Structure and spectra of the molecules of manganese, iron, and cobalt trifluorides: A CCSD(T) study in the complete basis set

The coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method in triple-, quadruple-, and quintuple-zeta basis sets with extrapolation to the complete basis set limit is used to analyze the properties of MnF₃, FeF₃, and CoF₃ molecules. The relative energies of low-lying electronic states are determined. The Jahn-Teller effect is investigated in the ground electronic state ⁵ E?? of the MnF₃ molecule and the first excited electronic state ⁵ E?? of the CoF₃ molecule. Geometric parameters, atomization enthalpies, vibrational frequencies, intensities in the infrared and Raman spectra are found with high accuracy. The assignment of the bands observed in the low-frequency region of the IR and Raman spectra of MnF₃ and CoF₃ molecules are revised.     

CCSD(T) study of dimethyl-ether infrared and Raman spectra

CCSD(T) state-of-the-art ab initio calculations are used to determine a vibrationally corrected three-dimensional potential energy surface of dimethyl-ether depending on the two methyl torsions and the COC bending angle. The surface is employed to obtain variationally the lowest vibrational energies that can be populated at very low temperatures. The interactions between the bending and the torsional coordinates are responsible for the displacements of the torsional overtone bands and several combination bands. The effect of these interactions on the potential parameters is analyzed. Second order perturbation theory is used as a help for the understanding of many spectroscopic parameters and to obtain anharmonic fundamentals for the 3N - 9 neglected modes as well as the rotational parameters. To evaluate the surface accuracy and to verify previous assignments, the calculated vibrational levels are compared with experimental data corresponding to the most abundant isotopologue. The surface has been empirically adjusted for understanding the origin of small divergences between ab initio calculations and experimental data. Our calculations confirm previous assignments and show the importance of including the COC bending degree of freedom for computing with a higher accuracy the excited torsional term values through the Fermi interaction. Besides, this work shows a possible lack of accuracy of some available experimental transition frequencies and proposes a new assignment for a transition line. As an example, the transition 100 → 120 has been computed at 445.93 cm(-1), which is consistent with the observed transition frequency in the Raman spectrum at 450.5 cm(-1).     

On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies

The leading cause of error in standard coupled cluster theory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the one-particle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)-F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the one-particle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.     

Basis set limit CCSD(T) harmonic vibrational frequencies

Benchmark, frozen-core CCSD(T) equilibrium harmonic vibrational frequencies of 12 closed-shell and five open-shell molecules are computed to within 1 cm-1 of the basis set limit using the explicitly correlated CCSD(T)-R12 method. The convergence of the standard CCSD(T) method with the one-particle basis sets of Dunning and co-workers is examined and found to be slow, with mean and maximum absolute errors of 1.3 and 3.5 cm-1 remaining at the cc-pV6Z level. Finite basis set effects do not appear to introduce systematic errors in equilibrium harmonic frequencies, and mean absolute errors reduce by a factor of 2 for each basis set cardinal number increment. The convergence of individual equilibrium harmonic frequencies is not guaranteed to be monotonic due to the associated shift in the equilibrium structure. The inclusion of computed scalar relativistic effects and previously available corrections for core-valence correlation and higher-order excitations in the cluster operator results in an agreement with experimentally derived harmonic frequencies of 0.1, 0.3, and -0.4 cm-1 for HF, N2, and CO, respectively. F2 continues to present a challenge to computational chemistry with an error of 3.2 cm-1, primarily resulting from the high basis set dependence of the quadruples contribution.     

Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations

Stacking energies in low-energy geometries of pyrimidine, uracil, cytosine, and guanine homodimers were determined by the MP2 and CCSD(T) calculations utilizing a wide range of split-valence, correlation-consistent, and bond-functions basis sets. Complete basis set MP2 (CBS MP2) stacking energies extrapolated using aug-cc-pVXZ (X = D, T, and for pyrimidine dimer Q) basis sets equal to -5.3, -12.3, and -11.2 kcal/mol for the first three dimers, respectively. Higher-order correlation corrections estimated as the difference between MP2 and CCSD(T) stacking energies amount to 2.0, 0.7, and 0.9 kcal/mol and lead to final estimates of the genuine stacking energies for the three dimers of -3.4, -11.6, and -10.4 kcal/mol. The CBS MP2 stacking-energy estimate for guanine dimer (-14.8 kcal/mol) was based on the 6-31G(0.25) and aug-cc-pVDZ calculations. This simplified extrapolation can be routinely used with a meaningful accuracy around 1 kcal/mol for large aromatic stacking clusters. The final estimate of the guanine stacking energy after the CCSD(T) correction amounts to -12.9 kcal/mol. The MP2/6-31G(0.25) method previously used as the standard level to calculate aromatic stacking in hundreds of geometries of nucleobase dimers systematically underestimates the base stacking by ca. 1.0-2.5 kcal/mol per stacked dimer, covering 75-90% of the intermolecular correlation stabilization. We suggest that this correction is to be considered in calibration of force fields and other cheaper computational methods. The quality of the MP2/6-31G(0.25) predictions is nevertheless considerably better than suggested on the basis of monomer polarizability calculations. Fast and very accurate estimates of the MP2 aromatic stacking energies can be achieved using the RI-MP2 method. The CBS MP2 calculations and the CCSD(T) correction, when taken together, bring only marginal changes to the relative stability of H-bonded and stacked base pairs, with a slight shift of ca. 1 kcal/mol in favor of H-bonding. We suggest that the present values are very close to ultimate predictions of the strength of aromatic base stacking of DNA and RNA bases.     

The sensitivity of B3LYP atomization energies to the basis set and a comparison of basis set requirements for CCSD(T) and B3LYP

The atomization energies of the 55 G2 molecules are computed using the B3LYP approach with a variety of basis sets. The 6–311 + G(3df) basis set is found to yield superior results to those obtained using the augumented-correlation-consistent valence-polarized triple-zeta set. The atomization energy of SO₂ is found to be the most sensitive to basis set and is studied in detail. Including tight d functions is found to be important for obtaining good atomization energies. The results for SO₂ are compared with those obtained using the coupled-cluster singles and doubles approach including a perturbational estimate of the triple excitations.     

CCSD(T) study of CD3-O-CD3 and CH3-O-CD3 far-infrared spectra

From a vibrationally corrected 3D potential energy surface determined with highly correlated ab initio calculations (CCSD(T)), the lowest vibrational energies of two dimethyl-ether isotopologues, (12)CH(3)-(16)O-(12)CD(3) (DME-d(3)) and (12)CD(3)-(16)O-(12)CD(3) (DME-d(6)), are computed variationally. The levels that can be populated at very low temperatures correspond to the COC-bending and the two methyl torsional modes. Molecular symmetry groups are used for the classification of levels and torsional splittings. DME-d(6) belongs to the G(36) group, as the most abundant isotopologue (12)CH(3)-(16)O-(12)CH(3) (DME-h(6)), while DME-d(3) is a G(18) species. Previous assignments of experimental Raman and far-infrared spectra are discussed from an effective Hamiltonian obtained after refining the ab initio parameters. Because a good agreement between calculated and experimental transition frequencies is reached, new assignments are proposed for various combination bands corresponding to the two deuterated isotopologues and for the 020 → 030 transition of DME-d(6). Vibrationally corrected potential energy barriers, structural parameters, and anharmonic spectroscopic parameters are provided. For the 3N - 9 neglected vibrational modes, harmonic and anharmonic fundamental frequencies are obtained using second-order perturbation theory by means of CCSD and MP2 force fields. Fermi resonances between the COC-bending and the torsional modes modify DME-d(3) intensities and the band positions of the torsional overtones.     

Hydrogen-bonded nucleic acid base pairs containing unusual base tautomers: complete basis set calculations at the MP2 and CCSD(T) levels

The total interaction energies of altogether 15 hydrogen-bonded nucleic acid base pairs containing unusual base tautomers were calculated. The geometry properties of all selected adenine-thymine and guanine-cytosine hydrogen-bonded base pairs enable their incorporation into DNA. Unusual base pairing patterns were compared with Watson-Crick H-bonded structures of the adenine-thymine and guanine-cytosine pairs. The complete basis set (CBS) limit of the MP2 interaction energy and the CCSD(T) correction term, determined as the difference between the CCSD(T) and MP2 interaction energies, was evaluated. Extrapolation to the MP2 CBS limit was done using the aug-cc-pVDZ and aug-cc-pVTZ results, and the CCSD(T) correction term was determined with the 6-31G*(0.25) basis set. Final interaction energies were corrected while taking into account both tautomeric penalization determined at the CBS level and solvation/desolvation free energies. The situation for the adenine-thymine pairs is straightforward, and tautomeric pairs are significantly less stable than the Watson-Crick pair consisting of the canonical forms. In the case of the guanine-cytosine pair, the Watson-Crick structure made by canonical forms is again the most stable. The other two structures are, however, energetically rather similar (by 5 and 6 kcal/mol), which provides a very small but non-negligible chance of detecting these structures in the DNA double helix (1:5000). Due to the fact that DNA bases and base pairs incorporated into DNA are solvated less favorably than in isolated systems, this probability represents the very upper limit. The results clearly show how precisely the canonical building blocks of DNA molecules were chosen and how well their stability is maintained.     

Intrinsic conformational preferences of substituted cyclohexanes and tetrahydropyrans evaluated at the CCSD(T) complete basis set limit: implications for the anomeric effect

A series of MP2 and CCSD(T) computations have been carried out with correlation consistent basis sets as large as aug-cc-pV5Z to determine the intrinsic equatorial-axial conformational preference of CH(3)-, F-, OCH(3)-, and OH-substituted cyclohexane and tetrahydropyran rings. The high-accuracy relative electronic energies reported here shed new light on the intrinsic energetics of these cyclic prototypes for the anomeric effect. At the CCSD(T) complete basis set (CBS) limit, the energy of the equatorial conformation relative to the axial position (DeltaE (CBS)(CCSD(T))) is -1.75, -0.20, -0.21, and -0.56 kcal mol(-1) in methyl-, fluoro-, methoxy-, and hydroxycyclohexane, respectively, while DeltaE(CBS)(CCSD(T) is -2.83, +2.45, +1.27, and +0.86 kcal mol(-1) for 2-methyl-, 2-fluoro-, 2-methoxy-, and 2-hydroxytetrahydropyran, respectively. Note that the equatorial and axial conformers are nearly electronically isoenergetic in both fluoro- and methoxycyclohexane. For all eight cyclic species, a zero-point vibrational energy correction decreases Delta by a few tenths of a kilocalorie per mole. Relative energies obtained with popular methods and basis sets are unreliable, including Hartree-Fock theory, the B3LYP density functional, and the 6-31G and 6-311G families of split-valence basis sets. Even with the massive pentuple-zeta basis sets, the HF and B3LYP methods substantially overestimate the stability of the equatorial conformers (by as much as 0.99 and 0.73 kcal mol(-1), respectively, for 2-methoxytetrahydropyran). Only because of a consistent cancellation of errors do these popular approaches sometimes provide reasonable estimates of the anomeric effect.     

On geometries of stacked and H-bonded nucleic acid base pairs determined at various DFT, MP2, and CCSD(T) levels up to the CCSD(T)/complete basis set limit level

The geometries and interaction energies of stacked and hydrogen-bonded uracil dimers and a stacked adeninecdots, three dots, centeredthymine pair were studied by means of high-level quantum chemical calculations. Specifically, standard as well as counterpoise-corrected optimizations were performed at second-order Moller-Plesset (MP2) and coupled cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)] levels with various basis sets up to the complete basis set limit. The results can be summarized as follows: (i) standard geometry optimization with small basis set (e.g., 6-31G(*)) provides fairly reasonable intermolecular separation; (ii) geometry optimization with extended basis sets at the MP2 level underestimates the intermolecular distances compared to the reference CCSD(T) results, whereas the MP2/cc-pVTZ counterpoise-corrected optimization agrees well with the reference geometries and, therefore, is recommended as a next step for improving MP2/cc-pVTZ geometries; (iii) the stabilization energy of stacked nucleic acids base pairs depends considerably on the method used for geometry optimization, so the use of reliable geometries, such as counterpoise-corrected MP2/cc-pVTZ ones, is recommended; (iv) the density functional theory methods fail completely in locating the energy minima for stacked structures and when the geometries from MP2 calculations are used, the resulting stabilization energies are strongly underestimated; (v) the self-consistent charges-density functional tight binding method, with inclusion of the empirical dispersion energy, accurately reproduces interaction energies and geometries of dispersion-bonded (stacked) complexes; this method can thus be recommended for prescanning the potential energy surfaces of van der Waals complexes.     

Spectroscopic investigations on AsH(XΣ) radical using CCSD(T) theory in combination with correlation-consistent quintuple basis set

The equilibrium internuclear separations, harmonic frequencies and potential energy curves of the AsH(X³Σ⁻) radical have been calculated using the coupled-cluster singles–doubles–approximate-triples [CCSD(T)] theory in combination with the series of correlation-consistent basis sets in the valence range. The potential energy curves are all fitted to the Murrell–Sorbie function, which are used to reproduce the spectroscopic parameters such as D_e, ω_eχ_e, α_e, B_e and D₀. The present D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e obtained at the cc-pV5Z basis set are of 2.8004 eV, 2.9351 eV, 0.15137 nm, 2194.341 cm⁻¹, 43.1235 cm⁻¹, 0.2031 cm⁻¹ and 7.3980 cm⁻¹, respectively, which almost perfectly conform to the measurements. With the potential obtained at the UCCSD(T)/cc-pV5Z level of theory, a total of 18 vibrational states is predicted when the rotational quantum number J is set to equal zero (J = 0) by numerically solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0 for the first time, which are in excellent agreement with the experiments.     

On the physisorption of water on graphene: a CCSD(T) study

The electronic structure of the zero-gap two-dimensional graphene has a charge neutrality point exactly at the Fermi level that limits the practical application of this material. There are several ways to modify the Fermi-level-region of graphene, e.g. adsorption of graphene on different substrates or different molecules on its surface. In all cases the so-called dispersion or van der Waals interactions can play a crucial role in the mechanism, which describes the modification of electronic structure of graphene. The adsorption of water on graphene is not very accurately reproduced in the standard density functional theory (DFT) calculations and highly-accurate quantum-chemical treatments are required. A possibility to apply wavefunction-based methods to extended systems is the use of local correlation schemes. The adsorption energies obtained in the present work by means of CCSD(T) are much higher in magnitude than the values calculated with standard DFT functional although they agree that physisorption is observed. The obtained results are compared with the values available in the literature for binding of water on the graphene-like substrates.     

Convergence of triples energy in CCSD(T) and CC3 calculations with correlation-consistent basis sets

The convergence behavior of connected triples correlation energy in CCSD(T) and CC3 calculations with (aug-)cc-pVXZ basis sets has been accurately described in terms of a power law of the type E(X)=E(infinity)+AX(-4). Calculations ranging from double-Z through septuple-Z attest the validity of this X(-4) convergence model. Extrapolations generated from (X-1,X)-Z calculations yield energies of nearly (X+1)-Z quality. Typically, the fraction of triples correlation energy recovered is 0.92+/-0.05 in (D,T) extrapolations; 0.98+/-0.01 in (T,Q) extrapolations; 1.0002+/-0.0012 in (Q,5) extrapolations; and 0.9995+/-0.0005 in (5,6) extrapolations.     

Molecular orbitals and photoelectron spectra of some titanium(IV) organometallic compounds

The photoelectron spectra of some titanium(IV) organometallic compounds are reported, and the data and the bonding in the compounds are discussed with the aid of extended CNDO/2 calculations.     

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.     

Estimated MP2 and CCSD(T) interaction energies of n-alkane dimers at the basis set limit: comparison of the methods of Helgaker et al. and Feller

The MP2 (the second-order M?ller-Plesset calculation) and CCSD(T) (coupled cluster calculation with single and double substitutions with noniterative triple excitations) interaction energies of all-trans n-alkane dimers were calculated using Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation consistent basis sets. The estimated MP2 interaction energies of methane, ethane, and propane dimers at the basis set limit [EMP2(limit)] by the method of Helgaker et al. [J. Chem. Phys. 106, 9639 (1997)] from the MP2/aug-cc-pVXZ (X=D and T) level interaction energies are very close to those estimated from the MP2/aug-cc-pVXZ (X=T and Q) level interaction energies. The estimated EMP2(limit) values of n-butane to n-heptane dimers from the MP2/cc-pVXZ (X=D and T) level interaction energies are very close to those from the MP2/aug-cc-pVXZ (X=D and T) ones. The EMP2(limit) values estimated by Feller's [J. Chem. Phys. 96, 6104 (1992)] method from the MP2/cc-pVXZ (X=D, T, and Q) level interaction energies are close to those estimated by the method of Helgaker et al. from the MP2/cc-pVXZ (X=T and Q) ones. The estimated EMP2(limit) values by the method of Helgaker et al. using the aug-cc-pVXZ (X=D and T) are close to these values. The estimated EMP2(limit) of the methane, ethane, propane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, n-nonane, and n-decane dimers by the method of Helgaker et al. are -0.48, -1.35, -2.08, -2.97, -3.92, -4.91, -5.96, -6.68, -7.75, and -8.75 kcal/mol, respectively. Effects of electron correlation beyond MP2 are not large. The estimated CCSD(T) interaction energies of the methane, ethane, propane, and n-butane dimers at the basis set limit by the method of Helgaker et al. (-0.41, -1.22, -1.87, and -2.74 kcal/mol, respectively) from the CCSD(T)/cc-pVXZ (X=D and T) level interaction energies are close to the EMP2(limit) obtained using the same basis sets. The estimated EMP2(limit) values of the ten dimers were fitted to the form m0+m1X (X is 1 for methane, 2 for ethane, etc.). The obtained m0 and m1 (0.595 and -0.926 kcal/mol) show that the interactions between long n-alkane chains are significant. Analysis of basis set effects shows that cc-pVXZ (X=T, Q, or 5), aug-cc-pVXZ (X=D, T, Q, or 5) basis set, or 6-311G** basis set augmented with diffuse polarization function is necessary for quantitative evaluation of the interaction energies between n-alkane chains.     

Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs

MP2 and CCSD(T) complete basis set (CBS) limit interaction energies and geometries for more than 100 DNA base pairs, amino acid pairs and model complexes are for the first time presented together. Extrapolation to the CBS limit is done by using two-point extrapolation methods and different basis sets (aug-cc-pVDZ - aug-cc-pVTZ, aug-cc-pVTZ - aug-cc-pVQZ, cc-pVTZ - cc-pVQZ) are utilized. The CCSD(T) correction term, determined as a difference between CCSD(T) and MP2 interaction energies, is evaluated with smaller basis sets (6-31G** and cc-pVDZ). Two sets of complex geometries were used, optimized or experimental ones. The JSCH-2005 benchmark set, which is now available to the chemical community, can be used for testing lower-level computational methods. For the first screening the smaller training set (S22) containing 22 model complexes can be recommended. In this case larger basis sets were used for extrapolation to the CBS limit and also CCSD(T) and counterpoise-corrected MP2 optimized geometries were sometimes adopted.     

Improving upon CCSD(T): LambdaCCSD(T). II. Stationary formulation and derivatives

Analytical derivatives are formulated and implemented for the LambdaCCSD(T) method. As the historically first size-extensive and orbitally invariant extension of coupled-cluster (CC) theory to exploit the left-hand ground state eigenvector, it offers a vastly better treatment of bond breaking than does CCSD(T), and points the way toward further generalizations of single-reference CC theory that enhance its accuracy away from equilibrium geometries. Application to diatomic force curves and transition states of several well-characterized reactions are made. Surprisingly, despite LambdaCCSD(T) describing bond breaking much better than CCSD(T), for transition states both methods are extremely close in both structures and activation barriers. Force curves, however, demonstrate the overall superiority of LambdaCCSD(T).     

Molecular structure and vibrational spectra of 2,6-bis(benzylidene)cyclohexanone: a density functional theoretical study

The near-infrared Fourier transform (NIR-FT) Raman and Fourier transform infrared (FT-IR) spectral analyses of 2,6-bis(benzylidene)cyclohexanone (BBC) molecule, a potential drugs for the treatment of P388 leukemia cells, were carried out along with density functional computations. The optimized geometry of BBC using density functional theory shows that the energetically favored chair conformation is not observed for central cyclohexanone ring and is found to possess a nearly ‘half chair’ conformation and shows less expansion of the angles and more rotation about the bonds. The existence of intramolecular C–H?O improper, blue-shifted hydrogen bond was investigated by means of the NBO analysis. The lowering of carbonyl stretching vibration can be attributed to the mesomeric effect and the π-orbital conjugation induced by the unsaturation in the α-carbon atoms and co-planarity of the (–CHC–(CO)–CCH–) group.     

Infrared absorption spectra of matrix-isolated cis, cis-HOONO and its ab initio CCSD(T) anharmonic vibrational bands

The infrared absorption spectra of matrix-isolated cis, cis-peroxynitrous acid (HOONO and DOONO) in argon have been observed. Six of the nine fundamental vibrational modes for cis, cis-HOONO have been assigned definitively, and one tentatively. Coupled-cluster, ab initio anharmonic force field calculations were used to help guide some of the assignments. The experimental matrix frequencies (cm(-1)) for cis, cis-HOONO are (a' modes) nu1 = 3303+/-1, nu2 = 1600.6+/-0.6, nu3 = 1392+/-1, nu4 = 922.8+/-0.5, nu5 = 789.7+/-0.4, nu6 = 617+/-1; and (a" mode) nu8 = 462+/-1. The fundamentals for the deuterated isotopomer, cis, cis-DOONO, are (a' modes) nu1 = 2447.2+/-0.6, nu2 = 1595.7+/-0.7, nu3 = 1089.1+/-0.4, nu4 = 888.1+/-0.4, nu5 = 786.6+/-0.5, nu6 = 613.9+/-0.9; and (a" mode) nu8 = 456.5+/-0.5.