Variational Form of Van Vleck Degenerate Perturbation Theory with Particular Application to Electronic Structure Problems

1968 ◽  
Vol 49 (9) ◽  
pp. 3890-3894 ◽  
Author(s):  
Bernard Kirtman
Keyword(s):  
Perturbation Theory ◽  
Electronic Structure ◽  
Variational Form ◽  
Van Vleck ◽  
Degenerate Perturbation Theory

The application of analytical methods in degenerate perturbation theory

1974 ◽  
Vol 21 (3) ◽  
pp. 1229-1233
Author(s):  
A. G. Makhanek ◽  
V. S. Korol'kov ◽  
A. F. Fedorov
Keyword(s):  
Perturbation Theory ◽  
Analytical Methods ◽  
Degenerate Perturbation Theory

scholarly journals Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

2021 ◽  
Vol 8 ◽  
Author(s):  
Qin Yang ◽  
Marco Mendolicchio ◽  
Vincenzo Barone ◽  
Julien Bloino
Keyword(s):  
Perturbation Theory ◽  
Electronic Structure ◽  
Density Functional ◽  
Computational Cost ◽  
Theoretical Data ◽  
Infrared Region ◽  
Second Order ◽  
Basis Set ◽  
Molecular Systems ◽  
The Impact

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or “black-box” protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.

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