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.     

Electrostatic potential of several small molecules from density functional theory

A number of density functional theory (DFT) methods were used to calculate the electrostatic potential for the series of molecules N2, F2, NH3, H2O, CHF3, CHCl3, C6H6, TiF4, CO(NH2)2 and C4H5N3O compared with QCISD (quadratic configuration interaction method including single and double substitutions) results. Comparisons were made between the DFT computed results and the QCISD ab initio ones and MP2 ab initio ones, compared with the root-mean-square deviation and electrostatic potential difference contours figures. It was found that the hybrid DFT method B3LYP, yields electrostatic potential in good agreement with the QCISD results. It is suggest this is a useful approach, especially for large molecules that are difficult to study by ab initio methods.     

几个小分子静电势的密度泛函理论计算

运用多种密度泛函理论(DFT)方法和从头算(ab initio)方法,研究了具有代表性的一系列分子的静电势,选择QCISD计算出的分子静电势为标准静电势,通过比较多种DFT法和QCISD从头算,以及它们之间的均方根偏差和静电势差值曲线图,结果表明B3LYP-DFT法与QCISD-ab initio法计算结果较吻合,暗示了B3LYP-DFT法在得到分子静电势时是一个有用的工具,尤其对于从头计算难以进行研究的大分子体系.     

Eliminating interactions between non-neighboring qubits in the preparation of cluster states in quantum molecules

We propose a scheme to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the time of previous protocol leaving out the non-nearest-neighbor interactions.     

On the direct determination of constrained pure state one-electron density matrices: Part I. A new theoretical model for closed-shell systems

A new method based on the penalty-function way of satisfying equality constraints is proposed for the determination of constrained pure state one-electron density matrices for closed-shell many-electron systems. The algorithm suggested can handle many constraints simultaneously. Certain interesting features of the proposed algorithm are discussed with numerical examples.     

Reduced density matrices of the anisotropic Heisenberg model

The reduced density matrices of the anisotropic Heisenberg model are studied by means of a functional integral representation based on a generalized Poisson process. Integral equations, which are analogous to the classical Kirkwood-Salzburg equations, are then used to prove the existence of the infinite volume limit of the reduced density matrices, analyticity properties with respect to the fugacity (or magnetic field) and the potentials, and a cluster property, in the low fugacity (high magnetic field) region.The research reported in this paper was supported by the National Science Foundation.     

Symmetries of the electrodynamic interactions between chiral molecules

A quantum electrodynamics calculation of the dynamic microscopic interactions between molecules beyond the electric dipole approximation is presented. The symmetry of the resulting terms is examined with respect to rotations, parity and index permutations. Their relative importance is also considered in the short-distance limit. A dominant term which exists only in chiral molecules and which involves the coupling of the anisotropic parts of the molecular optical activities is evidenced. Associated with the coupling of the anisotropic parts of the molecular polarisabilities which is usually invoked to account for the isotropic–nematic phase transition of liquid crystals, that term accounts for the possibility of the helical order which is observed in chiral nematics (cholesterics). Introducing in addition both the short-range correlations due to the exclusion principle driven repulsive forces and the thermally-induced effect of the static multipole interactions can explain the temperature dependence of the helical pitch. No assumption will be made on the shape of the molecules.     

On the direct determination of constrained pure state one-electron density matrices: II. A modified algorithm and its applications

An algorithm recently proposed by us for the direct determination of pure state one-electron density matrices (P) under externally imposed constraints has been remodelled. The modified algorithm is applied to the construction of ground state potential energy curve of lithium hydride molecule usingknown values of dipole moments of LiH at various internuclear distances as theexternal constraint. The equilibrium internuclear distances (R _c) is seen to be unaffected by the constraint, but the force constant improves remarkably. The relevant features of the constrained density vis-a-vis those of the unconstrained one are analyzed revealing some of the improved features of the constrained density.     

Derivation of the density functional theory from the cluster expansion

The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.     

Quantum computing for the Lipkin model with unitary coupled cluster and structure learning ansatz

We report a benchmark calculation for the Lipkin model in nuclear physics with a variational quantum eigensolver in quantum computing. Special attention is paid to the unitary coupled cluster (UCC) ansatz and structure learning (SL) ansatz for the trial wave function. Calculations with both the UCC and SL ansatz can reproduce the ground-state energy well; however, it is found that the calculation with the SL ansatz performs better than that with the UCC ansatz, and the SL ansatz has even fewer quantum gates than the UCC ansatz.     

Relation between structure and enthalpy for stacking interactions of aromatic molecules

An approximately linear correlation has been found between the enthalpy of complexation and the area of overlap of the chromophores using published structural and thermodynamical data on the self- and hetero-association of aromatic molecules measured under similar solution conditions. This finding is consistent with the assumption that short-range van-der-Waals forces dominate over other contributions to the enthalpy of stacking of aromatic molecules. It provides a ‘model-independent’ approach for a priori estimation of the enthalpy of aromatic–aromatic stacking interactions from knowledge of the structural properties or vice versa.     

The love-hate relationship between the shell model and cluster models

We adopt a personal approach here reviewing several calculations over the years in which we have experienced confrontations between cluster models and the shell model. In previous cluster conferences, we have noted that cluster models go hand in hand with Skyrme-Hartree-Fock calculations in describing states which cannot easily, if at all, be handled by the shell model. These are the highly deformed (many particle-many hole) intruder states, linear chain states, etc. In the present work, we will consider several topics: the quadrupole moment of ⁶Li; the nonexistence of low-lying intruders in ⁸Be; and then jumping to the f _7/2 shell, we discuss the two-faceted nature of the nuclei, which sometimes display shell-model properties and other times cluster properties.     

Reduced density matrices of a system of N coupled oscillators: 4. The eigenstructure of the p-particle matrices for the 2-temperature canonical ensemble

It is proved that the reduced p-particle matrix (p?N) corresponding to a 2-temperature equilibrium state of a system of N coupled oscillators (the two temperatures T_tr and T_re1 relating to the translational and relative motion of the latter) coincides with the density matrix of a two-temperature canonical ensemble of an effective system of p coupled oscillators, the effective temperature T?_re1 being equal to T_re1 while $\text{T}\text{?}{}_{\mathrm{tr}}\text{≠T}{}_{\mathrm{tr}}$, and in particular $\text{T}\text{?}{}_{\mathrm{tr}}\text{>0}$ for T_tr=0.     

The effect of local approximations in the ground-state coupled cluster wave function on electron affinities of large molecules

A possibility to calculate electron affinities (EAs) by a software devised for electron excitations is exploited to examine the accuracy of a partly local EA-EOM-CCSD method. In the proposed approach local approximations are applied to the ground-state coupled cluster wave function, while the EAs themselves are obtained in a full configurational space. The results of a numerical test for 14 molecules show that already with standard local settings the method reproduces the nonlocal EAs with the average error of 0.009?eV. Since the EA-EOM step of the calculation requires less computational resources than the computation of the CCSD ground state, the proposed hybrid approach can become a valuable tool for obtaining the EAs for molecules, which are too large for a canonical CCSD calculation, but still small enough for the EA-EOM step to be performed in a nonlocal way.     

Effect of side by side interactions on the thermodynamic properties of adsorbed CO molecules on the Ni(111) surface: a cluster model study

The effect of electrostatic interactions on vibrational frequencies and thermodynamic properties of CO adsorbate on the Ni(111) surface is calculated by taking the first and second nearest-neighbour interactions into account. In order to obtain reasonable results, the cluster model of various surface adsorption sites with CO adsorbate is partially optimized, using Density Functional Theory and also the MP2 method for the hcp site. Comparison between DFT and MP2 results shows that DFT results are more reliable for this system. The stretching and bending frequencies of CO adsorbate are calculated using both Partial Hessian Analysis and Cluster–Adsorbate Coupling methods. Stretching and bending frequencies are both shifted by the side by side interactions. The coupling of surface phonons and adsorbate vibrations reduces the side effects. The largest side effects on the vibrational internal energy, isochoric heat capacity, entropy and total Helmholtz free energy of adsorbed CO molecule calculated using the CAC method are found for 0.5 ML coverage. The results of the CAC method are better, but the PHA method can be used as a simple upper bound estimation. The adsorptive phase acts as an intelligent material in such a way that it changes its configuration in order to reduce the side effects.     

Shifts of one-electron ions lines from n = 0 interactions with electrons in hot and dense plasma

This paper is concerned with lineshifts of hydrogen-like ions due to electron collisions in dense and hot plasmas. These collisions are treated by including all effects due to monopole, dipole, and quadrupole interactions between radiator and electron perturbers. The latter follow exact hyperbolic trajectories with a possible penetrating part inside atomic orbits. A simple closed form for the line shift has been derived. Comparison between our semi-classical results and the quantum mechanical ones shows good agreement for a large range of high electron densities and temperatures. Received: 30 June 1997 / Revised: 28 April 1998 / Accepted: 29 April 1998     

A comparison between microscopic and empirical estimates of the density dependence of effective interactions

The effective interaction W which was recently deduced empirically from saturation considerations as an addition to the Sussex matrix elements is compared with earlier estimates of corrections arising from an assumed short-range repulsion and from the tensor force in second order.