Augmented Correlation Consistent Basis Sets Research Articles

A systematical comparison of DFT methods in reproducing the interaction energies of halide series with protein moieties

A systematic theoretical investigation on the interaction energies of halogen-ionic bridges formed between halide ions and the polar H atoms bonded to N of protein moieties has been carried out by employing a variety of density functional methods. In this procedure, full geometry optimizations are performed at the Møller-Plesset second-order perturbation (MP2) level of theory in conjunction with the Dunning's augmented correlation-consistent basis set, aug-cc-pVDZ. Subsequently, two distinct basis sets, i.e. 6-311++G(df,pd) and aug-cc-pVTZ, are employed in the following single-point calculations so as to check the stability of the results obtained at the different levels of DFT. The performance of DFT methods has been evaluated by comparing the results with those obtained from the rigorous MP2 theory. It is shown that the B98, B97-1, and M05 give the lowest root-mean-square error (RMSE) for predicting fluoride-binding energies, M05-2X, MPW1B95, and MPW1PW91 have the best performance in reproducing chloride-binding energies, B97-1, PBEKCIS, and PBE1KCIS present the optimal result for bromide-binding energies, while B97-1, MPW1PW91, and TPSS perform most well on iodide-binding energies. The popular B3LYP functional seems to be quite modest for studying halide-protein moiety interactions. In addition, the PBE1KCIS functional provide accuracies close to the computationally expensive MP2 method for the calculation of interaction energies of all halide-binding systems.

Harmonic vibrational frequencies: Scale factors for pure, hybrid, hybrid meta, and double‐hybrid functionals in conjunction with correlation consistent basis sets

Scale factors for (a) low (<1000 cm(-1)) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy scale factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived scale factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used.

Electronic structure calculations on the Ar–C 6H 12 interaction: Application to the microsolvation of the chair conformer

We report a theoretical study of the intermolecular potential for Ar–C 6H 12, with the cyclohexane fixed in both chair and twisted-boat conformers; the geometry of these conformers has been optimized at different levels of theory and the results compared with available data in the literature. For constructing the intermolecular potential, we applied the MP2 methodology with two basis from the augmented correlation-consistent basis set family: aug-cc-pV NZ ( N = D and T). The accuracy of the MP2 calculations has been checked at the minima geometries obtained with the MP2/aug-cc-pVTZ level of theory, for all lines of approach of argon to cyclohexane considered here, by performing single-point CCSD(T)/aug-cc-pVDZ and MP2/aug-cc-pVQZ calculations. In turn, the best MP2 results (using the aug-cc-pVTZ) for the interaction energy have been fitted to a pairwise analytic potential for Ar–C 6H 12. Then, this potential function was employed in a global geometry optimization of the clusters Ar n C 6H 12 ( n = 1–20), with the cyclohexane fixed in the chair conformer.

The Dynamics of Allyl Radical Dissociation

Dissociation of the allyl radical, CH(2)CHCH(2), and its deuterated isotopolog, CH(2)CDCH(2), have been investigated using trajectory calculations on an ab initio ground-state potential energy surface calculated for 97,418 geometries at the coupled cluster single and double and perturbative treatment of triple excitations, with the augmented correlation consistent triple-ζ basis set level (CCSD(T)/AVTZ). At an excitation energy of 115 kcal/mol, corresponding to optical excitation at 248 nm, the primary channel is hydrogen loss with a quantum yield of 0.94 to give either allene or propyne in a ratio of 6.4:1. The total dissociation rate for CH(2)CHCH(2) is 6.3 × 10(10) s(-1), corresponding to a 1/e time of 16 ps. Methyl and C(2)H(2) are produced with a quantum yield of 0.06 by three different mechanisms: a 1,3 hydrogen shift followed by C-C cleavage to give methyl and acetylene, a double 1,2 shift followed by C-C cleavage to give methyl and acetylene, or a single 1,2 hydrogen shift followed by C-C cleavage to give methyl and vinylidene. In this last channel, the vinylidene eventually isomerizes to give internally excited acetylene, and the kinetic energy distribution is peaked at much lower energy (6.4 kcal/mol) than that for the other two channels (18 kcal/mol). The trajectory results also predict the v-J correlation, the anisotropy of dissociation, and distributions for the angular momentum of the fragments. The v-J correlation for the CH(3) + HCCH channel is strongest for high rotational levels of acetylene, where v is perpendicular to J. Methyl elimination is anisotropic, with β = 0.66, whereas hydrogen elimination is nearly isotropic. In the hydrogen elimination channel, allene is rotationally excited with a total angular momentum distribution peaked near J = 17. In the methyl elimination channel, the peak of the methyl rotational distribution is at J ≈ 12, whereas the peak of the acetylene rotational distribution is at J ≈ 28.

Physisorption and dissociative chemisorption of H2 on sub-nanosized Al $_{13}^{-}$ anion cluster: ab initio study

We have studied the interaction of Al $_{13}^{-}$ anion cluster with H2. Both the long range interaction and dissociative adsorption have been examined using the established correlated ab initio methods, MP2 and CCSD(T), in conjunction with the augmented correlation consistent basis sets up to aug-cc-pVTZ. The formation of the weakly bound (physisorbed) end-on anion complex Al $_{13}^{-}$ ...H2 is predicted for the interacting Al...H distances of 3.95 A with the H-H axis pointing towards the ‘hollow’ site of Al $_{13}^{-}$ and binding energy ( $D_{e})$ of 0.7 kcal/mol at the estimated complete basis set (CBS) limit of CCSD(T). The barrier height for H2 dissociation on Al $_{13}^{-}$ of 41.6 (42.9) kcal/mol calculated at the ZPVE-corrected CCSD(T)/aug-cc-pVTZ (estimated CCSD(T)/CBS) level is at least twice as large as that evaluated by us for a dissociative adsorption of H2 on an open-shell Al13 neutral cluster. To our knowledge, this report presents the first “benchmark” quality study of the physisorption and dissociative chemisorption of molecular hydrogen on Al $_{13}^{-}$ anion cluster.

Intermolecular potential energy surface for CS2 dimer

A new four-dimensional intermolecular potential energy surface for CS(2) dimer is obtained by ab initio calculation of the interaction energies for a range of configurations and center-of-mass separation distances for the first time. The calculations were performed using the supermolecular approach at the Møller-Plesset second-order perturbation (MP2) level of theory with the augmented correlation consistent basis sets (aug-cc-pVxZ, x = D, T) and corrected for the basis-set superposition error using the full counterpoise correction method. A two-point extrapolation method was used to extrapolate the calculated energy points to the complete basis set limit. The effect of using the higher levels of theory, quadratic configuration interaction containing single, double, and perturbative triple excitations QCISD(T) and coupled cluster singles, doubles and perturbative triples excitations CCSD(T), on the shape of potential energy surface was investigated. It is shown that the MP2 level of theory apparently performs extremely poorly for describing the intermolecular potential energy surface, overestimating the total energy by a factor of nearly 1.73 in comparison with the QCISD(T) and CCSD(T) values. The value of isotropic dipole-dipole dispersion coefficient (C(6) ) of CS(2) fluid was obtained from the extrapolated MP2 potential energy surface. The MP2 extrapolated energy points were fitted to well-known analytical potential functions using two different methods to represent the potential energy surface analytically. The most stable configuration of the dimer was determined at R = 6.23 au, α = 90°, β = 90°, and γ = 90°, with a well depth of 3.980 kcal mol(-1) at the MP2 level of theory. Finally, the calculated second virial coefficients were compared with experimental values to test the quality of the presented potential energy surface.

Accurate ab initio calculations of the ground states of FeC, FeC+, and FeC−

For the ground states of the diatomic carbide FeC(X (3)Delta) and its ions, FeC(+)(X (2)Delta) and FeC(-)(X (2)Delta), we report on accurate multireference variational ab initio results employing augmented correlation consistent basis sets of quintuple cardinality. The dissociation energies and bond lengths are found to be D(0) (0)=87+/-1, 95.2, and 84+/-1 kcal/mol at r(e)=1.581, 1.556, and 1.660 A for FeC, FeC(+), and FeC(-), respectively. All our final numbers are in agreement with the available experimental data.

Structural changes in the water tetramer. A combined Monte Carlo and DFT study

The heat capacity curve of the water tetramer has been calculated at various levels of theory and over a broad range of temperatures, T = 50-200 K. Parallel-tempering and multiple-histogram Monte Carlo methods have been used and combined with the Density Functional Theory calculations of intra-cluster interactions via the Boltzmann-reweighting approach. It is demonstrated that such a combination can yield well converged thermodynamic data even for a modest number of sample configurations, which makes the methodology particularly appropriate for the inclusion of quantum chemistry calculations in Monte Carlo simulations. The B97-1 exchange-correlation functional has been used in the present work together with augmented correlation-consistent basis sets of atomic orbitals up to triple-zeta quality. A structural change has been detected in the water tetramer in the temperature range considered. It is demonstrated that the change corresponds to the onset of rotations of the water molecules around hydrogen bonds with an almost rigid skeleton of the cluster (square cycle) conserved.

Calculations of rovibrational energies and dipole transition intensities for polyatomic molecules using MULTIMODE

We report rigorous calculations of rovibrational energies and dipole transition intensities for three molecules using a new version of the code MULTIMODE. The key features of this code which permit, for the first time, such calculations for moderately sized but otherwise general polyatomic molecules are briefly described. Calculations for the triatomic molecule BF(2) are done to validate the code. New calculations for H(2)CO and H(2)CS are reported; these make use of semiempirical potentials but ab initio dipole moment surfaces. The new dipole surface for H(2)CO is a full-dimensional fit to the dipole moment obtained with the coupled-cluster with single and double excitations and a perturbative treatment of triple excitations method with the augmented correlation consistent triple zeta basis set. Detailed comparisons are made with experimental results from a fit to relative data for H(2)CS and absolute intensities from the HITRAN database for H(2)CO.

Efficient Diffuse Basis Sets: cc-pVxZ+ and maug-cc-pVxZ.

We combine the diffuse basis functions from the 6-31+G basis set of Pople and co-workers with the correlation-consistent basis sets of Dunning and co-workers. In both wave function and density functional calculations, the resulting basis sets reduce the basis set superposition error almost as much as the augmented correlation-consistent basis sets, although they are much smaller. In addition, in density functional calculations the new basis sets, called cc-pVxZ+ where x = D, T, Q, ..., or x = D+d, T+d, Q+d, ..., give very similar energetic predictions to the much larger aug-cc-pVxZ basis sets. However, energetics calculated from correlated wave function calculations are more slowly convergent with respect to the addition of diffuse functions. We also examined basis sets with the same number and type of functions as the cc-pVxZ+ sets but using the diffuse exponents of the aug-cc-pVxZ basis sets and found very similar performance to cc-pVxZ+; these basis sets are called minimally augmented cc-pVxZ, which we abbreviate as maug-cc-pVxZ.

Heats of Formation of the H1,2OmSn (m, n = 0−3) Molecules from Electronic Structure Calculations

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted from high level ab initio electronic structure calculations using the coupled cluster CCSD(T) method with augmented correlation-consistent basis sets extrapolated to the complete basis set (CBS) limit for the H(1,2)O(m)S(n) (m, n = 0-3) compounds, as well as various radicals involved in different bond breaking processes. To achieve near chemical accuracy (+/-1.0 kcal/mol), additional corrections were added to the CBS binding energies based on the frozen core CCSD(T) energies including corrections for core-valence, scalar relativistic, and first-order atomic spin-orbit effects. Geometries were optimized up through the CCSD(T)/aV(T+d)Z level. Vibrational zero point energies were computed at the MP2/aV(T+d)Z level. The calculated heats of formation are in excellent agreement with the available experimental data and allow the prediction of adiabatic bond dissociation energies (BDEs) to within +/-1.0 kcal/mol. The decomposition mechanisms were largely determined by a preference to maintain a strong S=O bond in the dissociated products as opposed to O=O and S=S bonds, exactly matching the ordering of the BDEs in the diatomics. For the H(2)X(2) and H(2)X(3) systems, as well as the HX(3) radicals, the energetically favorable decomposition pathway leads to the formation of XH radicals and breaking the X-X bond as opposed to breaking the X-H bond. For the HX(2) radicals, however, the more thermodynamically favorable pathway leads to a breaking of the H-X bond and forming X(2) molecules.

Explicitly correlated intermolecular distances and interaction energies of hydrogen bonded complexes

We have optimized the lowest energy structures and calculated interaction energies for the H(2)O-H(2)O, H(2)O-H(2)S, H(2)O-NH(3), and H(2)O-PH(3) dimers with the recently developed explicitly correlated CCSD(T)-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that the results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. In general we find that CCSD(T)-F12 results obtained with the VTZ-F12 basis set are better than the conventional CCSD(T) results obtained with an aug-cc-pV5Z basis set. We also investigate two ways to reduce the effects of basis set superposition error with conventional CCSD(T), namely, the popular counterpoise correction and limiting diffuse basis functions to the heavy atoms only. We find that for a given cardinal number, these selectively augmented correlation consistent basis sets yield results that are closer to the complete basis set limit than the corresponding fully augmented basis sets. Furthermore, we find that the difference between standard and counterpoise corrected interaction energies and intermolecular distances is reduced with the selectively augmented basis sets.

An ab initio calculation of the vibrational energies and transition moments of HSOH

We report new ab initio potential energy and dipole moment surfaces for the electronic ground state of HSOH, calculated by the CCSD(T) method (coupled cluster theory with single and double substitutions and a perturbative treatment of connected triple excitations) with augmented correlation-consistent basis sets up to quadruple-zeta quality, aug-cc-pV(Q+ d)Z. The energy range covered extends up to 20 000 cm −1 above equilibrium. Parameterized analytical functions have been fitted through the ab initio points. Based on the analytical potential energy and dipole moment surfaces obtained, vibrational term values and transition moments have been calculated by means of the variational program TROVE. The theoretical term values for the fundamental levels ν SH (SH-stretch) and ν OH (OH-stretch), the intensity ratio of the corresponding fundamental bands, and the torsional splitting in the vibrational ground state are in good agreement with experiment. This is evidence for the high quality of the potential energy surface. The theoretical results underline the importance of vibrational averaging, and they allow us to explain extensive perturbations recently found experimentally in the SH-stretch fundamental band of HSOH.

Efficient Diffuse Basis Sets: cc-pVxZ+ and maug-cc-pVxZ.

We combine the diffuse basis functions from the 6-31+G basis set of Pople and co-workers with the correlation-consistent basis sets of Dunning and co-workers. In both wave function and density functional calculations, the resulting basis sets reduce the basis set superposition error almost as much as the augmented correlation-consistent basis sets, although they are much smaller. In addition, in density functional calculations the new basis sets, called cc-pVxZ+ where x = D, T, Q, ..., or x = D+d, T+d, Q+d, ..., give very similar energetic predictions to the much larger aug-cc-pVxZ basis sets. However, energetics calculated from correlated wave function calculations are more slowly convergent with respect to the addition of diffuse functions. We also examined basis sets with the same number and type of functions as the cc-pVxZ+ sets but using the diffuse exponents of the aug-cc-pVxZ basis sets and found very similar performance to cc-pVxZ+; these basis sets are called minimally augmented cc-pVxZ, which we abbreviate as maug-cc-pVxZ.

The water-nitric oxide intermolecular potential-energy surface revisited

The two lowest energy intermolecular potential-energy surfaces (IPESs) of the water-nitric oxide complex are evaluated using the spin-restricted coupled-cluster R-CCSD(T) model and the augmented correlation-consistent polarized-valence triple-zeta basis set extended with a set of the 3s3p2d1f1g midbond functions. A detailed characterization of the IPESs for both the (2)A(') and (2)A(") electronic states in the C(s)-symmetry configurations of the complex is performed. The global minimum for the (2)A(') state represented by the lowest energy of -461.8 cm(-1) is deeper than the global minimum in the (2)A(") state with an energy of -435.2 cm(-1). To explore the physics of the interaction an open-shell implementation of the symmetry-adapted perturbation theory is employed and the results are analyzed as a function of the intermolecular parameters. The electrostatic term shows the strongest geometric anisotropy, while the exchange, induction, and dispersion contributions mostly depend on the intermolecular distance. The energy separation between the (2)A(') and (2)A(") states is largely dominated by electrostatic contribution for long intermolecular distances. In the region of short intermolecular distances the exchange part is as important as the electrostatic one and the induction and dispersion effects are also substantial.

First principles study of the electronic structure and bonding of Mn2

We have examined the electronic structure and bonding of the Mn(2) molecule through multireference variational calculations coupled with augmented quadruple correlation consistent basis sets. The Mn atom has a (6)S(4s(2)3d(5)) ground state with its first excited state, (6)D(4s(1)3d(6)), located 2.145 eV higher. For all six molecular states (1)Sigma(g)(+), (3)Sigma(u)(+), (5)Sigma(g)(+), (7)Sigma(u)(+), (9)Sigma(g)(+), and (11)Sigma(u)(+)(1) correlating to Mn((6)S)+Mn((6)S), and for six undecets, i.e., (11)Pi(u), (11)Sigma(g)(+), (11)Delta(g), (11)Delta(u), (11)Sigma(u)(+)(2), and (11)Pi(g) with end fragments Mn((6)S)+Mn((6)D), complete potential energy curves have been constructed for the first time. We prove that the bonding in Mn(2) dimer is of van der Waals type. The interaction of two Mn (6)S atoms is hardly influenced by the total spin, as a result the six Sigma states, singlet ((1)Sigma(g)(+)) to undecet ((11)Sigma(u)(+)(1)), are in essence degenerate packed within an energy interval of about 70 cm(-1). Their ordering follows the spin multiplicity, the ground state being a singlet, X (1)Sigma(g)(+), with binding energy D(e) (D(0)) approximately 600 (550)cm(-1) at r(e) approximately 3.60 A. The six undecet states related to the Mn((6)S)+Mn((6)D) manifold, are chemically bound with binding energies ranging from 3 ((11)Pi(g)) to 25 ((11)Pi(u))kcal/mol and bond distances about 1 A shorter than the states of the lower manifold, Mn((6)S)+Mn((6)S). The lowest of the undecets is of Pi(u) symmetry located 30 kcal/mol above the X (1)Sigma(g)(+) state.

Low‐Temperature Rate Constants for Rotational Excitation and De‐excitation of C3(X 1Σ$^{+}_{g}$ ) by Collisions with He (1S)

The low-temperature rotational (de-) excitation of C3 (X1Σg+) by collisions with He (1S) is studied using an ab initio potential energy surface (PES). This PES has been calculated using the single- and double-excitation coupled-cluster approach with noniterative perturbational treatment of triple excitations [CCSD(T)] and the augmented correlation-consistent triple-ζ basis set (aug-cc-pVTZ) with bond functions. This PES is then incorporated in full close-coupling quantum scattering calculations for collision energies between 0.1 and 50 cm−1 in order to deduce the rate constants for rotational levels of C3 up to j = 10, covering the temperature range 5-15 K.

Calculated Band Profiles of the OH-Stretching Transitions in Water Dimer

We have calculated the band profiles of the OH-stretching fundamental and overtone transitions in the proton donor unit of the water dimer complex. We have used a local mode Hamiltonian that includes both OH-stretching and OO-stretching motion but separates these adiabatically. The variation of OH-stretching frequency and anharmonicity with OO displacement from equilibrium contributes to the effective OO-stretching potentials for each OH-stretching state. The resulting OO-stretching energy levels and wave functions are used to simulate the vibrational profile of each OH-stretching transition. The coupled cluster with singles, doubles, and perturbative triples ab initio method with an augmented triple-zeta correlation consistent basis set has been used to obtain the necessary parameters, potentials, and dipole moment functions. We find that the OO-stretching transitions associated with a given hydrogen bonded OH-stretching transition are spread significantly and this spread increases with overtone. The spread is minor for the free OH-stretching transition. The inclusion of the OO-stretching mode has a limited effect on the overall OH-stretching band intensity.

Calculation of the O−H Stretching Vibrational Overtone Spectrum of the Water Dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.

Structures and heats of formation of the neutral and ionic PNO, NOP, and NPO systems from electronic structure calculations

High level ab initio electronic structure calculations using the coupled cluster CCSD(T) method with augmented correlation-consistent basis sets extrapolated to the complete basis set limit have been performed on the PNO, NOP, and NPO isomers and their corresponding anions and cations. Geometries for all species were optimized up through the aug-cc-pV(Q+d)Z level and vibrational frequencies were calculated with the aug-cc-pV(T+d)Z basis set. The most stable of the three isomers is NPO and it is predicted to have a heat of formation of 23.3 kcal/mol. PNO is predicted to be only 1.7 kcal/mol higher in energy. The calculated adiabatic ionization potential of NPO is 12.07 eV and the calculated adiabatic electron affinity is 2.34 eV. The calculated adiabatic ionization potential of PNO is 10.27 eV and the calculated adiabatic electron affinity is only 0.24 eV. NOP is predicted to be much higher in energy by 29.9 kcal/mol. The calculated rotational constants for PNO and NPO should allow for these species to be spectroscopically distinguished. The adiabatic bond dissociation energies for the P[Single Bond]N, P[Single Bond]O, and N[Single Bond]O bonds in NPO and PNO are the same within approximately 10 kcal/mol and fall in the range of 72-83 kcal/mol.