Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.     

A state-specific multi-reference coupled-cluster approach with a cost-effective treatment of connected triples: implementation to geometry optimisation

Recently, we have suggested an approximate state-specific multi-reference coupled-cluster (SS-MRCC) singles, doubles and triples method based on the CCSDT-1a+d approximation applied to the single-reference CC approach, in which the contribution of the connected triple excitations is iteratively treated. The method, abbreviated as SS-MRCCSDT-1a+d is intruder-free and fully size-extensive. It has been employed for geometry optimisations of various systems possessing quasi-degeneracy of varying degrees (like N₂H₂ and O₃) by invoking numerical gradient scheme. The method is also applied to CH₂ and square cyclobutadiene in their excited states. For all systems under study, the computed values are in good accordance with state-of-the-art theoretical estimates indicating that the method might be a promising candidate for an accurate treatment of geometrical parameters of states plagued by electronic degeneracy in a computationally tractable manner.     

Optical absorption in boron clusters B6 and B 6 + : a first principles configuration interaction singles approach

The linear optical absorption spectra in neutral boron cluster B₆ and cationic B₆ ⁺ are calculated using a first principles correlated electron approach. The geometries of several low-lying isomers of these clusters were optimized at the coupled-cluster singles doubles (CCSD) level of theory. With these optimized ground-state geometries, excited states of different isomers were computed using the configuration-interaction singles (CIS) approach. The many-body wavefunctions of various excited states have been analyzed and the nature of optical excitation involved are found to be of collective, plasmonic type. We also benchmark our CIS results against more sophisticated equation-of-motion (EOM) CCSD approach for a few isomers.     

Many-body effects in hyperfine interactions in <Superscript>205</Superscript>Pb<Superscript>+</Superscript>

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of ²⁰⁵Pb⁺. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier.     

Analysis of the Photoelectron Spectra of Selenium Difluoride and Selenium Dichloride Based on Franck-Condon Factors

The vibrational structure of the photoelectron spectra of selenium difluoride and selenium dichloride have been simulated using the computed Franck-Condon factors in the harmonic oscillator approximation. Spectral simulations have been carried out employing the coupled-cluster singles, doubles, and triples (CCSD(T)) and the Becke three-parameter Lee, Yang, and Parr (B3LYP) values for the ground electronic states of the neutral molecules and the cations selenium difluoride and selenium dichloride, respectively. The Duschinsky rotations among the normal modes of two ground electronic states of species involved in the transition are fully taken into account. The ionization energies obtained for selenium difluoride and selenium dichloride are in reasonable agreement with the experimentally determined values. The spectral simulations of vibrational structures including frequency changes and Duschinsky rotation upon the electronic excitation are in agreement with the experimental results.     

A new four-dimensional ab initio potential energy surface and predicted infrared spectra for the Ne–CS2 complex

A new four-dimensional (4D) ab initio potential energy surface (PES) for Ne–CS₂ involving the Q₁ and Q₃ normal modes for the ν₁ symmetric stretching vibration and ν₃ antisymmetric stretching vibration of CS₂ is presented. The PES is constructed at the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)]-F12 level with a large basis set including midpoint bond functions. Two vibrationally averaged potentials with CS₂ at the vibrational ground and ν₁ + ν₃ excited states are generated from the 4D potential. Each potential contains a T-shaped global minimum and two equivalent linear local minima. The rovibrational energy levels and bound states are calculated employing radial discrete variable representation/angular finite basis representation and the Lanczos algorithm. In addition, the predicted band origin shift is 0.2514 cm^?1 for Ne–CS₂. The spectroscopic parameters are also predicted.     

A theoretical study of transition metal hydroxides: CuOH,AgOH and AuOH

Calculations have been performed on the transition metal hydroxides CuOH, AgOH, and AuOH using SCF and the coupled-cluster with singles, doubles, and perturbative triples (CCSD(T)) methods. The relativistic effect was included in the third-order Douglas—Kroll approximation. Equilibrium geometries, dissociation energies, vibrational frequencies, and dipole moments are reported for the ground state of each species. The relativistic stability of the valence s orbital weakens the ionic character and strengthens the covalent character of the metal—OH bond. For CuOH and AgOH the calculated results show good agreement with available experiment. The anomalous behaviour of AuOH is discussed from the relativistic point of view.     

A theoretical study of potential energy curves and spectroscopic constants of VC

Potential energy curves for the various low-lying electronic states of VC have been studied using complete active space multi-configuration self-consistent field (CASMCSCF) followed by first-order and multireference singles and doubles configuration interaction (FOCI, MRSDCI) calculations. The MRSDCI calculations included up to 6 million configurations. Two very low-lying electronic states are found as candidates for the ground state of VC, namely a high spin state ⁴Δ and a low-spin ²Δ state, which is favoured at higher levels. A number of low-lying excited electronic states of VC are predicted, which are yet to be observed. The low-lying electronic states of VC are found to be ionic as inferred from the dipole moments and the charge density calculations. Electron donation and the back-donation process are suggested to be operative in the V-C bond formation.     

Density dependence of the electric-field-gradient induced birefringence of the helium,neon and argon gases

An ab initio investigation of the density dependence of the electric-field-gradient induced birefringence (EFGB) for the noble gases helium, neon and argon is presented. To determine the second coefficient in the virial expansion of the molecular EFGB constant _mQ, the effect of two-body interactions has been studied by computing the internuclear dependence of the molecular quadrupole moment and of the dipole-dipole-quadrupole and dipole-magnetic dipole-dipole hyperpolarizabilities of the van der Waals dimers. A full-configuration-interaction approach as well as the coupled cluster singles and doubles and the coupled cluster singles and doubles plus perturbative triples approximations have been adopted, and extended basis sets including midbond functions have been employed. A semi-classical integration yields the virial coefficients. The effect of density for standard experimental conditions is found to be of the order of a few tens of parts per million for helium and neon, and of the order of a few parts per thousands for argon at low temperatures, and thus not detectable with present apparatus.     

Ab initio vibrational spectra and structure of the ground state of HeScH2+

Potential energy and dipole moment surfaces of the ¹A′ ground state of HeScH²⁺ have been calculated using both the internally contracted single and double excitation multireference configuration interaction and the coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations levels of theory. Analytical functions have been fitted to the discrete surfaces employing a multidimensional least squares approach. These analytical functions have subsequently been embedded within a rectilinear normal-coordinate vibrational Hamiltonian in order to calculate vibrational states and transition intensities for low-lying states of HeScH²⁺.     

Assessment of a composite CC2/DFT procedure for calculating 0–0 excitation energies of organic molecules

The task to assess the performance of quantum chemical methods in describing electronically excited states has in recent years started to shift from calculation of vertical (ΔE_ve) to calculation of 0–0 excitation energies (ΔE₀₀). Here, based on a set of 66 excited states of organic molecules for which high-resolution experimental ΔE₀₀ energies are available and for which the approximate coupled-cluster singles and doubles (CC2) method performs particularly well, we explore the possibility to simplify the calculation of CC2-quality ΔE₀₀ energies using composite procedures that partly replace CC2 with more economical methods. Specifically, we consider procedures that employ CC2 only for the ΔE_ve part and density functional theory methods for the cumbersome excited-state geometry optimisations and frequency calculations required to obtain ΔE₀₀ energies from ΔE_ve ones. The results demonstrate that it is indeed possible to both closely (to within 0.06–0.08 eV) and consistently approximate ‘true’ CC2 ΔE₀₀ energies in this way, especially when CC2 is combined with hybrid density functionals. Overall, the study highlights the unexploited potential of composite procedures, which hitherto have found widespread use mostly in ground-state chemistry, to also play an important role in facilitating accurate studies of excited states.     

On the orbital dependence of compact,weight-selected configuration interaction and coupled-cluster wave functions

We recently reported that very compact coupled-cluster wave functions may be generated by selecting the most important configurations, by weight, from the full coupled-cluster wave function. Here, we consider how the choice of orbitals may affect these wave functions in the case of the symmetric dissociation of H₂O. We employ unrestricted Hartree–Fock and complete-active-space self-consistent-field orbitals, as well as natural orbitals derived from a coupled-cluster singles and doubles wave function. For a given accuracy, some choices of orbitals can reduce the size of configuration interaction wave functions, but they have little effect on the weight-selected coupled-cluster wave functions.     

Theoretical study of the photoelectron spectrum of ethyl formate: Ab initio and density functional theory investigation

The first ionization energy and associated photoelectron spectrum of ethyl formate are investigated with quantum chemistry calculations. The geometries, harmonic vibrational frequencies and first ionization energy are computed at the Hartree-Fock (HF) and at the second order Møller-Plesset perturbation theory (MP2). Moreover, accurate ionization energies are obtained with the Coupled-Cluster theory including singles and doubles excitations (CCSD) as well as singles, doubles and perturbative triples excitations (CCSD(T)). Then, these ab initio results are assessed with respect to experimental values. Additionally, the ionization energies are also calculated with the computationally attractive density functional theory (DFT). In this case the accuracy of several exchange-correlation functionals is evaluated by comparison with the ab initio and experimental results. In a next step, the vibrational structure of the photoelectron spectrum is simulated at the HF, MP2 and DFT levels via the calculation of the Franck-Condon factors. These simulations are compared to the experimental photoelectron spectrum and allow an accurate reproduction of the vibrational progression.     

Quantum Monte Carlo study of small hydrocarbon atomization energies

A benchmark study of atomization energies is reported for 22 hydrocarbons using single determinant trial functions in the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo (QMC) method. The DMC atomization energies are compared to experiment, a complete basis set approach (CBS-Q), density functional theory with the B3LYP functional, and coupled-cluster singles, doubles and perturbative triples, CCSD(T), methods. Comparison of the DMC results to experiment yields a mean absolute deviation of 1.9kcalmol^?1, which is comparable to that of the B3LYP/cc-pVQZ (1.7kcalmol^?1) level of theory, but less accurate than that of CBS-Q (1.1kcalmol^?1). DMC performs similarly for both closed-shell and open-shell molecules with mean absolute deviations of 2.1kcalmol^?1 for the former and 1.7kcalmol^?1 for the latter systems. The use of experimental zero-point energies (ZPEs), rather than scaled B3LYP ZPEs, is found to have negligible effect on DMC atomization energies. The latter reported here provide a baseline from which further improvement in the calculation of DMC atomization energies, including the use of multi-determinant and other trial function improvements, can be measured.     

A comparative multi-property analysis of existing models for the He–N2 potential energy surface

The ability of an improved version of a recent three-dimensional ab initio potential energy surface for the He–N₂ interaction [Phys. Rev. A 66, 042703 (2002)], determined from high-level coupled-cluster calculations (including full singles and doubles, perturbative triples, and Brueckner orbitals), to predict scattering cross-sections and various bulk gas mixture properties is tested. The full three-dimensional potential energy surface has been employed for the calculation of vibrational relaxation rates, and a two-dimensional version (at a fixed N₂ bond length of 2.0743 a ₀) has been used for the calculation of molecular beam scattering cross-sections using quantum close-coupling methods and for the calculation of bulk gas phenomena using classical trajectory methods. The results obtained from the two-dimensional version of the present potential energy surface are compared with those obtained from three other recent accurate two-dimensional representations of the He–N₂ interaction.     

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.     

CH4-Ne体系的三维从头算势能面与光谱的模拟

本文在从头算CCSD(T)/AVXZ(X=T,Q)水平上计算了CH₄-Ne体系的三维势能面,同时在基组中加入了键函数,并且将基组外推到完全基组极限水平. 通过最小二乘法拟合摩斯长程势能函数形式,获得了三维分析势能面,其中对664个从头算格点的拟合的标准偏差仅为0.042 cm^-1. 随后,采用径向离散变量表象和角度有限基组表象相结合的杂化基函数方法,并基于Lanzcos迭代的方法获得了CH₄-Ne体系的振转能级,所预测的红外光谱与实验值非常吻合. 本文首次给出了CH₄-Ne体系的微波光谱数据. CH₄-Ne体系三维摩斯长程势能面分析的表达式为今后CH₄在Ne团簇动力学性质以及其碰撞诱导吸收光谱的研究中奠定了基础.