Abstract
In this chapter, we review some recent developments in our XP-PCM method to introduce the effect of high pressure (\(\text {p} >1\) GPa) in the quantum chemistry study of molecular properties and processes. After a presentation of the physical basis and the computational aspects of the XP-PCM model, we give examples of its recent applications. These applications regard the study and analysis of the electron distribution, of the equilibrium geometry, and of the vibrational frequencies of molecular systems under high pressure.
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Notes
- 1.
- 2.
The factor 1 / 2 in front to the operator \(\hat{V}_{e}({|\varPsi >})\) is due to the nonlinear nature of this operator, and \({\tilde{V}}_{nn}\) is the nuclei–nuclei interaction contribution in the presence of the external medium.
- 3.
Formally, the Pauli repulsion operator for N electrons of Eq. (12.2) may be written as \(\hat{V}_{r}=\hat{v}_r(\mathbf r)\) with \(\hat{v}_r(\mathbf r)=\delta (\mathbf {r}-\mathbf {r'}_i)V_0 \varTheta (\mathbf {r})\).
- 4.
An uncoupled molecular orbital (MO) perturbation scheme is a perturbation method that evaluates the effect of the perturbation on the molecular orbital by neglecting the effects that the perturbation has on the electron–electron repulsion contribution of the Fock operator.
- 5.
For reasons of space, we can no further discuss this connection between our XP-PCM theory with the Bell theory and its extensions.
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Here we assume that the geometry of the cavity remains fixed during the geometry optimization of the molecular solute. As pointed out in the previous section, this assumption implies that the electronic free-energy functional \(G_{e-r}\) acts as potential energy surface for the nuclei of the solute
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Acknowledgements
The author thanks Dr. M. Frisch (Gaussian Inc.) for collaboration, Prof. B. Kirtmann (University of California, Santa Barbara) for discussions on the pressure effects on the vibrational properties, and all the Editors for the invitation to contribute to this book. The systematic application of the XP-PCM method to the study of various molecular properties and processes under high pressure has required fruitful collaborations with many people (C. Cappelli, B. Mennucci, J. Tomasi, G. Cardini, M. Pagliai, V. Schettino, M. Ehara, and R. Fukuda) that are here collectively acknowledged. Dr. M. Paglia (University of Florence, Italy) is also thanked for graphic material used in Fig. 12.2.
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Cammi, R. (2018). Quantum Chemistry at the High Pressures: The eXtreme Pressure Polarizable Continuum Model (XP-PCM). In: Wójcik, M., Nakatsuji, H., Kirtman, B., Ozaki, Y. (eds) Frontiers of Quantum Chemistry. Springer, Singapore. https://doi.org/10.1007/978-981-10-5651-2_12
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