Quadruple-zeta Basis Set Research Articles

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the 7p elements, with atomic and molecular applications

Relativistic basis sets of double-zeta, triple-zeta, and quadruple-zeta quality have been optimized for the 7p elements at the Dirac-Coulomb self-consistent field level of theory with a Gaussian nuclear charge distribution. For all of these sets, valence and outer-core correlating functions have been optimized in multireference CI calculations on the valence pn states. Diffuse functions are also provided. Prescriptions are given for constructing contracted basis sets, based on MRCI calculations for correlation of the atoms. The basis sets are applied to a range of atomic and molecular properties, to provide information on how to use the basis sets. Tests of the basis sets with an explicit representation of the 8s showed that the 8s is not needed. The basis sets are available as an internet archive and from the Dirac program web site, http://dirac.chem.sdu.dk.

Basis set convergence of molecular correlation energy differences within the random phase approximation

The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruple-zeta valence basis sets offer a good balance between accuracy and efficiency.

Low-energy rotational inelastic collisions of H+ + CO system

The quantum mechanical state-to-state rotational excitation cross sections have been computed using the ab initio ground electronic state potential energy surface of the system [M. Mladenovic and S. Schmatz, J. Chem. Phys. 109, 4456 (1998)] computed at coupled-cluster single and double and triple perturbative excitations method using correlation-consistent polarized valence quadruple zeta basis set where the asymptotic potential have been computed using the dipole moment, quadrupole moment, and the molecular polarizability components and fitted to this interaction potential. The anisotropy of the surface has been analyzed in terms of the multipolar expansion coefficients for the rigid-rotor surface. The integral cross sections for rotational excitations have been computed by solving close-coupled equations at very low collision energies (5-200 cm(-1)) and the corresponding rates have been obtained for a range of low temperatures (5-175 K). The j = 0 → j(') = 1 rotational excitation cross section (and rate) is found to be the dominant followed by the j = 0 → j(') = 2 in these collision energies. The close-coupling, coupled-state, and infinite-order sudden approximations coupling calculations have been performed in the energy range of 0.1-1.0 eV using vibrational ground potential. The rotational cross sections have been obtained by performing computationally accurate close-coupling calculations at 0.1 eV using vibrationally averaged potential (ν = 1) and compared with the results of vibrational ground potential.

A new ab initio potential energy surface for the collisional excitation of O2 by H2

We present a new four dimensional (4D) potential energy surface for the O(2)-H(2) system. Both molecules were treated as rigid rotors. Potential was obtained from the electronic structure calculations using a partially spin-restricted coupled cluster with the single, double and perturbative triple excitations [RCCSD(T)] method. The four atoms were described using the augmented correlation-consistent quadruple zeta (aug-cc-pVQZ) basis sets. Bond functions were placed at mid-distance between the O(2) center of mass and the center of mass of H(2) for a better description of the van der Waals interaction. Additionally, at five characteristic geometries, we calculated perturbational components of the interaction energy using the Symmetry-Adapted Perturbation Theory [SAPT] approach to explain the anisotropy of the potential energy surface. Bound states of the O(2)-H(2) van der Waals complex are computed using this potential. Close coupling calculations of the inelastic integral cross sections of O(2) in collisions with para-H(2) and ortho-H(2) were also calculated at low energies. After Boltzmann thermal averaging, rate coefficients were obtained for temperatures ranging from 5 to 100 K. No significant differences exist between para- and ortho-H(2) results.

Theoretical study of spectroscopy, interaction, and dissociation of linear and T-shaped isomers of RgClF (Rg = He, Ne, and Ar) van der Waals complexes

Spectroscopy, interaction energy, and dissociation of linear and T-shaped isomers of HeClF, NeClF, and ArClF van der Waals complexes in their ground state have been studied in detail using MP2 and CCSD(T) methods in conjunction with correlation consistent valence triple and quadruple zeta basis sets. A method, called potential method, has been developed to remove the discrepancy between theoretical and experimental values for the depth of the potential well and dissociation energies for these complexes. This is also supported by the supermolecular approach. Most of the structural and spectroscopic properties of these complexes are first reported and the rest agree very well with the experimental and theoretical values wherever available. Two local minima corresponding to linear and asymmetric T-shaped are found for RgClF complexes. For NeClF complex, the predicted values for the equilibrium bond length and well depth are R NeCl = 3.096 A and $$ D_{\text{e}}^{\text{p}} $$ = 161.50 cm−1 for the linear isomer and R NeCl = 3.503 A and $$ D_{\text{e}}^{\text{p}} $$ = 126.10 cm−1 for the T-shaped isomer. Various dissociation channels are also investigated in detail.

Ab Initio Potential Energy Surfaces for Both the Ground (X̃1A′) and Excited (A∼1A′′) Electronic States of HSiBr and the Absorption and Emission Spectra of HSiBr/DSiBr

Ab initio potential energy surfaces for the ground (X̃1A′) and excited (A˜A′′1) electronic states of HSiBr were obtained by using the single and double excitation coupled-cluster theory with a noniterative perturbation treatment of triple excitations and the multireference configuration interaction with Davidson correction, respectively, employing an augmented correlation-consistent polarized valence quadruple zeta basis set. The calculated vibrational energy levels of HSiBr and DSiBr of the ground and excited electronic states are in excellent agreement with the available experimental band origins. In addition, the absorption and emission spectra of HSiBr and DSiBr were calculated using an efficient single Lanczos propagation method and are in good agreement with the available experimental observations.

Global ab initio potential energy surfaces for both the ground ($\tilde X{^1}A^{\prime} $X̃1A′) and excited ($\tilde A^1 A^{\prime \prime} $Ã1A′′) electronic states of HNO and vibrational states of the Renner-Teller $\tilde A^1 A^{\prime \prime} $Ã1A′′–$\tilde X{^1}A^{\prime} $X̃1A′system

The global potential energy surfaces for both the ground (X̃(1)A(')) and excited (Ã(1)A('')) electronic states of the HNO molecule have been constructed by three-dimensional cubic spline interpolation of more than 17,000 ab initio points, which have been calculated at the internal contracted multi-reference configuration interaction level with the Davidson correction using an augmented correlation-consistent polarized valence quadruple zeta basis set. The low-lying vibrational energy levels for the two electronic states of HNO have also been calculated on our potential energy surfaces including the diagonal Renner-Teller terms. The calculated results have shown a good agreement with the experimental vibrational frequencies of HNO and its isotopomers.

Towards highly accurate ab initio thermochemistry of larger systems: Benzene

The high accuracy extrapolated ab initio thermochemistry (HEAT) protocol is applied to compute the total atomization energy (TAE) and the heat of formation of benzene. Large-scale coupled-cluster calculations with more than 1500 basis functions and 42 correlated electrons as well as zero-point energies based on full cubic and (semi)diagonal quartic force fields obtained with the coupled-cluster singles and doubles with perturbative treatment of the triples method and atomic natural orbital (ANO) triple- and quadruple-zeta basis sets are presented. The performance of modifications to the HEAT scheme and the scaling properties of its contributions with respect to the system size are investigated. A purely quantum-chemical TAE and associated conservative error bar of 5463.0 ± 3.1 kJ mol(-1) are obtained, while the corresponding 95% confidence interval, based on a statistical analysis of HEAT results for other and related molecules, is ± 1.8 kJ mol(-1). The heat of formation of benzene is determined to be 101.5 ± 2.0 kJ mol(-1) and 83.9 ± 2.1 kJ mol(-1) at 0 K and 298.15 K, respectively.

Full-dimensional analytical ab initio potential energy surface of the ground state of HOI

Extensive ab initio calculations using a complete active space second-order perturbation theory wavefunction, including scalar and spin-orbit relativistic effects with a quadruple-zeta quality basis set were used to construct an analytical potential energy surface (PES) of the ground state of the [H, O, I] system. A total of 5344 points were fit to a three-dimensional function of the internuclear distances, with a global root-mean-square error of 1.26 kcal mol(-1). The resulting PES describes accurately the main features of this system: the HOI and HIO isomers, the transition state between them, and all dissociation asymptotes. After a small adjustment, using a scaling factor on the internal coordinates of HOI, the frequencies calculated in this work agree with the experimental data available within 10 cm(-1).

Testing the parametric two-electron reduced-density-matrix method with improved functionals: Application to the conversion of hydrogen peroxide to oxywater

Parametrization of the two-electron reduced density matrix (2-RDM) has recently enabled the direct calculation of electronic energies and 2-RDMs at the computational cost of configuration interaction with single and double excitations. While the original Kollmar energy functional yields energies slightly better than those from coupled cluster with single-double excitations, a general family of energy functionals has recently been developed whose energies approach those from coupled cluster with triple excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. In this paper we test the parametric 2-RDM method with one of these improved functionals through its application to the conversion of hydrogen peroxide to oxywater. Previous work has predicted the barrier from oxywater to hydrogen peroxide with zero-point energy correction to be 3.3-to-3.9 kcal/mol from coupled cluster with perturbative triple excitations [CCSD(T)] and -2.3 kcal/mol from complete active-space second-order perturbation theory (CASPT2) in augmented polarized triple-zeta basis sets. Using a larger basis set than previously employed for this reaction-an augmented polarized quadruple-zeta basis set (aug-cc-pVQZ)-with extrapolation to the complete basis-set limit, we examined the barrier with two parametric 2-RDM methods and three coupled cluster methods. In the basis-set limit the M parametric 2-RDM method predicts an activation energy of 2.1 kcal/mol while the CCSD(T) barrier becomes 4.2 kcal/mol. The dissociation energy of hydrogen peroxide to hydroxyl radicals is also compared to the activation energy for oxywater formation. We report energies, optimal geometries, dipole moments, and natural occupation numbers. Computed 2-RDMs nearly satisfy necessary N-representability conditions.

Anharmonic rovibrational analysis for disilacyclopropenylidene (Si2CH2)

The global minimum on the Si(2)CH(2) electronic singlet potential energy surface has been theoretically predicted to be a peculiar hydrogen bridged (Si···H···Si) disilacyclopropenylidene structure (Si(2)CH(2)). An accurate quartic force field for Si(2)CH(2) has been determined employing ab initio coupled-cluster theory with single and double excitations and a perturbative treatment for triple excitations [CCSD(T)], in combination with the correlation consistent core-valence quadruple zeta (cc-pCVQZ) basis set. The vibration-rotation coupling constants, equilibrium and zero-point vibration corrected rotational constants, centrifugal distortion constants, and harmonic and fundamental vibrational frequencies for six isotopologues of Si(2)CH(2) are predicted using vibrational second-order perturbation theory (VPT2). The anharmonic corrections for the vibrational motions involving the H bridged bonds are found to be more than 5% with respect to the corresponding harmonic vibrational frequencies. In this light, an experimental detection and characterization of disilacyclopropenylidene (Si(2)CH(2)) is highly desired.

New ab initio potential energy surfaces for both the ground (X̃1A′) and excited (Ã1A″) electronic states of HSiCl and the absorption and emission spectra of HSiCl/DSiCl

New ab initio potential energy surfaces for the ground (X̃1A') and excited (Ã1A″) electronic states of HSiCl were obtained by using the single and double excitation coupled-cluster theory with a noniterative perturbation treatment of triple excitations and the multi-reference configuration interaction with Davidson correction, respectively, employing an augmented correlation-consistent polarized valence quadruple zeta basis set. For the excited state Ã1A″, an extended active space (18 electrons in 12 orbitals) was used. The calculated vibrational energy levels of HSiCl and DSiCl of the ground and excited electronic states are in better agreement with the available experimental values than the previous theoretical results. In addition, with the calculated transition dipole moment, the absorption and emission spectra of HSiCl and DSiCl were calculated using an efficient single Lanczos propagation method and are in reasonable agreement with the available observed spectra.

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the 6d elements Rf–Cn

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the 6d elements Rf–Cn

Determination of a silane intermolecular force field potential model from anab initiocalculation

Intermolecular interaction potentials of the silane dimer in 12 orientations have been calculated by using the Hartree-Fock (HF) self-consistent theory and the second-order M\o{}ller-Plesset (MP2) perturbation theory. We employed basis sets from Pople's medium-size basis sets [up to 6-$311+$$+$$G$($3\mathit{df}$, $3\mathit{pd}$)] and Dunning's correlation consistent basis sets (up to the triply augmented correlation-consistent polarized valence quadruple-zeta basis set). We found that the minimum energy orientations were the $G$ and $H$ conformers. We have suggested that the Si-H attractions, the central silicon atom size, and electronegativity play essential roles in weakly binding of a silane dimer. The calculated MP2 potential data were employed to parametrize a five-site force field for molecular simulations. The Si-Si, Si-H, and H-H interaction parameters in a pairwise-additive, site-site potential model for silane molecules were regressed from the ab initio energies.

Relativistic effects in HgHe and HgXe CCSD(T) ground state potential curves. Low-density viscosity simulations of Hg:Xe mixture

The comparison of coupled cluster with single and double excitations and with perturbative correction of triple excitations [CCSD(T)] ground state potential curves of mercury with rare gases (RG): HgHe and HgXe, at several levels of theory is presented. The scalar relativistic (REL) effects and spin-orbit coupling effects in the ground state potential curves of these weakly bounded dimers are considered. The CCSD(T) ground state potential curves at the level of the Dirac-Coulomb Hamiltonian (DCH) are compared with CCSD(T) curves at the level of 4-component spin-free modified DCH, the scalar 2nd order Douglas-Kroll-Hess (DKH2) and the nonrelativistic (NR-LL) (Lévy-Leblond) Hamiltonian. In addition, London-Drude formula and SCF interaction energy curves are employed in the analysis of different contributions of REL effects in dissociation energies of HgRG and Hg(2) dimers. Moreover, the large anharmonicity of the HgHe ground state potential curve is highlighted. The computationally less demanding scalar DKH2 Hamiltonian is employed to calculate the HgXe, Hg(2) , and Xe(2) all electron CCSD(T) ground state potential curves in highly augmented quadruple zeta basis sets. These potential curves are used to simulate the shear viscosity of mercury, xenon, and mercury-xenon (Hg:Xe) mixture.

Recoupled Pair Bonding in PFn(n= 1−5)†

Following our previous studies of hypervalency in SF(n) (n = 1-6) and ClF(n) (n = 1-7), we have characterized the structures and energetics of PF(n) (n = 1-5) species with RCCSD(T) coupled cluster calculations and triple- and quadruple-zeta quality correlation consistent basis sets. The prior studies demonstrated that hypervalent bonding occurs when it is energetically favorable to uncouple a pair of electrons to form new bonds, a process we describe as recoupled pair bonding. In contrast to S and Cl, ground state P((4)S) has no 3p(2) pairs that can be recoupled, but the 3s(2) pair of all three elements is susceptible to recoupled pair bonding when more energetically accessible bonding pathways have been exhausted. We found that this can first occur when F is added to PF(2)(X(2)B(1)), which yields PF(3)(X(1)A(1)) via normal covalent bonding but yields PF(3)(a(3)B(1)) via recoupled pair bonding. PF(3)(a(3)B(1)) lies 92.1 kcal/mol above PF(3)(X(1)A(1)) but is still bound by 42.0 kcal/mol with respect to PF(2)(X(2)B(1)) + F at the RCCSD(T)/aug-cc-pVQZ level. We characterized both of the isomers of PF(4): the more stable and familiar one that has two covalent equatorial bonds and two axial hypervalent bonds (that use both electrons of the recoupled 3s(2) pair) and the less-studied one that has three covalent bonds and only one hypervalent bond. The transition state between these two minima was also located. In addition to the states that can be formed from P((4)S), there is another group of low-lying excited state species that can be formed from P((2)D) via various combinations of covalent and recoupled pair bonding. Additions of the latter type include PF(B(3)Pi) formed from P((1)D) + F and PF(2)(B(2)B(2)) formed from either PF(a(1)Delta) + F or PF(B(3)Pi) + F.

Analytic Calculation of First-order Molecular Properties at the Explicitly-correlated Second-order Møller-Plesset Level

Abstract Formulae are derived and implemented for the analytic calculation of first-order molecular properties at the level of explicitly-correlated second-order Møller-Plesset perturbation theory. In this theory, which is denoted as MP2-F12 theory, Slater-type geminals are used to expand the first-order wave function. A second-order perturbation theory correction for single excitations into a complementary auxliary basis set is also included. At the MP2-F12 level, it seems sufficient to restrict the analytic calculation of energy derivatives to the level of standard approximation A of MP2-F12 theory and to assume the extended Brillouin condition to hold. Smooth and rapid convergence towards the basis-set limit is observed for the dipole moments of a selection of small closed- and open-shell molecules when calculated at the RI-MP2-F12/2A*[T+V] + CABS singles level in augmented correlation-consistent polarized valence double-, triple-, and quadruple-zeta basis sets that have been optimized especially for use in MP2-F12 theory.

Accurate ab initio potential energy curve of O2. I. Nonrelativistic full configuration interaction valence correlation by the correlation energy extrapolation by intrinsic scaling method

The recently introduced method of correlation energy extrapolation by intrinsic scaling is used to calculate the nonrelativistic electron correlations in the valence shell of the O(2) molecule at 24 internuclear distances along the ground state (3)Sigma(g)(-) potential energy curve from 0.9 to 6 A, the equilibrium distance being 1.207 52 A. Using Dunning's correlation-consistent triple- and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to sextuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits.

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the lanthanides La–Lu

Relativistic basis sets of double-zeta, triple-zeta, and quadruple-zeta quality have been optimized for the lanthanide elements La–Lu. The basis sets include SCF exponents for the occupied spinors and for the 6p shell, exponents of correlating functions for the valence shells (4f, 5d and 6s) and the outer core shells (4d, 5s and 5p), and diffuse functions, including functions for dipole polarization of the 4f shell. A finite nuclear size was used in all optimizations. The basis sets are illustrated by calculations on YbF. Prescriptions are given for constructing contracted basis sets. The basis sets are available as an internet archive and from the Dirac program web site, http://dirac.chem.sdu.dk .

Reductive half-reaction of aldehyde oxidoreductase toward acetaldehyde: Ab initio and free energy quantum mechanical/molecular mechanical calculations

Energy and free energy barriers for acetaldehyde conversion in aldehyde oxidoreductase are determined for three reaction pathways using quantum mechanical/molecular mechanical (QM/MM) calculations on the solvated enzyme. Ab initio single-point QM/MM energies are obtained at the stationary points optimized at the DFT(B3LYP)/MM level. These ab initio calculations employ local correlation treatments [LMP2 and LCCSD(T0)] in combination with augmented triple- and quadruple-zeta basis sets, and the final coupled cluster results include MP2-based corrections for basis set incompleteness and for the domain approximation. Free energy perturbation (FEP) theory is used to generate free energy profiles at the DFT(B3LYP)/MM level for the most important reaction steps by sampling along the corresponding reaction paths using molecular dynamics. The ab initio and FEP QM/MM results are combined to derive improved estimates of the free energy barriers, which differ from the corresponding DFT(B3LYP)/MM energy barriers by about 3 kcal mol(-1). The present results confirm the qualitative mechanistic conclusions from a previous DFT(B3LYP)/MM study. Most favorable is a three-step Lewis base catalyzed mechanism with an initial proton transfer from the cofactor to the Glu869 residue, a subsequent nucleophilic attack that yields a tetrahedral intermediate (IM2), and a final rate-limiting hydride transfer. The competing metal center activated pathway has the same final step but needs to overcome a higher barrier in the initial step on the route to IM2. The concerted mechanism has the highest free energy barrier and can be ruled out. While confirming the qualitative mechanistic scenario proposed previously on the basis of DFT(B3LYP)/MM energy profiles, the present ab initio and FEP QM/MM calculations provide corrections to the barriers that are important when aiming at high accuracy.