. Chem. Phys. 132, 054108 ͑2010͒
Theoretical Chemistry Accounts, 2012
We construct a reference benchmark set for atomic and molecular random phase approximation (RPA) correlation energies in a density functional theory framework at the complete basis-set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies, accurate results, clearly outperforming raw data, are achievable with twopoint extrapolation schemes based on quintuple-and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be obtained by using a semiempirical extrapolation procedure based on quadruple-and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.
The Journal of Chemical Physics, 2013
An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO-MOLPRO interface allows to include highlevel electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code. Different model systems illustrate the implementation: 4 He 2 dimer as a protype of a weakly bound van der Waals system; isotopomers of [He-H-He] + molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations. The possible improvements and future developments are outlined. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4803546\] 2