Correlation-consistent Basis Sets cc-pVXZ Research Articles

The AuSc, AuTi, and AuFe molecules: Determination of the bond energies by Knudsen effusion mass spectrometry experiments combined with ab initio calculations.

The AuTi gaseous molecule was for the first time identified in vapors produced at high temperature from a gold-titanium alloy. The homogeneous equilibria AuTi(g) = Au(g) + Ti(g) (direct dissociation) and AuTi(g) + Au(g) = Au2(g) + Ti(g) (isomolecular exchange) were studied by Knudsen effusion mass spectrometry in the temperature range 2111-2229K. The so determined equilibrium constants were treated by the "third-law method" of thermodynamic analysis, integrated with theoretical calculations, and the dissociation energy at 0K was derived as D0K ° (AuTi) = 241.0 ± 5.2 kJ/mol. A similar investigation was carried out for the AuSc and AuFe species, whose dissociation energies were previously reported with large uncertainties. The direct dissociation and the isomolecular exchange with the Au2 dimer were studied in the 1969-2274 and 1842-2092K ranges for AuSc and AuFe, respectively, and the dissociation energies derived as D0K ° (AuSc) = 240.4 ± 6.0 and D0K ° (AuFe) = 186.2 ± 4.2 kJ/mol. The experimental bond energies are compared with those calculated here by coupled cluster with single, double, and perturbative triple excitations with the correlation-consistent basis sets cc-pVXZ(-PP) and cc-pwCVXZ(-PP) (with X = T, Q, 5), also in the limit of complete basis set, and with those from complete active space self-consistent field-multi-reference configuration interaction calculations, recently available in the literature. The stronger bond of AuTi compared to AuFe parallels the trend observed in monochlorides. This analogy is shown to be more generally observed in the AuM and MCl diatomic series (with M = first row transition metal), in accordance with a picture of "pseudo-halogen" bonding behavior of gold.

Effect of Core Electrons in Defining the Total Energy, Correlation Energy, and Binding Energy of Graphene, Graphite, and Diamond: a First-Principles Study

Effects of core electrons on total energy, correlation energy, and binding energy of graphene, graphite, and diamond have been investigated along with density functional theory (DFT) calculations at the PBE level of theory using all electron and frozen-core calculations. For these calculations, correlation-consistent basis sets cc-pVXZ and cc-pCVXZ have been used where X is the cardinal number that represents the maximum angular momentum number in the basis set. By taking the difference between all electron and frozen-core calculations, core-electron binding energy contribution for each basis set has been obtained. It has been shown that to reduce the effects of core electrons, large basis sets should be used.

On the convergence of zero-point vibrational corrections to nuclear shieldings and shielding anisotropies towards the complete basis set limit in water

ABSTRACTThe method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.

Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn-Sham complete basis set limit.

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested.The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies.Graphical In this study, the performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, and 6) was tested. For the first time, we demonstrated regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limitElectronic supplementary materialThe online version of this article (doi:10.1007/s00894-015-2902-z) contains supplementary material, which is available to authorized users.

The cyanate and 2-phosphaethynolate anion congeners ECO- (E = N, P, As, Sb, Bi): prelude to experimental characterization.

Pioneering synthetic research by the groups of Grutzmacher and Goicoechea have made possible the preparation of 2-phosphaethynolates (PCO(-)). The obvious question arises: can progress be made toward AsCO(-), SbCO(-), and BiCO(-)? Here the properties of all five anion congeners ECO(-) (E = N, P, As, Sb, Bi) were systematically investigated using ab initio coupled-cluster methods with correlation-consistent basis sets cc-pVXZ (X = D, T, Q). These anions exhibit linear structures with significant natural bond orbital negative charge on both the E and O atoms. These species should react with electrophiles via attack at either center. On going from nitrogen to bismuth, with the atomic radius increasing, the bond between E and C becomes weaker, while the C-O bond tends to be slightly stronger. By the time one gets to BiCO(-), the C-O bond distance is 1.181 Å, indicating a very strong double bond. Relative to the PCO(-) anion, which is reactive toward several unsaturated compounds, the As/Sb/BiCO(-) anions may undergo cycloaddition more readily with unsaturated substrates. The dissociation energy of the E-C bond, except for that of NCO(-), is predicted to be much less than that of the C-O bond. These dissociation energies are 76 kcal/mol (P(-)-CO), 58 kcal/mol (As(-)-CO), 37 kcal/mol (Sb(-)-CO), and 28 kcal/mol (Bi(-)-CO). Even the BiCO(-) anion should be achievable in the laboratory. The vibrational frequencies for these anions are predicted, and our results should assist in the experimental characterization and exploration of the heavier congeners ECO(-).

Accurate ab initio quartic force fields of cyclic and bent HC2N isomers

Highly correlated ab initio quartic force fields (QFFs) are used to calculate the equilibrium structures and predict the spectroscopic parameters of three HC(2)N isomers. Specifically, the ground state quasilinear triplet and the lowest cyclic and bent singlet isomers are included in the present study. Extensive treatment of correlation effects were included using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted as CCSD(T). Dunning's correlation-consistent basis sets cc-pVXZ, X = 3,4,5, were used, and a three-point formula for extrapolation to the one-particle basis set limit was used. Core-correlation and scalar relativistic corrections were also included to yield highly accurate QFFs. The QFFs were used together with second-order perturbation theory (PT) (with proper treatment of Fermi resonances) and variational methods to solve the nuclear Schrödinger equation. The quasilinear nature of the triplet isomer is problematic, and it is concluded that a QFF is not adequate to describe properly all of the fundamental vibrational frequencies and spectroscopic constants (though some constants not dependent on the bending motion are well reproduced by PT). On the other hand, this procedure (a QFF together with either PT or variational methods) leads to highly accurate fundamental vibrational frequencies and spectroscopic constants for the cyclic and bent singlet isomers of HC(2)N. All three isomers possess significant dipole moments, 3.05 D, 3.06 D, and 1.71 D, for the quasilinear triplet, the cyclic singlet, and the bent singlet isomers, respectively. It is concluded that the spectroscopic constants determined for the cyclic and bent singlet isomers are the most accurate available, and it is hoped that these will be useful in the interpretation of high-resolution astronomical observations or laboratory experiments.

The empirical equilibrium structure of diacetylene

High-level quantum-chemical calculations are reported at the MP2 and CCSD(T) levels of theory for the equilibrium structure and the harmonic and anharmonic force fields of diacetylene, H C C C C H. The calculations were performed employing Dunning’s hierarchy of correlation-consistent basis sets cc-pV XZ, cc-pCV XZ, and cc-pwCV XZ, as well as the ANO2 basis set of Almlöf and Taylor. An empirical equilibrium structure based on experimental rotational constants for 13 isotopic species of diacetylene and computed zero-point vibrational corrections is determined ( r e emp : r C H = 1.0615 Å , r C C = 1.2085 Å , r C C = 1.3727 Å ) and in good agreement with the best theoretical structure (CCSD(T)/cc-pCV5Z: r C H = 1.0617 Å , r C C = 1.2083 Å , r C C = 1.3737 Å ). In addition, the computed fundamental vibrational frequencies are compared with the available experimental data and found in satisfactory agreement.

Extrapolation of electron correlation energies to finite and complete basis set targets

The electron correlation energy of two-electron atoms is known to converge asymptotically as approximately (L+1)(-3) to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence approximately X(-3) with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X(-beta) that for an effective exponent beta=beta(eff)(X,X+1,X+N) provides the correct energy E(X+N), when extrapolating from results for two smaller basis sets, E(X) and E(X+1). This analysis is first applied to "model" expansions available from analytical theory, and then to a large body of finite basis set results (X=D,T,Q,5,6) for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2-R12 and CCSD-R12 calculations. beta(eff) is generally found to vary monotonically with the target of extrapolation, X+N, making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlation energies, between hydrogen-rich and hydrogen-free molecules, and, for He, between partial-wave expansions and correlation-consistent basis sets. Deviations from asymptotic convergence behavior tend to get smaller as X increases, but not always monotonically, and are still quite noticeable even for X=5. Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single "optimal" exponent beta(opt)(X,X+1,infinity) for the entire set of molecules, and compared to similar approaches reported in the literature.

In search of definitive signatures of the elusive NCCO radical

Previous experimental assignments of the fundamental vibrational frequencies of NCCO have been brought into question by subsequent unsuccessful attempts to observe IR signatures of this radical at these frequencies. Here we compute the fundamental vibrational frequencies by applying second-order vibrational perturbation theory to the complete quartic force field computed at the all-electron (AE) coupled cluster singles, doubles, and perturbative triples level [CCSD(T)] with the correlation-consistent, polarized core-valence quadruple-zeta (cc-pCVQZ) basis set, which has tight functions to correctly describe core correlation. The AE-CCSD(T)/cc-pCVQZ geometric parameters are r(e)(N-C)=1.1623 A, r(e)(C-C)=1.4370 A, r(e)(C-O)=1.1758 A, theta(e)(N-C-C)=168.55 degrees , and theta(e)(C-C-O)=132.22 degrees . Our CCSD(T)/cc-pCVQZ values of the characteristic stretching frequencies nu(1) and nu(2) are 2171 and 1898 cm(-1), respectively, in stark contrast to the experimentally derived values of 2093 and 1774 cm(-1). Finally, focal-point extrapolations using correlation-consistent basis sets cc-pVXZ (X=D,T,Q,5,6) and electron correlation treatments as extensive as full coupled cluster singles, doubles, and triples (CCSDT) with perturbative accounting of quadruple excitations [CCSDT(Q)] determine the vibrationless barrier to linearity of NCCO and the dissociation energy (D(0)) of NCCO-->NC+CO to be 8.4 and 26.5 kcal mol(-1), respectively. Using our precisely determined dissociation energy, we recommend a new 0 K enthalpy of formation for NCCO of 50.9+/-0.3 kcal mol(-1).

Accurate ab Initio Binding Energies of Alkaline Earth Metal Clusters

The effects of basis set superposition error (BSSE) and core-correlation on the electronic binding energies of alkaline earth metal clusters Y(n) (Y = Be, Mg, Ca; n = 2-4) at the Moller-Plesset second-order perturbation theory (MP2) and the single and double coupled cluster method with perturbative triples correction (CCSD(T)) levels are examined using the correlation consistent basis sets cc-pVXZ and cc-pCVXZ (X = D, T, Q, 5). It is found that, while BSSE has a negligible effect for valence-electron-only-correlated calculations for most basis sets, its magnitude becomes more pronounced for all-electron-correlated calculations, including core electrons. By utilizing the negligible effect of BSSE on the binding energies for valence-electron-only-correlated calculations, in combination with the negligible core-correlation effect at the CCSD(T) level, accurate binding energies of these clusters up to pentamers (octamers in the case of the Be clusters) are estimated via the basis set extrapolation of ab initio CCSD(T) correlation energies of the monomer and cluster with only the cc-pVDZ and cc-pVTZ sets, using the basis set and correlation-dependent extrapolation formula recently devised. A comparison between the CCSD(T) and density functional theory (DFT) binding energies is made to identify the most appropriate DFT method for the study of these clusters.

Ab initio and Density Functional Study of Thionitroso XNS and Thiazyl Isomers XSN, X: H, F, Cl, Br, OH, SH, NH2, CH3, CF3, and SiF3.

Standard enthalpies of formation of several thionitroso (XNS) and thiazyl (XSN) isomers, with X = H, F, Cl, Br, OH, SH, NH 2 , CH 3 , CF 3 , and SiF 3 , were determined using coupled cluster (CC) theory with Dunning's correlation consistent basis sets cc-pVXZ and aug-cc-pV(X+d)Z, G3 and CBS-QB3 model chemistries, as well as the B3LYP DFT method. The results support the idea that the electronegativity of the bonding atom in the substituent is correlated, albeit not perfectly, with the relative stability of the XNS over the XSN isomer. detailed study was performed on the parent isomers HNS and HSN. They exhibit a singlet 1 A' ground state (as all the other molecules) at 5.4 and 9.4 kcal/mol below their first excited 3 A state, respectively (CCSD(T)/CBS calculations). The enthalpies of formation of the isomers at the CCSD(T)/CBS limit, including core valence correlation, and spin-orbit splitting, are f H° 2 9 8 (HNS) = 55.3 ′ 1 kcal/mol and Δ f H° 2 9 8 (HSN) = 75.4 ′ 1 kcal/mol. The activation energy at 0 K for the HNS → HSN isomerization was determined as 63.0 and 64.2 kcal/mol at the CCSD(T)/CBS and B3LYP/6-311+G(3df,2p) levels of theory, respectively. Additional calculations were performed for the cationic isomeric pairs XNS + /XSN + with the general result that ionization increases the relative stability of the thionitroso isomer with respect to the thiazyl isomer. In the cases of ClSN and BrSN, for which the thiazyl isomer is the most stable neutral species, the thionitroso isomer is more stable for the cations. The average deviation of the B3LYP/6-311+G(3df,2p) ionization potentials with respect to the G3 model chemistry is only 0.1 eV.

Ab Initio and Density Functional Study of Thionitroso XNS and Thiazyl Isomers XSN, X = H, F, Cl, Br, OH, SH, NH2, CH3, CF3, and SiF3

Standard enthalpies of formation of several thionitroso (XNS) and thiazyl (XSN) isomers, with X = H, F, Cl, Br, OH, SH, NH2, CH3, CF3, and SiF3, were determined using coupled cluster (CC) theory with Dunning's correlation consistent basis sets cc-pVXZ and aug-cc-pV(X+d)Z, G3 and CBS-QB3 model chemistries, as well as the B3LYP DFT method. The results support the idea that the electronegativity of the bonding atom in the substituent is correlated, albeit not perfectly, with the relative stability of the XNS over the XSN isomer. A detailed study was performed on the parent isomers HNS and HSN. They exhibit a singlet 1A‘ ground state (as all the other molecules) at 5.4 and 9.4 kcal/mol below their first excited 3A‘ ‘ state, respectively (CCSD(T)/CBS calculations). The enthalpies of formation of the isomers at the CCSD(T)/CBS limit, including core valence correlation, and spin−orbit splitting, are ΔfH°298(HNS) = 55.3 ± 1 kcal/mol and ΔfH°298(HSN) = 75.4 ± 1 kcal/mol. The activation energy at 0 K for the HNS → HSN isomerization was determined as 63.0 and 64.2 kcal/mol at the CCSD(T)/CBS and B3LYP/6-311+G(3df,2p) levels of theory, respectively. Additional calculations were performed for the cationic isomeric pairs XNS+/XSN+ with the general result that ionization increases the relative stability of the thionitroso isomer with respect to the thiazyl isomer. In the cases of ClSN and BrSN, for which the thiazyl isomer is the most stable neutral species, the thionitroso isomer is more stable for the cations. The average deviation of the B3LYP/6-311+G(3df,2p) ionization potentials with respect to the G3 model chemistry is only 0.1 eV.

Effects of Basis Set Choice upon the Atomization Energy of the Second-Row Compounds SO2, CCl, and ClO2 for B3LYP and B3PW91

The atomization energies of the species SO2, ClO2, and CCl have been calculated using the hybrid density functional approaches B3LYP and B3PW91. These functionals have been used in combination with the correlation-consistent basis sets cc-pVxZ and aug-cc-pVxZ (where x = D(2), T(3), Q(4), or 5). The impact of the newly revised correlation-consistent basis sets for second-row atoms (cc-pV(x+d)Z, aug-cc-pV(x+d)Z) upon the description of these systems has been assessed. Smooth convergence toward the Kohn−Sham limit is observed. The impact of the tight d function is particularly significant in the description of atomization energies for ClO2 and SO2 at the double-ζ and triple-ζ levels of basis sets, improving the energies by 13−17 and 9−10 kcal/mol, respectively.

Accurate Structures and Binding Energies for Stacked Uracil Dimers

The face-to-face and face-to-back stacked uracil dimers have been investigated by second-order Moller−Plesset (MP2) perturbation theory and by the coupled-cluster singles and doubles method augmented with a perturbative contribution from connected triple substitutions [CCSD(T)]. Full MP2 geometry optimizations were performed with a TZ2P(f,d)++ basis and with the 6-31G* basis for which harmonic vibrational frequencies were computed as well. Complete basis set MP2 binding energies were obtained from basis set extrapolations using the correlation-consistent basis sets cc-pVXZ (X = D−5) and aug-cc-pVXZ (X = D−Q). Higher-order correlation effects were gauged by computing the MP2 → CCSD(T) shift in the counterpoise-corrected binding energy using a modified 6-31G* basis set. By adding this correction to the infinite basis set limit MP2 binding energies, final estimates of 9.7 and 8.8 kcal mol-1 are obtained for the binding energies of the face-to-face and face-to-back structures, respectively.