Comparison of MBPT and coupled-cluster methods with full CI. Importance of triplet excitation and infinite summations

Results from full fourth-order perturbation theory [SDTQ MBPT(4)], and the coupled-cluster single- and double-excitation model (CCSD). are compared with recent full CI results for BH, HF, NH₃, and H₂O. For H₂O, studies include large symmetric displacements of the OH bonds, which offer a severe test for any single-reference MBPT/CC method. In every case. CCSD plus fourth-order triple-excitation terms provide agreement with the full CI to < 2 kcal/mole. SDTQ MBPT(4) has an error 10 kcal/mole for displaced H₂O.     

Applicability of multi-reference many-body perturbation theory to the determination of potential energy surfaces: A model study

The recently written CI -based multi-reference many-body perturbation theory (MR-MBPT ) program package is exploited to study a simple ab initio minimum basis set model involving four hydrogen atoms in a rectangular configuration. This model was examined earlier by several authors using both coupled cluster (CC ) and finite-order MBPT approaches. Here we present the MR-MBPT results up to the 50th order and examine the effect of various shifting techniques on the convergence behavior of this approach. It is shown that in contrast with CC methods, both single and MR finite-order MBPT potential energy calculations are plagued with convergency and intruder state problems, which can be particularly severe when the latter approach is employed for non-degenerate situations.     

求解弱相互作用分子A-BC的振转能级和波函数的SCF-CI方法

给出了一种计A－BC型弱相互作用分子体系的分子间振转激发态的自洽场-组态相互作用(SCF－CI)方法. 首先使用SCF方法代化径向伸缩振动和弯曲振动的基函数,再用CI方法确定精确的振转激发态能级. 在求解-维的伸缩振动SCF方程时,采用Numerov－Johnson算法在给定区间上求解获得振动波函数的数值解. 具体计算了Ar－HCI和Ar－N₂体系的振转激发态的能级以验证该方法. 结果表明,本方法可用较少的组态就能获得可与其它大计算量的方法具有相比拟的精度的结果.     

Predictions of molecular geometries and electronic spectra of complex unsaturated molecules from MC-LCAO-MO method with particular reference to triplet-triplet transitions of naphthalene

An MC-LCAO-MO approach which has been proposed for open-shell systems of unsaturated hydrocarbons having degenerate MO's is applied to naphthalene, calculating its molecular geometry and electronic spectrum. The results are compared with those obtained by the usual semi-empirical SCF-CI method and with experiment. As for benzene, anthracene, phenanthrene and triphenylene, the bond lengths and the -electron energies in their ground states are calculated in the same manner. Most of the calculated bond lengths are in fairly good agreement with experiment. The total -electron energies of the ground states obtained by the MC-LCAO-MO and SCF-CI methods agree within about 0.01 eV when CI is included and within about 0.1 eV when CI is not invoked. It is found that the electronic spectrum of naphthalene obtained by the present method is in good agreement with that derived from the SCF-CI method and also explains most part of experiments. A detailed discussion is given on the calculated triplet-triplet absorption spectrum and its intensity distribution of naphthalene.     

An SCF-CI method for determining the potential energy surface of a triatomic molecule

A self-consistent-field (SCF)-configuration interaction (CI) (SCF-CI) method for determining the potential energy surface of a triatomic molecule from the observed vibrational band origins has been suggested. By this method, the SCF-CI procedure in the internal coordinates is used to calculate the vibrational bond origins and their first derivatives with respect to parameters in the potential energy function using the exact vibrational Hamiltonian, and the optimizer LMF in the nonlinear-squares problem is employed to optimize parameters in the potential energy function. This approach is used to optimize the potential energy function of the water molecule. The standard deviation of this fitting to the 70 observed band origins is 1.154cm-1.     

Many-body perturbation theory and polarization propagator studies of the structure, energetics and excitation spectrum of CO3

Geometry optimization has been performed on CO₃ in the SCF approximation and in the second-, third-, and fourth-order MBPT approximations limited to single and double substitutions using a double-zeta plus polarization basis set. The energetics of the formation and decomposition of CO₃ from the reactions CO₂ + O(¹D) → CO₃ and CO₃ + CO → 2CO₂, respectively, have been calculated in several approximations including full fourth-order MBPT. In addition first-order polarization propagator calculations have been performed to identify the low-lying excited states.     

A comparison of different many-body perturbation theory calculations of the ground state of SiS

A comparison of different many-body perturbation theory (MBPT ) calculations of the ground state rotational and vibrational constants of SiS is made. The calculations are performed up to the complete fourth-order MBPT level, and in all cases two basis sets are utilized. The results of the third-order and some incomplete fourth-order calculations are in good agreement, but the complete fourth-order is among the worst as compared with the experimental data. Analysis of the different contributions to the calculated correlation eneriges points towards the necessity of including even higher-order terms of the(MBPT ) expansion.     

Many-body perturbation theory,coupled-pair many-electron theory,and the importance of quadruple excitations for the correlation problem

Many-body (diagrammatic) perturbation theory (MBPT ), coupled-pair many-electron theory (CPMET ), and configuration interaction (CI ) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO₂, HCN, N₂, CO, BH₃, and NH₃. It is demonstrated that the sum of double and quadruple excitation diagrams through fourth-order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the ¹∑ potential curve of Be₂. This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R. This is resolved once the quadruple excitation terms are fully included by CPMET .     

Is fifth-order MBPT enough?

Fifth- and higher-order MBPT results are reported for a series of examples, BH, Be₂, HF and H₂O, for which higher-order perturbation theory might be important. MBPT(5) differs from MBPT(4) by as much as 4.3 mh, and by constructing the size-extensive [2,1] Padé approximant, which is possible with E⁽⁵⁾, one can get exceptional agreement with the full CI results. Variational perturbation results are also reported.     

Near-degeneracy effects and efficiency of MBPT calculations of molecular properties. Polarizability curve of H2

The polarizability curve of H₂ is calculated by using the finite-field perturbation method. All self-consistency effects are accounted for at the HF level and many-body perturbation theory (MBPT) is used to evaluate the correlation contributions. Using a single HF determinant as a reference in MBPT calculations makes the near-degeneracy effects of essential importance on increasing the interatomic distance. Nevertheless, applying the MBPT scheme with appropriate fourth-order terms gives nearly exact values of both components of the polarizability tensor for interatomic distances up to ≈3.6 au.     

SCF and localized orbitals in ethylene: MBPT/CC results and comparison with one-million configuration Cl

Many-body perturbation theory (MBPT) and coupled-cluster (CC) calculations are performed on the ethylene molecule employing canonical SCF and simple bond-orbital localized orbitals (LO). Full fourth-order MBPT [i.e. SDTQ MBPT(4)], CC doubles (CCD) and CC singles and doubles (CCSD) energies are compared with the over one-million configuration ‘bench-mark” Cl calculation of Saxe et al. Though the SCF and LO reference determinant energies differ by 0.29706 hartree, the CCSD energy difference is only 1.7 mhartrees (mh). Our most extensive SCF orbital calculation, CCSD plus fourth-order triples, is found to be lower in energy than the CI result by 5.3 mh.     

13C carbonyl chemical shielding tensors: Comparing SCF,MBPT (2), and DFT predictions to experiment

In this work, we calculate the ¹³C nuclear magnetic resonance chemical shielding tensors for 18 carbonyl-containing compounds. The many-body perturbation theory (MBPT), self-consistent field (SCF), and density functional theory (DFT) formalisms were used with gauge including atomic orbitals (GIAO) to calculate the shielding tensors. Our data suggest that shielding tensors can be efficiently estimated by performing one MBPT(2) correlated calculation (e.g., at a reference geometry) and SCF-level calculations at other geometries and taking the SCF-to-correlated tensor element differences to be geometry independent. That is, the correlation contribution to the chemical shielding seems to be relatively constant over a considerable range of distortions. Treatment of correlation using DFT methods is shown to not be as systematically reliable as with MBPT(2). Data on 18 carbonyl compounds show that the single largest influence on the shielding tensor is the presence of nearby electron-withdrawing or electron-donating groups. Finally, although good agreement with powder or single-crystal experimental data is achieved for two or three tensor eigenvalues, systematic differences remain for one element; the origins of these differences are discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 875–894, 1997     

On multireference superdirect configuration interaction in third order

The superdirect configuration interaction (Sup-CI ) method has the usual versatility and stability of the CI methods with computational efficiency typical to that of the many-body methods, such as the many-body perturbation theory (MBPT ). The Hamilton operator is projected into a space of a few trial vectors, such as Krylov, Nesbet, or Møller–Plesset correction vectors. In this space, Hamiltonian matrix elements may be directly computed in the many-body fashion, as weighted sums of integral products over orbital indices. The variation-perturbation method based on the first-order wave function is equivalent to the Sup-CI method with a single correction vector of the Møller–Plesset type. Different points of view on the superdirect CI method are discussed and a version in which third-order contributions are computed for a relatively small (10–100) space of reference and correction vectors is tested. Selection of the best “effective first-order spaces” and size-extensivity corrections in Sup-CI are briefly discussed. Møoller–Plesset, Epstein–Nesbet, and other correction vectors are included in the model calculations on the symmetric stretch of bonds in water, acetylene, and the NH₂ molecule. Errors are almost independent of molecular geometry and the method appears to be superior than the multireference second-order perturbation methods. © 1994 John Wiley & Sons, Inc.     

CCSD(T) expectation value calculations of first-order properties

An expectation value approach to calculations of first-order properties using the non-iterative, triple-excitation amplitudes in the coupled cluster wave function is exploited. Three methods are suggested and analysed using the many body perturbation theory (MBPT) expansion arguments. The first method, in which non-iterative triple-excitation amplitudes are used in the expression for the expectation values, makes the wave function accurate through the second order of MBPT. In the second method, which is an extension of the first, effects of triple-excitation amplitudes are coupled with single- and double-excitation amplitudes. The correlated density matrix equivalent through the fourth order to that obtained when CCSDT-la amplitudes are used is employed in the third method. The suggested methods are tested on dipole moment and polarizability calculations for several diatomic closed-shell molecules and are compared to other related approaches. Received: 15 May 1997 / Accepted: 5 June 1997     

Elastic scattering of low-energy electrons by N2 including the effect of target electronic correlation

A procedure to use configuration-interaction (CI) target wave-functions in the electron–molecule collision theory is applied to study the elastic e⁻–N₂ scattering in the (5–20) eV incident energy range. Correlated static and exchange contributions to the interaction potential are presented. Two different atomic basis sets are used. Differential cross sections (DCS) obtained by using Hartree–Fock or CI wave-functions are presented and compared. In the CI case, single and double, and single, double and triple excitations are considered. The effect of electron correlation is analyzed in all the cases. The continuum wave-functions were obtained via the Schwinger variational iterative method. The influence on the DCS of both the size of the atomic basis set and the inclusion of higher-order excitations in the CI calculation is discussed.     

Use of coupled-cluster based linear response theory and multireference hermitian MBPT to IP calculations of HF

We report in this paper the results of outer and inner valence IP calculations for the HF molecule using two different many-body methods for the direct evaluation of energy differences. The first is the nonperturbative coupled-cluster based linear response theory (LRT) and the second is the hermitian open-shell many-body perturbation theory (MBPT). A Huzinaga-Dunning (9s5p→ 5s3p/3s) basis has been used. LRT uses an “ionization operator” S as in the equation of motion method (EOM) to generate the ionized states from a coupled-cluster type of ground state. S is chosen to consist of single ionization and ionization-cum-shake-up operators, thus treating the Koopmans as well as the shake-up states on equal footing. LRT would thus be capable of computing both the outer and the inner valence regions with equal facility. This is borne out by the results. For the open-shell MBPT, the model space is chosen to be spanned by the singly ionized determinants. The convergence of the results for the inner valence region is slow, and the results obtained from the [2, 1] Pade' approximants are presented. Unlike the LRT, the inner valence region is not reproduced with full complexity in MBPT, indicating that it is essential to modify the theory by way of expanding the model space to contain the shake-up determinants also.     

Integral dependent spin couplings in symmetry-adapted cluster (SAC) calculations

Numerical examples illustrate the single and double CI (SD CI) and symmetry-adapted cluster (SAC) results with integral dependent spin couplings for correlation energies compared to those with all spin couplings. The SAC with integral dependent spin couplings provides a practically useful method of incorporating higher order electron correlation only when the SCF reference function is a good zeroth-order approximation.     

Direct versus indirect many-body methods for calculating vertical electron affinities: applications to F−, OH− , NH2−, CN−, Cl−, SH− and PH2−

Electron propagator theory (EPT) is applied to calculating vertical ionization energies of the anions F⁻, Cl⁻, OH⁻,SH⁻, NH₂⁻, PH₂⁻ and CN⁻. Third-order and outer valence approximation (OVA) quasiparticle calculations are compared with ΔMBPT(4) (MBPT, many-body perturbation theory) results using the same basis sets. Agreement with experiment is satisfactory for EPT calculations except for F⁻ and OH⁻, while the ΔMBPT treatments fail for CN⁻. EPT(OVA) estimates are reliable when the discrepancy between second- and third-order results is small. Computational aspects are discussed, showing relative merits of direct and indirect methods for evaluating electron binding energies.     

Application of quadratic CI with singles,doubles, and triples (QCISDT): An attractive alternative to CCSDT

The size-extensive quadratic CI method with single(s), double(D ), and triple (T ) excitations, QCISDT , is compared with QCISD, QCISD (T ), CCSDT -n, and CCSDT . It is shown that QCISDT results are more accurate than are either QCISD or QCISD (T ) results. In particular, QCISDT turns out to be more stable than are QCISD and QCISD (T ) in cases with considerable multireference character. QCISDT and CCSDT results are of similar accuracy with slight advantages for the former method. Since QCISDT is much easier to implement on a computer than is CCSDT , it is an attractive alternative to CCSDT . © 1996 John Wiley & Sons, Inc.     

Theoretical study of the energetics of the O3(X̃ 1A1) → O2(X 3Σ−g) + O(3P) dissociation process

The dissociation energy (D_e) for the O₃(X̃ ¹A₁) → O₂(X ³Σ⁻_g) + O(³P) process is computed using MC SCF, CI, MBPT, and CCD methods. A full-valence MC SCF calculation utilizing a [9s5p3d1f/5s3p2d1f] basis set yields a D_e value of 0.43 eV, far below the experimental value of 1.13 eV, demonstrating the importance of correlation effects involving non-valence orbitals. A CI calculation in the same basis set allowing for all single and double excitations from three-reference configuration yields a D_e value of 0.72 eV. This value is increased to 1.06 eV when the Davidson correction is included. When the number of reference configurations is increased to eight, the resulting CI calculation gives a D_e value of 0.82 eV prior to the Davidson correction and 1.10 eV after this correction.