基于CASSCF参考函数的块相关耦合簇方法对烷烃中单键解离势能面研究

用以完全活化空间自洽场(CASSCF)波函数为参考波函数的块相关耦合簇(BCCC)方法(简称CAS-BCCC)研究了烷烃(甲烷和乙烷)中的单键解离过程的势能面(PES). 与其它理论方法比较的结果表明, 该方法可以对所研究的整个解离势能面给出定量准确的描述.     

Block-correlated coupled cluster theory: the general formulation and its application to the antiferromagnetic Heisenberg model

The general formalism of the block-correlated coupled cluster (BCCC) method, an alternative multireference coupled cluster method for calculating the ground-state electronic structures of molecular systems, has been presented. The BCCC theory is constructed in terms of a complete set of many-electron states of individual blocks, assumed that the whole system could be partitioned into a set of blocks. The reference state in the BCCC is selected as a tensor product of the most important many-electron state of each system block. By truncating the cluster operator to a certain n-block correlation level, an approximate but size-extensive BCCC method, denoted as BCCCn, is defined. For reducing the computational effort but without much loss of accuracy, the reduced density matrix is introduced to generate an optimal subset of many-electron states for each block. I have implemented the BCCCn (n=2,3) methods within the S=1/2 Heisenberg Hamiltonian, and applied them to calculate the ground-state energies of one-dimensional spin chains and quasi-one-dimensional two-leg spin ladders. The calculated results show that with the appropriate partition of the studied systems the BCCC3 method can yield quite satisfactory ground-state energies for these spin systems.     

Alternative single-reference coupled cluster approaches for multireference problems: the simpler, the better

We report a general implementation of alternative formulations of single-reference coupled cluster theory (extended, unitary, and variational) with arbitrary-order truncation of the cluster operator. These methods are applied to compute the energy of Ne and the equilibrium properties of HF and C(2). Potential energy curves for the dissociation of HF and the BeH(2) model computed with the extended, variational, and unitary coupled cluster approaches are compared to those obtained from the multireference coupled cluster approach of Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)] and the internally contracted multireference coupled cluster approach [F. A. Evangelista and J. Gauss, J. Chem. Phys. 134, 114102 (2011)]. In the case of Ne, HF, and C(2), the alternative coupled cluster approaches yield almost identical bond length, harmonic vibrational frequency, and anharmonic constant, which are more accurate than those from traditional coupled cluster theory. For potential energy curves, the alternative coupled cluster methods are found to be more accurate than traditional coupled cluster theory, but are three to ten times less accurate than multireference coupled cluster approaches. The most challenging benchmark, the BeH(2) model, highlights the strong dependence of the alternative coupled cluster theories on the choice of the Fermi vacuum. When evaluated by the accuracy to cost ratio, the alternative coupled cluster methods are not competitive with respect to traditional CC theory, in other words, the simplest theory is found to be the most effective one.     

Comparison of some multireference electronic structure methods in illustrative applications

The performances of several multireference electronic structure methods including complete active space self-consistent field (CASSCF)-based second-order perturbation theory (CASPT2), multireference configuration interaction with single and double excitations (MR-CISD), MR-CISD with the Davidson correction (MR-CISD+Q), and the CASSCF-based block-correlated coupled cluster method (CAS-BCCC4) we developed recently are compared by applying them to study several different chemical problems involving computation...     

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).     

Initial excited‐state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited‐state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight‐membered ring (locked‐11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS‐CASPT2, MS‐CASPT2) as well as single‐reference coupled‐cluster CC2 method. The analysis of XMCQDPT2‐based geometries reveals rather weak coupling between in‐plane and out‐of‐plane structural evolution and minor energetical relaxation of three locked‐11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out‐of‐plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground‐state structures, the excited‐state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4–0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked‐11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.     

Multireference State-specific Coupled Cluster Approach with the CAS Reference: Inserting Be into H2

An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled cluster (CC) method with an arbitrary level of the electronic excitations developed earlier in our laboratory have been employed to generate the CAS(2,2)CCSD code. CAS(2,2)CCSD is the state-specific, multireference coupled cluster (SSMRCC) approach with single and double excitations based on the CASSCF(2,2) reference wave function. The CAS(2,2)CCSD was used to describe the model process of inserting the Be atom into the H₂ molecule. We show that our method performs better than the “fully-blown” SSMRCC approach of Mukherjee and coworkers (J Chem Phys 110:6171, 1999).     

Basis set limit electronic excitation energies, ionization potentials, and electron affinities for the 3d transition metal atoms: Coupled cluster and multireference methods

Recently developed correlation consistent basis sets for the first row transition metal elements Sc-Zn have been utilized to determine complete basis set (CBS) scalar relativistic electron affinities, ionization potentials, and 4s(2)3d(n-2)-4s(1)d(n-1) electronic excitation energies with single reference coupled cluster methods [CCSD(T), CCSDT, and CCSDTQ] and multireference configuration interaction with three reference spaces: 3d4s, 3d4s4p, and 3d4s4p3d'. The theoretical values calculated with the highest order coupled cluster techniques at the CBS limit, including extrapolations to full configuration interaction, are well within 1 kcal/mol of the corresponding experimental data. For the early transition metal elements (Sc-Mn) the internally contracted multireference averaged coupled pair functional method yielded excellent agreement with experiment; however, the atomic properties for the late transition metals (Mn-Zn) proved to be much more difficult to describe with this level of theory, even with the largest reference function of the present work.     

A new size extensive multireference perturbation theory

A new multireference perturbation series is derived based on the Rayleigh–Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller–Plesset perturbation theory. It is demonstrated numerically that the present multireference second‐ and third‐order energies are size extensive by two types of supermolecules composed of H₂ and BH monomers. Spectroscopic constants of as well as the ground state energies of H₂O, NH₂, and CH₂ at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH₄ and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances. © 2013 Wiley Periodicals, Inc.     

Ab initio treatment of the chemical reaction precursor complex Cl(2P)-HF. 1. Three-dimensional diabatic potential energy surfaces

The three adiabatic potential surfaces of the Cl(2P)-HF complex that correlate with the 2P ground state of the Cl atom were calculated with the ab initio RCCSD(T) method (partially spin-restricted coupled cluster theory including single and double excitations and perturbative correction for the triples). With the aid of a geometry-dependent diabatic mixing angle, calculated by the complete active space self-consistent field (CASSCF) and multireference configuration-interaction (MRCI) methods, these adiabatic potential surfaces were converted to a set of four distinct diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the angle theta between the HF bond axis r and the Cl-HF intermolecular axis R. The dependence of the expansion coefficients on the Cl-HF distance R and the HF bond length r(HF) was fit to an analytic form. The strongest binding occurs for the hydrogen-bonded linear Cl-HF geometry, with D(e) = 676.5 cm(-1) and R(e) = 6.217 a0 when r(HF) = r(e) = 1.7328 a0. This binding energy D(e) depends strongly on r(HF), with larger r(HF) causing stronger binding. An important contribution to the binding energy is provided by the interaction between the quadrupole moment of the Cl(2P) atom and the dipole of HF. In agreement with this electrostatic picture, the ground state of linear Cl-HF is a 2-fold degenerate electronic Pi state. For the linear Cl-FH geometry the states are in opposite order, i.e., the Sigma state is lower in energy than the Pi state. The following paper in this issue describes full three-dimensional computations of the bound states of the Cl-HF complex, based on the ab initio diabatic potentials of this paper.     

Photoluminescence of oxygen-containing surface defects in germanium oxides: a theoretical study

Photoabsorption and photoluminescence properties of nonbridging oxygen -O-Ge[triple bond](NBO), -OO-Ge[triple bond] (peroxy radical), O=Ge=, and (O2)Ge= defects in germanium oxides have been investigated by high-level ab initio calculations. Geometry optimization for excited electronic states of model clusters simulating these defects was carried out at the complete-active-space self-consistent-field level, and relative energies were calculated by various methods including time-dependent density-functional theory, outer-valence Green's functions, equation-of-motion coupled cluster theory with single and double excitations, symmetry-adapted cluster configuration interaction, multireference second-order perturbation theory, and multireference configuration interaction. The results demonstrate that the considered excited states of the aforementioned defects normally exhibit large Stokes shifts and that, with few exceptions, UV photoabsorption is accompanied by red or IR photoluminescence.     

Higher excitations for an exponential multireference wavefunction Ansatz and single-reference based multireference coupled cluster Ansatz: application to model systems H(4), P(4), and BeH(2)

This article reports on the convergence of the exponential multireference wavefunction Ansatz (MRexpT) [J. Chem. Phys. 123, 84102 (2005)] and the single-reference based multireference coupled cluster Ansatz [J. Chem. Phys. 94, 1229 (1991)] with respect to higher cluster excitations. The approaches are applied to the H(4), P(4), and BeH(2) model systems according to the recently published analysis by Evangelista et al. [J. Chem. Phys. 125, 154113 (2006)]. The results show both MRexpT and SRMRCC to be highly accurate although SRMRCC shows problems due to its lack of Fermi vacuum invariance (symmetry breaking).     

Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method

We present the analytic gradient theory and its pilot implementation for the multireference Brillouin-Wigner coupled cluster (BWCC) method and for the state-universal multireference coupled cluster method. The analytic gradient has been derived for three cases: (i) BWCC method without a size-extensivity correction, (ii) BWCC method with the iterative size-extensivity correction, and (iii) for the rigorously size-extensive state-universal method. The pilot implementation is based on full-configuration interaction expansions and is presently limited to single and double excitation levels; however, the resulting equations are general. For BWCC methods, they also do not contain terms explicitly mixing amplitudes of different reference configurations and can thus be implemented in an efficient way. The analytic gradients have been verified with respect to numerically computed ones on the example of CH2 molecule, and geometry optimizations of CH2 and SiH2 have been carried out.