Effects on spectroscopic parameters of several low-lying electronic states of GeS by core-valence correlation and relativistic corrections

The potential energy curves (PECs) of six low-lying electronic states (X¹Σ⁺, a³Σ⁺, b³Π, A¹Π, 1³Σ⁻ and 1⁵Σ⁺) of GeS molecule have been investigated employing the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach with large correlation-consistent basis sets for internuclear separations from 0.08 to 2.00 nm. The effects on the spectroscopic parameters by the core-valence correlation, relativistic and nonadiabatic corrections have been discussed in detail. The core-valence correlation correction is carried out at the aug-cc-pCVTZ basis set. The nonadiabatic correction is performed at the aug-cc-pVTZ basis set. And the relativistic correction is made at the level of cc-pV5Z basis set. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian (DKH2) approximation. To obtain more reliable PECs, the Davidson modification is also included in the present study. To reduce the incomplete basis set error, the PECs of these electronic states are extrapolated to the complete basis set (CBS) limit. With these PECs, the spectroscopic parameters of these low-lying electronic states are determined. On the one hand, analyses demonstrate that the effects on the spectroscopic parameters by the core-valence correlation correction, relativistic correction and Davidson modification are very obvious, whereas the effect on the spectroscopic parameters by the nonadiabatic correction is very small. On the other hand, comparison with the RKR data shows that the two-point total-energy extrapolation could improve the quality of spectroscopic parameters. On the whole, as expected, the most accurate spectroscopic parameters of GeS molecule are determined by the MRCI+Q/CV+DK+Q5 calculations.     

Coupled cluster investigation on the thermochemistry of dimethyl sulphide,dimethyl disulphide and their dissociation products: the problem of the enthalpy of formation of atomic sulphur

By means of coupled cluster theory and correlation consistent basis sets we investigated the thermochemistry of dimethyl sulphide (DMS), dimethyl disulphide (DMDS) and four closely related sulphur-containing molecules: CH₃SS, CH₃S, CH₃SH and CH₃CH₂SH. For the four closed-shell molecules studied, their enthalpies of formation (EOFs) were derived using bomb calorimetry. We found that the deviation of the EOF with respect to experiment was 0.96, 0.65, 1.24 and 1.29 kcal/mol, for CH₃SH, CH₃CH₂SH, DMS and DMDS, respectively, when ΔH_f,0 = 65.6 kcal/mol was utilised (JANAF value). However, if the recently proposed ΔH_f,0 = 66.2 kcal/mol was used to estimate EOF, the errors dropped to 0.36, 0.05, 0.64 and 0.09 kcal/mol, respectively. In contrast, for the CH₃SS radical, a better agreement with experiment was obtained if the 65.6 kcal/mol value was used. To compare with experiment avoiding the problem of the ΔH_f,0 (S), we determined the CH₃–S and CH₃–SS bond dissociation energies (BDEs) in CH₃S and CH₃SS. At the coupled cluster with singles doubles and perturbative triples correction level of theory, these values are 48.0 and 71.4 kcal/mol, respectively. The latter BDEs are 1.5 and 1.2 kcal/mol larger than the experimental values. The agreement can be considered to be acceptable if we take into consideration that these two radicals present important challenges when determining their EOFs. It is our hope that this work stimulates new studies which help elucidate the problem of the EOF of atomic sulphur.     

On one-electron basis set extrapolation of atomic and molecular correlation energies

It is well known that the convergence of correlation energies in atomic and molecular calculations is relatively slow and that calculations aimed at high accuracy must explicitly make corrections for this. In this work we consider 1e ^? basis set extrapolation as a means of obtaining high accuracy. The correlation consistent basis sets of Dunning et al. have provided a convenient platform for extrapolation, with the independent variable being X?=?D,?T,?Q,?5,?…?. There has been much debate in the literature about the functional form to use for the extrapolation, with contention between the ‘theoretically justified’ (X?+?1)^?3 form and empirical forms based on exponentials or variable powers. We will dissect the theoretical justification of the (X?+?1)^?3 form by considering MP2 calculations on He and Ne as a function of the maximum angular momentum (?) in the basis using basis sets having converged radial extent. Calculations with ? up to 14 were carried out for Ne. It is shown that while the asymptotic form of (??+?1)^?3 is clearly reached, higher order terms are very important in the range of ? normally used in molecular calculations. We also use similar analysis techniques for an open shell atom and a small molecule. The functional form for the dependence of molecular properties with ? is complex and it is safer to extrapolate fitting parameters than energies.     

Accurate equilibrium inversion barrier of ammonia by extrapolation to the one-electron basis set limit

A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite one-electron basis-set limit. The dual-level method is tested on the extrapolation of the full correlation in coupled-cluster singles and doubles and in the case also a noniterative perturbative correction for connected triple energies for the C3v and D3h structures of ammonia, with correlation-consistent basis sets of the type cc-pVXZ （X = D, T, Q, 5, 6） and aug-cc-pVXZ （X = D, T, Q, 5）. For testing and comparison purposes, the energies reported by Klopper [J. Comput. Chem. 22 1306 （2001）] have been taken. From a corresponding extrapolation of CCSD（T）/AVXZ energies for X = 4, 5, we obtain total inversion barriers of 1833.87 cm-1/1832.33 cm^-1 for the two/three-parameter extrapolation rules, which are in good agreement with other theoretical extrapolation and empirical values in the literature.     

Theoretical characterization of the HSOH,H2SO and H2OS isomers

The HSOH, H₂SO and H₂OS isomers have been investigated employing the CCSD(T) methodology and the cc-pV(X + d)Z X = 3,4,5,6 basis sets. The anharmonic force fields have been calculated to predict the fundamental vibrational frequencies, rotational constants, vibration–rotation corrections, anharmonic corrections to zero-point energies, and structural parameters. In addition to this, a spectroscopic characterization of the deuterated isomers D₂SO and D₂OS was performed. At the CCSD(T)/CBS limit and including corrections for scalar relativistic, spin orbit and core-valence correlation effects, the estimated enthalpies of formation are ?28.1 ± 1, ?12.3 ± 1, and 10.1 ± 1 kcal/mol for HSOH, H₂SO and H₂OS, respectively. Finally, we discuss the problems faced during the extrapolation to the CBS limit of the properties investigated.     

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

ABSTRACT

The 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.     

Enthalpy difference between conformations of normal alkanes: effects of basis set and chain length on intramolecular basis set superposition error

The quantum chemistry of conformation equilibrium is a field where great accuracy (better than 100?cal?mol^?1) is needed because the energy difference between molecular conformers rarely exceeds 1000–3000?cal?mol^?1. The conformation equilibrium of straight-chain (normal) alkanes is of particular interest and importance for modern chemistry. In this paper, an extra error source for high-quality ab initio (first principles) and DFT calculations of the conformation equilibrium of normal alkanes, namely the intramolecular basis set superposition error (BSSE), is discussed. In contrast to out-of-plane vibrations in benzene molecules, diffuse functions on carbon and hydrogen atoms were found to greatly reduce the relative BSSE of n-alkanes. The corrections due to the intramolecular BSSE were found to be almost identical for the MP2, MP4, and CCSD(T) levels of theory. Their cancelation is expected when CCSD(T)/CBS (CBS, complete basis set) energies are evaluated by addition schemes. For larger normal alkanes (N?>?12), the magnitude of the BSSE correction was found to be up to three times larger than the relative stability of the conformer; in this case, the basis set superposition error led to a two orders of magnitude difference in conformer abundance. No error cancelation due to the basis set superposition was found. A comparison with amino acid, peptide, and protein data was provided.     

Gaussian basis set of triple zeta valence quality for the atoms from K to Kr: Application in DFT and CCSD(T) calculations of molecular properties

A contracted basis set of triple zeta (TZ) valence quality for the atoms from K to Kr was constructed from fully-optimized Gaussian basis sets generated in this work. Gaussian polarization functions (d, f, and g symmetries), which were optimized at the second-order Mφller–Plesset level, were added to the TZ set. This extends earlier work on segmented contracted TZ basis set for atoms H-Ar. This set along with the BP86 non-hybrid and B3LYP hybrid functionals were used to calculate geometric parameters, dissociation energy, harmonic vibrational frequency, and electric dipole moment of a sample of molecules and, then, comparison with results obtained with other basis sets and with experimental data reported in the literature is done. CCSD(T) atomic excitation energies and bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatomics were also evaluated. Using density functional theory and gauge-including atomic orbitals, ⁵⁷Fe and ⁷⁷Se nuclear magnetic resonance chemical shifts in Fe(C₅H₅)₂, H₂Se, (CH₃)SeH, CSe₂, SeCO, H₂CSe, and SeF₆ were calculated. Comparison with theoretical and experimental values previously published in the literature was done. It is verified that in general these results give good agreement with experimental and benchmark values.     

The heats of formation of the haloacetylenes XCCY [X,Y = H,F, Cl]: basis set limit ab initio results and thermochemical analysis

The heats of formation of haloacetylenes are evaluated using the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects. and (where relevant) first-order spin-orbit coupling. The heats of formation determined using W2 theory are: δH₁ ²⁹⁸(HCCH) = 54.48 kcal mol^?1, δH_f ²⁹⁸(HCCH) = 25.15 kcal mol, δH_f ²⁹⁸(FCCF) = 1.38 kcal mol^?1, δH_f ²⁹⁸(HCCC1) = 54.83 kcal mol^?1, δH_f ²⁹⁸(CICCC1) = 56.21 kcal mol^?1, and δH_f ²⁹⁸(FCCC1) = 28.47 kcal mo1^?1. Enthalpies of hydrogenation and destabilization energies relative to acetylene were obtained at the WI level of theory. So doing we find the following destabilization order for acetylenes: FCCF > ClCCF > HCCF > ClCCCl > HCCCI > HCCH. By a combination of WI theory and isodesmic reactions. we show that the generally accepted heat of formation of 1,2-dichloroethane should be revised to ?31.8 ± 0.6 kcal mol^?1, in excellent agreement with a very recent critically evaluated review. The performance of compound thermochemistry schemes, such as G2, G3, G3X and CBS-QB3 theories, has been analysed.     

Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions

ABSTRACT

With the aim of systematically comparing two popular approaches to density functional theory – all-electron calculations with local basis sets, and periodic calculations employing plane wave basis sets and norm-conserving pseudopotentials – we have computed complete-basis binding energies across the S22 set of intermolecular interactions, a dataset consisting of noncovalent interactions of small- and medium-sized molecules containing first- and second-row atoms, using the Troullier-Martins norm-conserving pseudopotentials with SPW92, a local spin-density approximation; and PBE, a generalised gradient approximation. We have found that it is challenging to reach the basis set limit with these periodic calculations; for the methods and systems examined, a minimum vacuum distance of 30?Å between a system and its nearest images is necessary – unless some form of dipole correction is employed – as is a kinetic energy cutoff of at least 80 Ry. The trends in convergence with respect to vacuum size and kinetic energy cutoff are largely independent of the level of density functional approximation employed. A sense of the impact of each hyperparameter on basis set error provides a foundation for ensuring quality calculations in future studies and allows us to quantify the basis set errors incurred in existing studies on similar systems.     

The keto-enol equilibrium in substituted acetaldehydes: focal-point analysis and ab initio limit

High-level ab initio electronic structure calculations up to the CCSD(T) theory level, including extrapolations to the complete basis set (CBS) limit, resulted in high precision energetics of the tautomeric equilibrium in 2-substituted acetaldehydes (XH₂C-CHO). The CCSD(T)/CBS relative energies of the tautomers were estimated using CCSD(T)/aug-cc-pVTZ, MP3/aug-cc-pVQZ, and MP2/aug-cc-pV5Z calculations with MP2/aug-cc-pVTZ geometries. The relative enol (XHC?=?CHOH) stabilities (ΔE _{e,CCSD(T)/CBS}) were found to be 5.98?±?0.17, ?1.67?±?0.82, 7.64?±?0.21, 8.39?±?0.31, 2.82?±?0.52, 10.27?±?0.39, 9.12?±?0.18, 5.47?±?0.53, 7.50?±?0.43, 10.12?±?0.51, 8.49?±?0.33, and 6.19?±?0.18?kcal?mol^?1 for X?=?BeH, BH₂, CH₃, Cl, CN, F, H, NC, NH₂, OCH₃, OH, and SH, respectively. Inconsistencies between the results of complex/composite energy computations methods Gn/CBS (G2, G3, CBS-4M, and CBS-QB3) and high-level ab initio methods (CCSD(T)/CBS and MP2/CBS) were found. DFT/aug-cc-pVTZ results with B3LYP, PBE0 (PBE1PBE), TPSS, and BMK density functionals were close to the CCSD(T)/CBS levels (MAD?=?1.04?kcal?mol^?1).     

Uniform upper bounds (and thermodynamic limit) for the correlation functions of symmetric coulomb-type systems

Uniform upper bounds are proven for the correlation functions in the strictly charge-neutral canonical and grand canonical ensembles for charge-symmetric two-component systems. For the grand canonical ensemble the increase of the correlation functions along the thermodynamic-limit sequence is shown as well, implying the existence of the states. The particles have bounded pair interactions of positive type. Both classical and quantum systems with Boltzmann statistics are considered. Coulomb systems with regularized interactions are included as a special case.     

Small and efficient basis sets for the evaluation of accurate interaction-induced linear and non-linear electric properties in model hydrogen-bonded complexes

Interaction-induced electric dipole moment, polarisability and first hyperpolarisability are investigated in model hydrogen-bonded clusters built of hydrogen fluoride molecules organised in three linear chains parallel to each other. The properties are evaluated within the finite field approach, using the second order Møller–Plesset method, and the LPol-m (m = ds, dl) and the optical rotation prediction (ORP) basis sets. These bases and correlation method are selected after a systematic basis set and correlation method convergence study carried out on the smallest of the complexes and taking properties obtained with Dunning's bases and the coupled cluster singles and doubles (CCSD) and the CCSD including connected triple corrections (CCSD(T)) methods as reference. Results are analysed in terms of many-body and cooperative effects.     

Gaussian basis set of double zeta quality for atoms Rb through Xe: application in non-relativistic and relativistic calculations of atomic and molecular properties

The all-electron contracted Gaussian basis set of double zeta valence quality plus polarization functions (DZP) for the atoms from Rb to Xe is presented. The Douglas–Kroll–Hess (DKH) basis set for fourth-row elements is also reported. The original DZP basis set has been recontracted, i.e. the values of the contraction coefficients were re-optimized using the relativistic DKH Hamiltonian. This extends earlier works on segmented contracted DZ basis set for atoms H-Kr. These sets along with ab initio methods were used to calculate ionization energies of some atoms and spectroscopic constants of a sample of molecules and, then, comparison with results obtained with other basis sets was made. It was shown that experimental and benchmark bond lengths and harmonic vibrational frequencies can be reproduced satisfactorily with DZP-DKZ.     

Analyticity properties and a convergent expansion for the inverse correlation length of the low-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(z) of the truncated spin-spin correlation function of theZ ^d Ising model with + or — boundary conditions admits the representationm(z) = –(4d–4)ln z(1–_d1) + r(z) for smallz=e ^–, i.e., large inverse temperatures is ad-dependent analytic function atz = 0, already known in closed form ford = 1 and 2; ford = 3 b_n can be computed explicitly from a finite number of the Z^d limits of z = 0 Taylor series coefficients of the finite lattice correlation function at a finite number of points ofZ ^d.     

On the use of the resting potential and level set methods for identifying ischemic heart disease: An inverse problem

The electrical activity in the heart is modeled by a complex, nonlinear, fully coupled system of differential equations. Several scientists have studied how this model, referred to as the bidomain model, can be modified to incorporate the effect of heart infarctions on simulated ECG (electrocardiogram) recordings.We are concerned with the associated inverse problem; how can we use ECG recordings and mathematical models to identify the position, size and shape of heart infarctions? Due to the extreme CPU efforts needed to solve the bidomain equations, this model, in its full complexity, is not well-suited for this kind of problems. In this paper we show how biological knowledge about the resting potential in the heart and level set techniques can be combined to derive a suitable stationary model, expressed in terms of an elliptic PDE, for such applications. This approach leads to a nonlinear ill-posed minimization problem, which we propose to regularize and solve with a simple iterative scheme.Finally, our theoretical findings are illuminated through a series of computer simulations for an experimental setup involving a realistic heart in torso geometry. More specifically, experiments with synthetic ECG recordings, produced by solving the bidomain model, indicate that our method manages to identify the physical characteristics of the ischemic region(s) in the heart. Furthermore, the ill-posed nature of this inverse problem is explored, i.e. several quantitative issues of our scheme are explored.