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.     

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.     

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.     

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.     

Beryllium dimer,a critical test case of MBPT and CI methods

The ground-state potential curve for the beryllium dimer is calculated as a critical test case for methods based on many-body perturbation theory (MBPT ) and configuration interaction (CI ). In particular, the recently proposed double excitation (DE ) MBPT method is compared to the standard SCF-CI method including single and double excitations from a single reference determinant. The SCF-CI method is shown to give surprisingly accurate results compared to more complete CI calculations including a larger configuration space, whereas the DE-MBPT method breaks down more or less completely, particularly for larger basis sets. The results thus demonstrate the importance of including the renormalization terms in this case. Finally, Davidson's correction and related methods lead to an even more severe breakdown than the DE-MBPT method.     

Finite-field many-body perturbation theory IV. Basis set optimization in MBPT calculations of molecular properties. Molecular quadrupole moments

The choice of truncated basis sets and their optimization for MBPT calculations of molecular properties are discussed. It is pointed out that computing the correlation corrections to some kth order property by using the MBPT approach requires the knowledge of accurate perturbed orbitals through the kth order. Hence, it is argued that the basis set functions can be optimized with respect to the perturbed energies calculated within the coupled Hartree-Fock method. The proposed procedure is illustrated by MBPT calculations of quadrupole moments of H₂ and FH. Additionally, also some estimates of the quadrupole polarizability tensor components for these molecules are obtained.     

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     

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.     

Electronic structure and vertical excitation spectrum of methylene amidogen CH2N

Ab initio electronic structure calculations are reported for five electronic states of the methylene amidogen radical. Structure parameters for the ground electronic state are predicted by RHF and D -MBPT (4) calculations. Vertical excitation energies were determined using four different theoretical chemical models: complete active space (CAS ) MCSCF , CAS /MCSCF plus singles and doubles Cl, fourth-order many-body perturbation theory SDQ -MBPT (4), and coupled-cluster theory.     

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.     

Finite-field many-body perturbation theory. X. Electric field gradients and other properties of N2

Finite-field MBPT calculations have been carried out for the electric field gradient and other electric properties of the nitrogen molecule. On the basis of correlation corrections computed through the fourth order in the electron correlation perturbation the infinite order MBPT result for the electric field gradient at the nitrogen nucleus has been estimated. The corresponding result combined with the NQR coupling constant for N₂ leads to the ¹⁴N nuclear quadrupole moment of 0.0205 ± 0.0010 barn in agreement with the experimental atomic measurement and other molecular calculations. The MBPT estimate of the quadrupole moment of N₂ gives −1.107 ± 0.038 au in agreement with the most recent experimental value.     

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.     

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     

Application of many-body perturbation theory in the localized representation for the all-trans conjugated polyenes

Ab initio self-consistent field (SCF ) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C_2n+2H_2n+4. The canonical occupied and virtual molecular orbitals (MO s) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT , the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.     

A note on the direct calculation of excitation energies by quasi-degenerate MBPT and coupled-cluster theory

For excitation energy calculations using quasi-degenerate MBPT or coupled-cluster (CC) theory, the hitherto chosen strategy has been to have particle-hole (p-h) determinants forming the model space and to use standard formalisms originally developed for complete model spaces. In view of our recent analysis, the p-h determinants constitute an incomplete model space for which intermediate normalization (IN) of the wave-operator Ω is not appropriate if a linked formulation is desired. The theoretical status of earlier applications which had used formulae appropriate to IN, yet ignored disconnected diagrams, is analyzed. It is shown that if only excitation energies, rather than the full Ω, are desired, then no theoretical error is made. The situation is, however, fortuitous in that for mp-mh model spaces with m > 1, a similar procedure using IN would necessarily generate disconnected diagrams.     

Information theoretic indices for characterization of chemical structures. By Danail Bonchev Wiley,New York, 1983

Wilson, Jankowski, and Paldus have recently applied nondegenerate many-body perturbation theory (MBPT ) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H₄). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low-order sum of the perturbation series is not very meaningful, depends strongly on details of the zero-order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.     

Localized orbitals for the description of molecular interaction

The intermolecular interaction between the molecules CH₂O and NH₃ was investigated by the supermolecule method. The interaction energies were first calculated at the ab initio SCF level, and the electron correlation was included via second-order Møller-Plesset perturbation theory (MP 2). The basis set superposition error (BSSE ) was taken into account by the counter-poise (CP ) method. The occupied and the virtual canonical molecular orbitals (CMOS ) of the supermolecule were separately localized by the Boys' procedure. The correlation correction was calculated by the many-body perturbation theory (MBPT ) in the localized representation. Contributions of the third- and fourth-order localized diagrams were added to those of the second-order canonical diagram. This procedure gives a correction nearly equivalent to that of MP 2. The possibility to separate LMO contributions responsible for the dispersion interaction was investigated.     

Synthesis and Crystal Structure of [NiL_2(H_2O)_2](ClO_4)_2L=MBPT=4-P-methylphenyl-3,5-bis-(pyridin-2-yl)-1,2,4-triazole

The substituted l,2,4-triazoles are very useful ligands in coordination chemistry'-'. It isvery interesting that some complexes containing substituted l,2,4-triazoles ligands havethe spin-crossover phenomena, which could be used as magnetic materials4-5. However,complexes containing triaryltriazole ligands have been little known so far. We haverecently synthesized some triaryltriazole compounds'-', and we first report here thesynthesis and crystal structure of [Ni(MBPT),(H,O),](CIO.),.Expe…     

Quadratic Padé approximants and the intruder state problem of multireference perturbation methods

Simple and quadratic Padé resummation methods are applied to high‐order series from multireference many‐body perturbation theory (MR‐MBPT) calculations using various partitioning schemes (Møller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low‐lying excited states of (i) CH₂, (ii) BeH₂ at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Padé approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Padé method generally outperforms the simple Padé resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

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.