4.3.5 Symmetry

Symmetry is a powerful branch of mathematics and is often exploited in quantum chemistry, both to reduce the computational workload and to classify the final results obtained. ¹¹⁷³ Takada T., Dupuis M., King H. F.
J. Chem. Phys.
(1981), 75, pp. 332. Link ^{, 308} Dupuis M., King H. F.
Int. J. Quantum Chem.
(1977), 11, pp. 613. Link ^{, 309} Dupuis M., King H. F.
J. Chem. Phys.
(1978), 68, pp. 3998. Link Q-Chem is able to determine the point group symmetry of the molecular nuclei and, on completion of the SCF procedure, classify the symmetry of molecular orbitals, and provide symmetry decomposition of kinetic and nuclear attraction energy (see Chapter 10).

Molecular systems possessing point group symmetry offer the possibility of large savings of computational time, by avoiding calculations of integrals which are equivalent i.e., those integrals which can be mapped on to one another under one of the symmetry operations of the molecular point group. The Q-Chem default is to use symmetry to reduce computational time, when possible.

There are several keywords that are related to symmetry, which causes frequent confusion. SYM_IGNORE controls symmetry throughout all modules. The default is FALSE. In some cases it may be desirable to turn off symmetry altogether, for example if you do not want Q-Chem to reorient the molecule into the standard nuclear orientation, or if you want to turn it off for finite difference calculations. If the SYM_IGNORE keyword is set to TRUE then the coordinates will not be altered from the input, and the point group will be set to $C_1$.

The SYMMETRY keyword controls symmetry in some integral routines. It is set to TRUE by default. Note that setting it to FALSE does not turn point group symmetry off, and does not disable symmetry in the coupled-cluster suite (CCMAN and CCMAN2), which is controlled by CC_SYMMETRY (see Chapters 6 and 7), although we noticed that sometimes it may interfere with the determination of orbital symmetries, possibly due to numerical noise. In some cases, SYMMETRY = TRUE can cause problems (poor convergence and wildly incorrect SCF energies) and turning it off can avoid these problems.

The symmetry is turned off when ghost atoms are used because their placement may break the symmetry of the molecular structure. However, the user can force calculation to use symmetry by FORCE_SYMMETRY_ON keyword; this is illustrated in example 7.10.8.2.

Note:  The user should be aware about different conventions for defining symmetry elements. The arbitrariness affects, for example, $C_{\mathrm{2}\mathbf{}v}$ point group. The specific choice affects how the irreducible representations in the affected groups are labeled. For example, $b_{\mathrm{1}}$ and $b_{\mathrm{2}}$ irreducible representations in $C_{\mathrm{2}\mathbf{}v}$ are flipped when using different conventions. Q-Chem uses non-Mulliken symmetry convention. See http://iopenshell.usc.edu/howto/symmetry for detailed explanations.