Post-Hartree-Fock Methods and Electron Correlation: A Very Brief Overview

2020 ◽  
pp. 379-399
Author(s):  
Jochen Autschbach
Keyword(s):  
Electron Correlation ◽  
Electron System ◽  
Open Shell ◽  
Basis Set ◽  
Coupled Cluster ◽  
Hartree Fock ◽  
Dynamic Correlation ◽  
Static Correlation ◽  
Full Ci ◽  
Virtual Orbitals

‘This chapter sketches how the electron correlation is treated in post-Hartree-Fock (HF) wavefunction methods. The distinction between static and dynamic correlation is explained. A configuration interaction (CI) wavefunction is a linear combination of several or many Slater determinants (SDs). Following a HF calculation, different SDs can be constructed by replacing 1, 2, 3, … occupied orbitals in the HF wavefunction with 1, 2, 3,… unoccupied or virtual orbitals, leading to pseudo-excited electron configurations at the singles, doubles, triples, … (S, D, T, …) level. The virtual orbitals are usually available as a by-product of the HF calculation in a basis set. Full CI (FCI) considers all possible substitutions, up to N-fold for an N-electron system. FCI is impractical for all but the smallest molecules. CI truncated at a lower level, e.g. S and D, suffers from lack of size extensitivity. Truncated coupled-cluster (CC) is size extensive. Open-shell systems generally require a multi-reference treatment. The chapter concludes with a treatment of the static correlation in the bond breaking of H2.

Accuracy Assessment of the ROHF-CCSD(T) Calculationsof Dipole Moments of Small Radicals

1998 ◽  
Vol 63 (9) ◽  
pp. 1409-1430 ◽  
Author(s):  
Miroslav Urban ◽  
Pavel Neogrády ◽  
Juraj Raab ◽  
Geerd H. F. Diercksen
Keyword(s):  
Large Deviation ◽  
Theoretical Calculations ◽  
Dipole Moments ◽  
Accuracy Assessment ◽  
Open Shell ◽  
Basis Set ◽  
Coupled Cluster ◽  
Hartree Fock ◽  
Experimental Values

Dipole moments of a series of radicals, OH, NO, NS, SF, SO, PO, ClO, CN, LiO, NO2, and ClO2 were calculated by the Coupled Cluster CCSD(T) method with the single determinant restricted open shell Hartree-Fock (ROHF) reference. For all molecules theoretical dipole moments were carefully compared to experimental values. The size and the quality of the basis set were systematically improved. Spin adaptation in the ROHF-CCSD(T) method, largest single and double excitation amplitudes and the T1 diagnostics were considered as indicators in the quality assessment of calculated dipole moments. For most molecules the accuracy within 0.01-0.03 D was readily obtained. For ClO and CN the spin adaptation was necessary - its contribution was as large as 0.03-0.045 D. Large deviation from experiment is observed for OH in its A2Σ+ excited state (0.135 D) and especially for LiO in its 2Π ground state (0.22 D). No indication of the failure of theoretical calculations was found which leads to the conclusion that, even if there is still a space for the improvement of theoretical calculations, experimental values should be reconsidered.

Analytic energy gradients for open-shell coupled-cluster singles and doubles (CCSD) calculations using restricted open-shell Hartree—Fock (ROHF) reference functions

1991 ◽  
Vol 182 (3-4) ◽  
pp. 207-215 ◽  
Author(s):  
Jürgen Gauss ◽  
Walter J. Lauderdale ◽  
John F. Stanton ◽  
John D. Watts ◽  
Rodney J. Bartlett
Keyword(s):  
Open Shell ◽  
Coupled Cluster ◽  
Hartree Fock ◽  
Reference Functions

Ab initio predictions of the zero field splittings and the singlet–triplet transition strengths for the n → π* transition of selenoformaldehyde

1993 ◽  
Vol 71 (10) ◽  
pp. 1706-1712 ◽  
Author(s):  
D.C. Moule ◽  
L. Chantranupong ◽  
R.H. Judge ◽  
D.J. Clouthier
Keyword(s):  
Energy Levels ◽  
Random Phase ◽  
Open Shell ◽  
Oscillator Strengths ◽  
Basis Set ◽  
Zero Field ◽  
Zero Field Splitting ◽  
Hartree Fock ◽  
Lower Valence ◽  
Polarization Functions

The energy levels of the lower valence and Rydberg states of selenoformaldehyde, CH2Se, have been calculated by the SCF/CI method. Wavefunctions for the ROHF (restricted open shell Hartree–Fock) states were obtained with the Binnings–Curtis double-ζ basis set, augmented with Rydberg and polarization functions. Configuration interaction was applied to the parent configurations, PCMO (parent configuration molecular orbital). Oscillator strengths were evaluated for the allowed electric dipole transitions by the RPA (random phase approximation), and SOPPA (second-order polarization propagator approximation) methods. The spin-orbit contribution to the zero field splitting of the first triplet state, 3A2(n,π*) as well as the oscillator strengths to the three spin components were calculated by perturbation theory. These calculations predict that the Sx, Sy, and Sz components are shifted by −96.091,−96.707, and + 29.167 cm−1, respectively, from their unperturbed position. The oscillator strengths for the three components fx, fy, and fz of the 3A2(n,π*) ← 1A1(g.s.) transition were calculated to be 3.45 × 10−7, 1.15 × 10−7, and 173.0 × 10−7.

Spin adapted restricted Hartree–Fock reference coupled cluster theory for open shell systems

1994 ◽  
Vol 100 (5) ◽  
pp. 3706-3716 ◽  
Author(s):  
Pavel Neogrády ◽  
Miroslav Urban ◽  
Ivan Hubac̆
Keyword(s):  
Open Shell ◽  
Coupled Cluster ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Hartree Fock
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