De glaciēbus or deductive molecular mechanics of ice polymorphs

• Published in: Theoretical chemistry accounts 2018-11, Vol.137 (11), p.1-17, Article 138
• Main Author: Tchougréeff, Andrei L.
• Format: Article
• Language: English
• Subjects: Ammonia; Atomic/Molecular Structure and Spectra; Chemistry; Chemistry and Materials Science; CHITEL 2017 - Paris - France; Critical pressure; Cubane; Cyclobutane; Cyclopropane; Dipoles; Electronic structure; Hydrogen atoms; Inorganic Chemistry; Mathematical analysis; Matrix methods; Molecular structure; Orbitals; Organic Chemistry; Physical Chemistry; Pressure dependence; Regular Article; Theoretical and Computational Chemistry
• ISSN: 1432-881X; 1432-2234
• DOI: 10.1007/s00214-018-2322-0

Yet in 1960s Del Re with coworkers considered the electronic structure of organic molecules using hybrid orbitals. They studied the simplest molecules: CH 4 , NH 3 , H 2 O, and more complex ones: cyclopropane, cyclobutane, cubane, using either the optimal overlap or maximal localization principles to determine the hybrids. Later Malrieu with coworkers used hybrid orbitals in the PCILO method. Later, we determined either the form and orientation of the hybrid orbitals or two-electron functions of the two-center bonds constructed on the basis of these hybrids from the minimum condition for total electronic energy as implemented in the SLG method. This gave us significant improvement in the efficiency: the dependence of the required computational resources on the molecule size reduces down to O ( N ). The paradigm based on the usage of the variation principle for determination of either the hybrid orbitals or the elements of the reduced density matrices in their basis allows one to formulate and prove exact statements about electronic structure. We start from establishing the energy expression for highly symmetric non-molecular ice X and prove mathematically the stability of this polymorph above a critical pressure. Below it, we derive the pressure dependence of the interaction energy of the effective dipoles emerging in the system when the symmetric layout of the hydrogen atoms, specific for ice X, breaks down. This reproduces semiquantitatively the characteristic and unusual (as compared to the others—practically vertical) form of the boundary between the areas of the ordered and disordered ice VIII and VII. We also discuss the possibility of describing the differences between the ice phases existing at lower pressures (down to normal) by including the long-range electrostatic contributions: charge-charge and dipole-dipole in the crystal energy.