Prediction of vibrational frequencies of UO2(2+) at the CCSD(T) level

Electronic structure calculations at the coupled cluster (CCSD(T)) and density functional theory levels with relativistic effective core potentials and large basis sets were used to predict the isolated uranyl ion frequencies. The effects of anharmonicity and spin-orbit corrections on the harmonic frequencies were calculated. The anharmonic effects are larger than the spin-orbit corrections, but both are small. The anharmonic effects decreased all the frequencies, whereas the spin-orbit corrections increased the stretches and decreased the bend. Overall, these two corrections decreased the harmonic asymmetric stretch frequency by 6 cm-1, the symmetric stretch by 3 cm-1, and the bend by 3 cm-1. The best calculated values for UO22+ for the asymmetric stretch, symmetric stretch, and bend were 1113, 1032, and 174 cm-1, respectively. The separation between the asymmetric and the symmetric stretch band origins was predicted to be 81 cm-1, which is consistent with experimental trends for substituted uranyls in solution and in the solid state. The anharmonic vibrational frequencies of the isoelectronic ThO2 molecule also were calculated and compared to experiment to calibrate the UO22+ results.     

From CCSD(T)/aug-cc-pVTZ-J to CCSD(T) complete basis set limit isotropic nuclear magnetic shieldings via affordable DFT/CBS calculations

It is shown that a linear correlation exists between nuclear shielding constants for nine small inorganic and organic molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6) and C(6)H(6)) calculated with 47 methods (42 DFT methods, RHF, MP2, SOPPA, SOPPA(CCSD), CCSD(T)) and the aug-cc-pVTZ-J basis set and corresponding complete basis set results, estimated from calculations with the family of polarization-consistent pcS-n basis sets. This implies that the remaining basis set error of the aug-cc-pVTZ-J basis set is very similar in DFT and CCSD(T) calculations. As the aug-cc-pVTZ-J basis set is significantly smaller, CCSD(T)/aug-cc-pVTZ-J calculations allow in combination with affordable DFT/pcS-n complete basis set calculations the prediction of nuclear shieldings at the CCSD(T) level of nearly similar accuracy as those, obtained by fitting results obtained from computationally demanding pcS-n calculations at the CCSD(T) limit. A significant saving of computational efforts can thus be achieved by scaling inexpensive CCSD(T)/aug-cc-pVTZ-J calculations of nuclear isotropic shieldings with affordable DFT complete basis set limit corrections.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Basis set and correlation energy dependence of geometry and harmonic frequencies of difluoroethane,CHF2CH3

Optimum geometries and harmonic frequencies calculated at the Hartree–Fock and the MP2 level are reported for the fluorohydrocarbon CHF₂CH₃; basis sets employed range from STO-3G to 6-311G**. The significantly shortened C? C distance of 1.50 Å is reproduced already with the simplest split-valence basis set; the C? F distance of 1.36 Å on the other hand needs MP2 correction at least at the double-ζ or 6-311G* level. Symmetry coordinates defined in terms of internal coordinates are in qualitative agreement with available experimental evidence. Even the best basis set yields frequencies that differ from experimental (anharmonic) values by up to 200 cm^?1 indicating the well-known necessity of including higher-order force constants if quantitative agreement with experiment is to be achieved.     

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.     

Impact of local and density fitting approximations on harmonic vibrational frequencies

Harmonic vibrational frequencies are computed using second-order M?ller-Plesset perturbation theory (MP2) with and without local (LMP2) and density fitting (DF) approximations. Results for a test set of 17 small and medium size molecules (366 normal modes) are presented, and frequency scaling factors for LMP2 in combination with two different basis sets are determined. Comparison of the MP2 and LMP2 frequencies with experimental data reveals that the introduction of local approximations leads to a slightly better agreement with experiment. This is attributed to the reduction of basis set superposition errors in local calculations. Introduction of DF approximations within the LMP2 formalism leads to negligible deviations but significantly reduces the computational cost. These facts extend the applicability of the method to larger systems with large basis sets. As an example, the method is applied to a full DF-LMP2/cc-pVTZ frequency calculation for testosterone (49 atoms).     

Molecular structure and spectra of titanium and vanadium trifluorides: Complete basis set CCSD(T) study

Quantum chemical study on TiF₃ and VF₃ molecules was carried out using the CCSD(T) coupled cluster method using the triple-, quadruple-, and quintuple-zeta basis set and an extrapolation to the complete basis set limit. The methods of multireference configuration interaction MRCISD+Q and perturbation theory MCQDPT2 were used also. The symmetry of the ground electronic state was determined: ² A′₁ and ³ E″ in TiF₃ and VF₃, respectively. The adiabatic excitation energies were evaluated: AEE(TiF₃, $\tilde A^2 E'' \leftarrow \tilde X^2 A'_1 $ ) = 5000 cm^?1, AEE(VF₃, $\tilde A^3 A'_2 \leftarrow \tilde X^3 E''$ ) = 1000 cm^?1. The Jahn-Teller effect in $\tilde A^2 E''$ state of TiF₃ and $\tilde X^3 E''$ state of VF₃ was investigated. The computed Jahn-Teller stabilization energy D _3h → C _2v amounts to 555 and 292 cm^?1, respectively. The spin-orbit coupling effect on the VF₃ molecular structure and spectrum of electronic states is shown to be quite significant. The calculated vibrational frequencies of TiF₃ are in excellent agreement with IR spectroscopy data. The atomization enthalpies were evaluated: Δ_at H ₂₉₈ ^pO = 430 kcal/mol (TiF₃), 393 kcal/mol (VF₃).     

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.     

CCSD(T) expectation value calculations of first-order properties

An expectation value approach to calculations of first-order properties using the non-iterative, triple-excitation amplitudes in the coupled cluster wave function is exploited. Three methods are suggested and analysed using the many body perturbation theory (MBPT) expansion arguments. The first method, in which non-iterative triple-excitation amplitudes are used in the expression for the expectation values, makes the wave function accurate through the second order of MBPT. In the second method, which is an extension of the first, effects of triple-excitation amplitudes are coupled with single- and double-excitation amplitudes. The correlated density matrix equivalent through the fourth order to that obtained when CCSDT-la amplitudes are used is employed in the third method. The suggested methods are tested on dipole moment and polarizability calculations for several diatomic closed-shell molecules and are compared to other related approaches. Received: 15 May 1997 / Accepted: 5 June 1997     

基于图形处理单元与密度拟合近似的单精度耦合簇CCSD和CCSD(T)程序

作者此前工作表明, 在耦合簇CCSD (Coupled-Cluster approaches within the singles and doubles approximation)与CCSD(T) (CCSD approaches augmented by a perturbative treatment of triple excitations)计算中结合单精度数与消费型图形处理单元(GPU), 可以显著提高计算速度. 然而由于CCSD(T)计算对内存的巨大需求以及消费型GPU的内存限制, 在利用消费型GPU进行加速时, 不考虑利用空间对称性的情况下, 此前开发的CCSD(T)程序仅能用于计算300~400个基函数的体系. 利用密度拟合(Density-Fitting, DF)处理双电子积分可以显著降低CCSD(T)计算过程中的内存需求, 本工作发展了基于密度拟合近似并结合单精度数进行运算的DF-CCSD(T)程序, 该程序可用于包含700个基函数的无对称性体系的单点能计算, 以及包含1700个基函数的有对称性体系. 本工作所使用的计算节点配置了型号为Intel I9-10900k的CPU和型号为RTX3090的GPU, 与用双精度数在CPU上的计算相比, 利用单精度数结合GPU进行运算可以将CCSD的计算速度提升16倍, (T)部分可提升40倍左右, 而使用单精度数引入的误差可忽略不计. 在程序开发过程中, 作者发展了一套可利用GPU或CPU结合单精度数或双精度数进行含空间对称性的矩阵操作代码库. 基于该套代码库, 可以显著降低开发含空间对称性的耦合簇代码的难度.     

New scale factors for harmonic vibrational frequencies using the B3LYP density functional method with the triple-zeta basis set 6-311+G(d,p)

We have calculated optimal frequency scaling factors for the B3LYP/ 6-311+G(d,p) method for fundamental vibrational frequencies on the basis of a set of 125 molecules. Using the new scaling factor, the vibrational frequencies calculated with the triple-zeta basis set 6-311+G(d,p) give significantly better accuracy than those calculated with the double-zeta 6-31G(d) basis set. Scale factors were also determined for low-frequency vibrations using the molecular set of 125 molecules and for zero-point energies using a smaller set of 40 molecules. We have studied the effect on the calculated vibrational frequencies for various combinations of diffuse and polarization functions added to the triple-zeta 6-311G basis set. The 6-311+G(d,p) basis set is found to give almost converged frequencies for most molecules, and we conclude that our optimum scaling factors are valid for the basis sets 6-311G(d,p) to 6-311++G(3df,3pd). The new scale factors are 0.9679 for vibrational frequencies, 1.0100 for low-frequency vibrations, and 0.9877 for zero-point vibrational energies.     

Basis set dependence of phosphate frequencies in density functional theory calculations

The addition of extravalence, polarization and diffuse functions, were studied in order to conclude how they affect the P? O stretching frequencies of several biological relevant phosphate molecules. The results show that the polarization and the diffuse functions have opposite effects on the frequencies: the polarization functions downshift while the diffuse functions upshift the frequencies. The effect of the valence functions was more difficult to interpret. The effect of the conductor‐like screening model (CPCM)‐continuum model was also studied. The results show that the CPCM‐continuum model has a substantial effect on the frequencies for these small molecules. The continuum model's efficiency is mainly due to its effect on the geometries and not on the frequencies. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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.     

A simple and efficient CCSD(T)-F12 approximation

A new explicitly correlated CCSD(T)-F12 approximation is presented and tested for 23 molecules and 15 chemical reactions. The F12 correction strongly improves the basis set convergence of correlation and reaction energies. Errors of the Hartree-Fock contributions are effectively removed by including MP2 single excitations into the auxiliary basis set. Using aug-cc-pVTZ basis sets the CCSD(T)-F12 calculations are more accurate and two orders of magnitude faster than standard CCSD(T)/aug-cc-pV5Z calculations.     

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).     

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 influence of the basis set superposition error on calculated vibrational frequencies

The relation between the so called basis set superposition error and intramolecular vibrational frequencies calculated at the Hartree Fock SCF level of approximation was investigated. A linear conformation of HF dimer was chosen as test system for the investigation. It was found that the direct basis set superposition error for the studied system is rather small. It was further found that the shifts are mainly determined by the geometry parameters of the system. AcknowledgementsJ. M. H.-R. wishes to thank the Ministerio de Educación, Cultura y Deporte for the award of a research grant.