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.     

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.     

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.     

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.     

Electrostatic interactions between molecules from relaxed one-electron density matrices of the coupled cluster singles and doubles model

The influence of electron correlation on the electrostatic interaction between closed shell molecules is studied using the relaxed electron densities of the coupled cluster singles and doubles (CCSD) model. The corresponding CCSD one-electron density matrices are efficiently computed without full four-index transformation by employing the generalized exchange and Coulomb operator technique. Using several representative van der Waals and hydrogen bonded complexes it was found that in most cases the convergence of the M?ller-Plesset expansion of the electrostatic energy, restricted to single, double and quadruple excitations, is satisfactory and the fourth-order triple excitation term is more important than the sum of the fifth- and higher-order contributions from CCSD theory. The importance of the CCSD correlation correction to the electrostatic energy was gauged by comparison of the total interaction energy computed by symmetry-adapted perturbation theory (SAPT) and by the super-molecular CCSD(T) approach (coupled cluster singles and doubles model with a non-iterative inclusion of triple excitations). Except for the CO and N₂ dimers, very good agreement between the two sets of results is observed. For the difficult case of the CO dimer the difference between the SAPT and CCSD(T) results can be explained by the truncation of the SAPT expansion for the dispersion energy at second order in the intramonomer correlation operator.     

Solvent effects on optical excitations of poly <Emphasis Type="Italic">para</Emphasis> phenylene ethynylene studied by QM/MM simulations based on many-body Green's functions theory

Electronic excitations in dilute solutions of poly para phenylene ethynylene (poly-PPE) are studied using a QM/MM approach combining many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation with polarizable force field models. Oligomers up to a length of 7.5?nm (10 repeat units) functionalized with nonyl side chains are solvated in toluene and water, respectively. After equilibration using atomistic molecular dynamics (MD), the system is partitioned into a quantum region (backbone) embedded into a classical (side chains and solvent) environment. Optical absorption properties are calculated solving the coupled QM/MM system self-consistently and special attention is paid to the effects of solvents. The model allows to differentiate the influence of oligomer conformation induced by the solvation from electronic effects related to local electric fields and polarization. It is found that the electronic environment contributions are negligible compared to the conformational dynamics of the conjugated PPE. An analysis of the electron-hole wave function reveals a sensitivity of energy and localization characteristics of the excited states to bends in the global conformation of the oligomer rather than to the relative of phenyl rings along the backbone.     

Perturbative order analysis of the similarity transformed Hamiltonian in Fock-space coupled cluster theory: difference energy and electric response properties

A perturbative analysis of the ground-state similarity transformed Hamiltonian and its effect on the various Fock-space coupled cluster (FSCC) sectors is presented through calculation of ionisation potential, electron affinity, excitation energies and response properties. Various truncation schemes of the effective Hamiltonian are presented with explicit form of the defining equations. Based on such a truncation, the approximate methods are labelled as FSCC(n), where n represents the correlation energy of the ionised, electron attached or excited states corrected at least up to nth order within coupled cluster singles and doubles scheme (CCSD). A lower scaling CC2 type of approach (abbreviated as FS-CC2) is compared against the group of FSCC(n) methods for energies. Electric response properties have been compared and contrasted for the two lower scaling methods: FSCC(2) and FS-CC2. The various truncated methods are tested for a number of small molecules. The results obtained from a range of truncated methods are compared against full FSCCSD calculations.     

Optimal control theory in adaptive simulated annealing technique: optimisation of laser pulse for selective vibrational excitations and photo-dissociation of HBr+

An optimisation method using optimal control theory based adaptive simulated annealing technique has been explored to get optimised laser pulses for selective vibrational excitations and photo-dissociation of the HBr⁺ in its ground electronic state. Potential energy curve of the system has been obtained by coupled cluster singles and doubles (CCSD) level calculation, using aug-cc-pVTZ as basis set. To have a simple pulse, a limited number of parameters is chosen as variables and the technique so developed works well. The study is extended with chirping field frequency to explore the effect of chirping in dynamics.     

Vibrational spectrum at a water surface: a hybrid quantum mechanics/molecular mechanics molecular dynamics approach

A hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulation is applied to the calculation of surface orientational structure and vibrational spectrum (second-order nonlinear susceptibility) at the vapor/water interface for the first time. The surface orientational structure of the QM water molecules is consistent with the previous MD studies, and the calculated susceptibility reproduces the experimentally reported one, supporting the previous results using the classical force field MD simulation. The present QM/MM MD simulation also demonstrates that the positive sign of the imaginary part of the second-order nonlinear susceptibility at the lower hydrogen bonding OH frequency region originates not from individual molecular orientational structure, but from cooperative electronic structure through the hydrogen bonding network.     

基于参考势的从头算量子力学/分子力学混合方法研究Parvalbumin B蛋白结合钙、镁离子的选择性

蛋白的离子选择性与蛋白的功能密切相关,而离子选择性本质上来源于蛋白分子与离子结合自由能的差别. 尽管近几十年来分子力场在描述蛋白体系相互作用方面取得了长足的进步,由于缺乏对静电极化和电荷转移效应显式的描述,传统的分子力场依然难以精确地描述金属蛋白体系中蛋白质与金属离子的相互作用. 量子化学方法非常适合于蛋白质与金属离子之间相互作用的描述. 但是在分子模拟中采用量子化学方法则太昂贵了. 近年来发展起来的参考势方法在保证计算精度的前提下兼顾效率,可以有效地解决这个窘境. 在这个方法中,动力学模拟的轨迹是在分子力场的精度下获得的. 随后,通过从分子力场到量子化学方法的矫正,从而获得在量子化学势函数级别下的自由能信息. 本文采用参考势函数方法研究了Parvalbumin B蛋白的结合口袋对钙、镁离子的选择性. 计算结果表明电荷转移效应非常重要,而量子化学方法可以比较精确地预测离子的选择性. 并且,量子化学区域的选择对于结果的可靠性也是非常重要的.     

Efficient and portable acceleration of quantum chemical many-body methods in mixed floating point precision using OpenACC compiler directives

ABSTRACT

It is demonstrated how the non-proprietary OpenACC standard of compiler directives may be used to compactly and efficiently accelerate the rate-determining steps of two of the most routinely applied many-body methods of electronic structure theory, namely the second-order Møller-Plesset (MP2) model in its resolution-of-the-identity approximated form and the (T) triples correction to the coupled cluster singles and doubles model (CCSD(T)). By means of compute directives as well as the use of optimised device math libraries, the operations involved in the energy kernels have been ported to graphics processing unit (GPU) accelerators, and the associated data transfers correspondingly optimised to such a degree that the final implementations (using either double and/or single precision arithmetics) are capable of scaling to as large systems as allowed for by the capacity of the host central processing unit (CPU) main memory. The performance of the hybrid CPU/GPU implementations is assessed through calculations on test systems of alanine amino acid chains using one-electron basis sets of increasing size (ranging from double- to pentuple-ζ quality). For all but the smallest problem sizes of the present study, the optimised accelerated codes (using a single multi-core CPU host node in conjunction with six GPUs) are found to be capable of reducing the total time-to-solution by at least an order of magnitude over optimised, OpenMP-threaded CPU-only reference implementations.     

The QM/MM approach for wavefunctions,energies and response functions within self-consistent field and coupled cluster theories

This paper presents the coupled cluster/molecular mechanics (CC/MM) and self-consistent field/molecular mechanics (SCF/MM) approaches for wavefunctions, energies and response properties. Two physically different theories are derived, the mean-field and the direct-field interaction approaches, together with expressions for the optimization condition of both variational and non-variational wavefunctions and energies. Also derived are the linear response functions at the CC/MM and SCF/MM levels of theory, and the expressions are compared with the vacuum response functions.     

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     

Extreme tunnelling in methylamine dehydrogenase revealed by hybrid QM/MM calculations: potential energy surface profile for methylamine and ethanolamine substrates and kinetic isotope effect values

The rate-determining proton transfer step in the amine reduction reaction catalysed by the enzyme methylamine dehydrogenase has been studied using a hybrid quantum mechanical/molecular mechanical (QM/MM) model. Variational transition state theory, combined with multidimensional tunnelling corrections, has been employed to calculate reaction rate constants, and hence deuterium kinetic isotope effects (KIE). To render these calculations computationally feasible, the electronic structure was described using a PM3 method with specific reaction parameters obtained by a fit to energetics obtained at a high level for a small model system. Compared to the use of standard parameters, these revised parameters result in a considerable improvement in the predicted KIE values and activation energy. For both methylamine and ethanolamine substrates, through-barrier, rather than over-barrier, motion is found to dominate with KIE values that are large and close to the experimental values. A major difference between the two substrates is that, for ethanolamine, different hydrogen bonding structures involving the substrate hydroxyl are possible, leading to very different potential energy surfaces with KIE values covering a considerable range. We speculate that this is the origin of the differing temperature behaviour observed for the KIEs of the two substrates.     

The electron affinity of Al13H cluster: high level ab initio study

Al₁₃H clusters have been considered candidates for cluster assembled materials. Here we have carried out benchmark calculations for the Al₁₃H cluster, both neutral and anionic, with the aim of verifying the nature of stationary points on the potential energy surface, studying dynamics of H atom and determining an adiabatic electron affinity. A range of correlated methods applied include second-order perturbation theory (MP2), spin-component-scaled MP2, coupled electron pair (CEPA) and coupled cluster singles and doubles with perturbative triple corrections (CCSD(T)). These methods are used in combination with the correlation consistent basis sets through aug-cc-pVTZ including extrapolation to the complete basis set (CBS) limit. Performance of several different flavours of density functional theory (DFT) such as generalised gradient approximation (GGA), hybrid GGA, meta-GGA and hybrid-meta-GGA is assessed with respect to the ab initio correlated reference data. The harmonic force constant analysis is systematically performed with the MP2 and DFT methods. The MP2 results show that for neutral Al₁₃H only the hollow structure is a potential energy minimum, with the bridged structure being a transition state for the H shift from the hollow site to the adjacent hollow site. The CCSD(T)/aug-cc-pVTZ (CCSD(T)/CBS) estimate of the energy barrier to this H shift is 2.6 (2.9) kcal/mol, implying that the H atom movement over the Al₁₃H cluster surface is facile. By contrast, the DFT force constant analysis results suggest additional terminal and bridged minima structures. For the anion Al₁₃H^?, exhibiting ‘stiffer’ potential energy surface compared to the neutral, the existence of the hollow and terminal isomers is consistent with the earlier photoelectron spectroscopy assignment. The adiabatic electron affinity of Al₁₃H is determined to be 2.00 and 1.95 eV (the latter including the ΔZPE correction) based on the CCSD(T) energies extrapolated to the CBS limit, whereas the respective CCSD(T)/CBS thermodynamic EA values are 2.79 and 2.80 eV.     

运用R矩阵方法研究低能电子与NO_2分子的散射

基于静电-交换和密耦合两种模型,采用R矩阵方法,研究了低能电子与二氧化氮自由基分子的积分散射截面和动量迁移散射截面,包括弹性散射和从电子基态到电子激发态的非弹性散射.采用aug-cc-pVTZ基组进行靶分子结构优化和散射研究.在密耦合模型中,包含6个电子的最低三个占据轨道1b_2,1a_1,2a_1被冻结,其余17个电子自由运动在活化空间中,并给活化空间增加了2b_1和7a_1两个虚轨道.包含了所有垂直激发能小于20 eV的靶分子电子组态,得到了收敛的散射截面,并与最新理论和实验值进行了比较.当入射能量小于4 eV时,本文结果与实验值符合得更好,校正了以往部分理论结果在极低能量处过高的现象,表明关联效应对于极低能量散射是非常重要的.     

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.     

Small silver clusters at paramagnetic defects of silica surfaces: A density functional embedded-cluster study

We studied the interaction of small Ag_n clusters (n = 1–4) with paramagnetic defect centers of a dehydroxylated silica surface using an all-electron scalar relativistic density functional method. The surface and adsorption complexes on it were modeled with an accurate quantum mechanics/molecular mechanics (QM/MM) scheme of embedding QM clusters in an elastic polarizable environment, described at the molecular mechanics level (MM). We analyzed two types of frequent point defects as sites for trapping and growing of Ag clusters: a silicon atom with a dangling bond (E′ center), ≡ Si?, and a non-bridging oxygen center (NBO), ≡ Si–O?. The Ag clusters interact with these paramagnetic centers forming strong covalent metal-defect bonds. The high adsorption energy allows one to consider the NBO and E′ sites as traps of single Ag atoms and as centers of cluster growth. We also explored the effect of adsorption on observable electronic properties of the silver clusters and of the defects of the silica surface.