A local framework for calculating coupled cluster singles and doubles excitation energies (LoFEx-CCSD)

ABSTRACT

The recently developed Local Framework for calculating Excitation energies (LoFEx) is extended to the coupled cluster singles and doubles (CCSD) model. In the new scheme, a standard CCSD excitation energy calculation is carried out within a reduced excitation orbital space (XOS), which is composed of localised molecular orbitals and natural transition orbitals determined from time-dependent Hartree–Fock theory. The presented algorithm uses a series of reduced second-order approximate coupled cluster singles and doubles (CC2) calculations to optimise the XOS in a black-box manner. This ensures that the requested CCSD excitation energies have been determined to a predefined accuracy compared to a conventional CCSD calculation. We present numerical LoFEx-CCSD results for a set of medium-sized organic molecules, which illustrate the black-box nature of the approach and the computational savings obtained for transitions that are local compared to the size of the molecule. In fact, for such local transitions, the LoFEx-CCSD scheme can be applied to molecular systems where a conventional CCSD implementation is intractable.     

Applicability of medium-size basis sets in calculations of molecular dynamic polarisabilities

Static and dynamic average polarisabilities and polarisability anisotropies of seven linear non-polar and polar molecules are calculated within the CCS, CC2, and CC3 approximations using a range of medium-sized basis sets: the polarised LPol-n (n = ds, dl, fs, fl), the aug-pc-n (n = 1, 2), the def2-SVPD, and -TZVPD basis sets. Reference values are obtained using a hierarchy of Dunning's (d-)aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The results are discussed together with the available CCSD values in terms of basis set and correlation method errors, and their ratio. Detailed analysis shows that already the def2-SVPD basis set can be used in CCS polarisability calculations. When affordable, the slightly larger aug-pc-1 basis set is recommended, as it leads to significant reduction of basis set error. The def2-TZVPD, LPol-ds, and aug-pc-2 basis sets are optimal choice within the CC2 approximation, with the latter allowing to approach the CC2 basis set limit. The LPol-ds, -dl, and def2-TZVPD sets outperform the aug-cc-pVTZ set in average polarisability CCSD calculations, with the def2-TZVPD being competitive to other reduced-size sets also in determination of polarisability anisotropy. The aug-pc-2 basis is a particularly attractive choice for CCSD, giving the accuracy of aug-cc-pVQZ at a significantly reduced computational cost. The polarisability anisotropy is shown to be more computationally demanding than the average polarisability, in particular with respect to the accuracy of the correlation method and an accurate evaluation of this property requires at least the CCSD model.     

A coupled cluster study of the magnetisability,rotational g-tensor and quadrupole moment of NF3, PF3 and AsF3

ABSTRACT

A coupled-cluster investigation of magnetic and electric properties of NF₃, PF₃ and AsF₃ provides for a comparison with recent experimental data. For PF₃, achieving reliable values for the magnetisability and rotational g-tensor of PF₃ has been particularly challenging. We report the most accurate calculations to date for PF₃; for the vibrationally corrected anisotropic magnetisability, our extrapolated CCSD(T)/CBS value of ?0.290 a.u is within the uncertainty limits of the most recent experimental value of ?0.286 ± 0.042 a.u. For the rotational g-tensor of PF₃, agreement between theory and experiment for the g_⊥ component is excellent (deviation of less than 0.0006 a.u.). However, the g_|| component remains problematic even though our vibrationally corrected CCSD(T)/CBS value of ?0.0387 a.u is in closer agreement with the recently revised experimental value of ?0.0470 ± 0.0020 a.u. than the original value of ?0.0815 ± 0.0020 a.u. The origin of the remaining discrepancy remains unclear. Dipole and quadrupole moments have also been investigated.     

Electronic structure and molecular spectroscopic constants of ScN and ScP investigated by several quantum chemistry methods

The electronic structure of the ScN and ScP molecules is a subject of controversy and turns out to be a challenging problem in quantum chemistry. We show that the ground-state electronic structure for both molecules depends critically on the choice of methods used which incorporate different ways of accounting for electron correlation. A parallel ab initio, DFT and TD-DFT study is performed for this purpose and uses sufficiently flexible basis sets able to reproduce accurate electronic structures, as well as correct spectroscopic constants.

In the ab initio methodology, results have been obtained with methods such as Hartree-Fock (HF), M?ller-Plesset perturbation theory (MPn), direct configuration interaction (CI), quadratic configuration interaction (QC), coupled cluster configuration interaction (CC), complete active space self-consistent field (CASSCF) and multireference configuration interaction (CIPSI) methods. In the DFT methodology, various ‘pure’ and ‘hybrid’ density functionals are used and the corresponding results are compared to sophisticated ab initio methods and to available experimental data.

All the methods used show that the ground state of both molecules is ¹Σ⁺, but two electronic structure natures, ¹Σ⁺ open-shell or ¹Σ⁺ closed-shell, are competitive and depend on the method employed. All the ab initio methods based on a single determinant wavefunction suffer seriously in predicting clearly the exact nature of the ground state or its correct structural and spectroscopic parameters. However, the ab initio methods based on a multiconfigurational wavefunction appear to be successful in describing correctly, within one shot, the electronic structure and the molecular spectroscopic constants. The ground state, particularly for the ScN molecule, presents an unusual electronic structure: the presence of degenerate determinants, quasidegeneracy with other states and one avoided crossing in the region around the equilibrium distances. The bonding of the ground state is a two open-shell ¹Σ⁺ state described as a π double bond and a Σ dative bond; the real triple bond ¹Σ⁺ state, i.e. closed-shell state, is found to lie higher in energy. The potential energy curves of the lowlying electronic states, the derived electronic structures and various molecular spectroscopic constants are presented and discussed for each method employed.     

Potential use of small basis set on the calculations of electronic properties of some four-membered heterocycles: a conformational study

The potential use of small basis sets upon a low level of theory was studied on the calculations of electronic properties (dipole moment, static polarisability and static hyperpolarisabilities) of a series of 16 four-membered heterocycles with an exocyclic double bond at the position 3 (1–16). First, the calculations were performed within the Hartree–Fock (HF) approximation using 6-31G, 6-31G(d,p) and 6-31+G(d,p) as basis sets for the different conformational states of each molecule, and the results obtained were compared with the MP2/6-31+G(d,p) results reported. In the second place, in order to know the real potential of HF calculations, these were compared with those calculated using larger approaches such as MP2/6-311+G(d,p), MP2/aug-cc-pVDZ, CCS/6-311+G(d,p), CCS/aug-cc-pVDZ, CCS/aug-cc-pVTZ, CCSD/6-31+G(d) and CCSD/cc-pVDZ, taken into account only the planar and equilibrium geometries of each molecules. The HF approaches permit us to obtain a good qualitative representation of the dipole moment as a function of puckering angle in comparison with MP2, CCS and CCSD levels for all tested molecules. However, only HF/6-31+G(d,p) provides quantitative values of dipole moment for the heterocycles 1, 5 and 13 in comparison with MP2, CCS and CCSD levels. On the other hand, the polarisability and hyperpolarisabilities were quite sensitive to the quality of level of theory and basis sets. In particular, HF/6-31+G(d,p) predicted a representative approximation of alpha for the molecule 16 in comparison with larger methods as MP2/aug-cc-pVDZ, CCS/aug-cc-pVDZ and CCS/aug-cc-pVTZ, while a detailed analysis showed that HF can be used in the calculation of alpha for the molecules 3, 7, 11 and 15, but it requires the use of extended basis sets. Also, HF/6-31+G(d,p) predicted values of beta very similar to those calculated at the MP2 and CCSD levels used, for the planar and equilibrium geometry of the molecules 10 and 14. Furthermore, HF/6-31+G(d,p) described a representative dependence of this property with the puckering angle for the heterocycles 9, 10 and 14, compared with the MP2 curves.     

Molecular cluster perturbation theory. I. Formalism

We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.     

Theoretical study of the helio hydrogen cyanide dication HeCNH2+

The structure and stability of the helio hydrogen cyanide molecular ion, HeCNH²⁺, is investigated by standard quantum chemical methods. Single reference calculations are carried out using second-order perturbation theory (MP2), the coupled cluster expansion in the CCSD approximation, and the hybrid approach using a perturbative estimate of the triple excitation energy component designated CCSD(T). Multireference calculations using a complete active space (CASSCF) and a second-order perturbation theory estimate of correlation effects (CASPT2) are reported.     

A CC2 dielectric continuum model and a CC2 molecular mechanics model

In this paper we present theory and applications for the second-order approximate singles and doubles coupled cluster (CC2) electronic structure method coupled to either a dielectric continuum (the CC2/DC model) or a molecular mechanical intermolecular force field (the CC2/MM model). Calculations of the interaction energy, solvation energy, electric dipole moment and electric quadrupole moment of liquid water are presented using the correlated CC2 approach. The results are compared to the corresponding results using the uncorrelated Hartree-Fock (HF) and the correlated coupled cluster singles and doubles (CCSD) methods. Also, a hierarchy in the coupling between the quantum mechanical (QM) and the molecular mechanical (MM) part of the system is investigated in the QM/MM model for the three different electronic structure methods.     

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.     

Semiexperimental equilibrium molecular structures of the maleimide and phthalimide

ABSTRACT

Semiexperimental (SE) equilibrium molecular structures of the title compounds are determined using rotational and ab initio data. Cubic force constants for the parent molecules and a number of isotopologues are calculated at the B2PLYP double hybrid functional with the correlation-consistent triple-ζ cc-pVTZ basis set. Rovibrational and electronic corrections necessary for the transformation of observed ground-state rotational constants to equilibrium ones are calculated using cubic force constants and rotational g tensors. The SE structure parameters are compared with those obtained with CCSD(T) method and basis set of quadruple-ζ quality.

Abbreviations: MP2: Møller–Plesset perturbation theory; CCSD(T): coupled-cluster theory including single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations; VnZ: cc-pVnZ, Dunning's correlation-consistent basis, where n?=?T or Q; CVnZ: cc-pCVnZ, Dunning's correlation-consistent basis, where n?=?T or Q; wCVnZ: cc-pwCVnZ, Dunning's correlation-consistent basis, where n?=?T or Q; AwCVQZ: aug-cc-pwCVQZ, Dunning's correlation-consistent basis; AE: all-electrons; FC: frozen core; QM: quantum mechanics; MAD: mean absolute deviation; SE: semiexperimental equilibrium structure; BO: best ab initio Born–Oppenheimer composite structure; HOMA: harmonic oscillator model of aromaticity; ICSS: iso-chemical shielding surface (isosurface of magnetic shielding value or isosurface of NICS with inverted sign); ICSSZZ: component of magnetic shielding tensor perpendicular to molecular plane; NICS: nuclear independent chemical shift; AIM: atoms in molecules method; ACID: anisotropy of current induced density     

Behind the success of modified coupled-cluster methods: addition by subtraction

ABSTRACT

Modified coupled-cluster (CC) methods such as linearized coupled-cluster doubles (LinCCD), approximate coupled pair (ACP D14), 2CC (from nCC family), parameterized CCSD (pCCSD) and distinguishable cluster (DCSD) can have their advantages over general CC methods. Though these methods include connected clusters of single and double excitations at most, distinguishable cluster, parameterized CC and approximate coupled pair methods, in particular, have been shown to produce quantitatively correct results in benchmark studies. To put these methods on a stronger foothold, it is essential to understand the rationale for their success: mimicking the effect of connected triple excitations. We exploit the relation between CC and many body perturbation theory (MBPT) in general, and between CCSD and MBPT(4)/MP4 in particular, to take a step towards bringing clarity to this persisting conundrum. Our aim here is to look for numerical signs of ‘addition by subtraction’ or ‘inclusion by deletion’ effect that is likely behind the success of these modified CCD or CCSD methods. We achieve this by revisiting well-studied examples of single and multiple bond dissociation and comparing the performance of these modified CCSD methods with higher-level CC methods. Though our results are qualitative in nature, we hope this would lead to more rigorous analysis in future studies.     

UNO DMRG CASCI calculations of effective exchange integrals for m-phenylene-bis-methylene spin clusters

ABSTRACT

Theoretical examinations of the ferromagnetic coupling in the m-phenylene-bis-methylene molecule and its oligomer were carried out. These systems are good candidates for exchange-coupled systems to investigate strong electronic correlations. We studied effective exchange integrals (J), which indicated magnetic coupling between interacting spins in these species. First, theoretical calculations based on a broken-symmetry single-reference procedure, i.e. the UHF, UMP2, UMP4, UCCSD(T) and UB3LYP methods, were carried out with a GAUSSIAN program code under an SR wave function. From these results, the J value by the UHF method was largely positive because of the strong ferromagnetic spin polarisation effect. The J value by the UCCSD(T) and UB3LYP methods improved an overestimation problem by correcting the dynamical electronic correlation. Next, magnetic coupling among these spins was studied using the CAS-based method of the symmetry-adapted multireference methods procedure. Thus, the UNO DMRG CASCI (UNO, unrestricted natural orbital; DMRG, density matrix renormalised group; CASCI, complete active space configuration interaction) method was mainly employed with a combination of ORCA and BLOCK program codes. DMRG CASCI calculations in valence electron counting, which included all orbitals to full valence CI, provided the most reliable result, and support the UB3LYP method for extended systems.     

Reduced multireference coupled cluster method IV: open-shell systems

The reduced multireference coupled cluster method with singles and doubles (RMR CCSD) is extended to handle high spin open-shell systems within the framework of the unitary group based coupled cluster theory (UGA CCSD). The method is applied to several states of multiply bonded diatomics, namely to the X ²     

Analytical energy gradients for local second-order Møller-Plesset perturbation theory using intrinsic bond orbitals

ABSTRACT

We present the theory and an implementation for PAO-LMP2 analytical energy gradients (local second-order Møller-Plesset perturbation theory with domains of projected atomic orbitals), using intrinsic bond orbitals (IBOs). The accuracy of optimised LMP2 geometry parameters relative to canonical MP2 and CCSD(T) ones is benchmarked for more than 100 small- to medium-sized molecules. Using augmented triple-ζ basis sets, the deviations of computed LMP2 bond lengths and bond angles from the corresponding MP2 ones are small and quickly decrease with increasing domain sizes. For small domains, a systematic compensation between the intrinsic error of MP2 and the errors due to the local approximations is found, so that the LMP2 results deviate less from CCSD(T) than the MP2 ones. On the other hand, with extended domains, the differences between LMP2 and MP2 geometry parameters become negligible.     

A high level computational study of the CH4/CF4 dimer: how does it compare with the CH4/CH4 and CF4/CF4 dimers?

The interaction within the methane–methane (CH₄/CH₄), perfluoromethane–perfluoromethane (CF₄/CF₄) methane–perfluoromethane dimers (CH₄/CF₄) was calculated using the Hartree–Fock (HF) method, multiple orders of Møller–Plesset perturbation theory [MP2, MP3, MP4(DQ), MP4(SDQ), MP4(SDTQ)], and coupled cluster theory [CCSD, CCSD(T)], as well as the PW91, B97D, and M06-2X density functional theory (DFT) functionals. The basis sets of Dunning and coworkers (aug-cc-pVxZ, x?=?D, T, Q), Krishnan and coworkers [6-311++G(d,p), 6-311++G(2d,2p)], and Tsuzuki and coworkers [aug(df, pd)-6-311G(d,p)] were used. Basis set superposition error (BSSE) was corrected via the counterpoise method in all cases. Interaction energies obtained with the MP2 method do not fit with the experimental finding that the methane–perfluoromethane system phase separates at 94.5?K. It was not until the CCSD(T) method was considered that the interaction energy of the methane–perfluoromethane dimer (?0.69?kcal?mol^?1) was found to be intermediate between the methane (?0.51?kcal?mol^?1) and perfluoromethane (?0.78?kcal?mol^?1) dimers. This suggests that a perfluoromethane molecule interacts preferentially with another perfluoromethane (by about 0.09?kcal?mol^?1) than with a methane molecule. At temperatures much lower than the CH₄/CF₄ critical solution temperature of 94.5?K, this energy difference becomes significant and leads perfluoromethane molecules to associate with themselves, forming a phase separation. The DFT functionals yielded erratic results for the three dimers. Further development of DFT is needed in order to model dispersion interactions in hydrocarbon/perfluorocarbon systems.     

以一组统一的高斯函数为基函数的双原子分子的Hartree-Fock-Roothaan波函数(Ⅱ)——H2和第一列元素的同核双原子体系A2,A2~±和A2

采用文献的一组统一的doublezeta收缩高斯型函数为基函数,从头计算H₂和第一列元素的同核双原子体系的电子波函数和轨道能量、总能量等物理量。电子态包括同核体系的基态A₂,一些低激发态A₂~*和正负离子态A₂~±,A表示周期表中Li到F的各种元素。计算限于闭壳层电子组态或只带一个未填满的开壳层电子组态。作为例子,报道了H₂和几种基态A₂的电子波函数表。 关键词：