Ice Ih is arguably the most important molecular crystal in nature, yet our understanding of its structural and dynamical properties is still far from complete. We present embedded-fragment calculations of the structures and vibrational spectra of the three-dimensional, proton-disordered phase of ice Ih performed at the level of second-order many-body perturbation theory with a basis-set superposition error correction. Our calculations address previous controversies such as the one related to the O-H bond length as well as the existence of two types of hydrogen bonds with strengths differing by a factor of two. For the latter, our calculations suggest that the observed spectral features arise from the directionality or the anisotropy of collective hydrogen-bond stretching vibrations rather than the previously suggested vastly different force constants. We also report a capability to efficiently compute infrared and Raman intensities of a periodic solid. Our approach reproduces the infrared and Raman spectra, the variation of inelastic neutron scattering spectra with deuterium concentration, and the anomaly of heat capacities at low temperatures for ice Ih.

Conspectus Molecular crystals are chemists' solids in the sense that their structures and properties can be understood in terms of those of the constituent molecules merely perturbed by a crystalline environment. They form a large and important class of solids including ices of atmospheric species, drugs, explosives, and even some organic optoelectronic materials and supramolecular assemblies. Recently, surprisingly simple yet extremely efficient, versatile, easily implemented, and systematically accurate electronic structure methods for molecular crystals have been developed. The methods, collectively referred to as the embedded-fragment scheme, divide a crystal into monomers and overlapping dimers and apply modern molecular electronic structure methods and software to these fragments of the crystal that are embedded in a self-consistently determined crystalline electrostatic field. They enable facile applications of accurate but otherwise prohibitively expensive ab initio molecular orbital theories such as Møller-Plesset perturbation and coupled-cluster theories to a broad range of properties of solids such as internal energies, enthalpies, structures, equation of state, phonon dispersion curves and density of states, infrared and Raman spectra (including band intensities and sometimes anharmonic effects), inelastic neutron scattering spectra, heat capacities, Gibbs energies, and phase diagrams, while accounting for many-body electrostatic (namely, induction or polarization) effects as well as two-body exchange and dispersion interactions from first principles. They can fundamentally alter the role of computing in the studies of molecular crystals in the same way ab initio molecular orbital theories have transformed research practices in gas-phase physical chemistry and synthetic chemistry in the last half century. In this Account, after a brief summary of formalisms and algorithms, we discuss applications of these methods performed in our group as compelling illustrations of their unprecedented power in addressing some of the outstanding problems of solid-state chemistry, high-pressure chemistry, or geochemistry. They are the structure and spectra of ice Ih, in particular, the origin of two peaks in the hydrogen-bond-stretching region of its inelastic neutron scattering spectra, a solid-solid phase transition from CO2-I to elusive, metastable CO2-III, pressure tuning of Fermi resonance in solid CO2, and the structure and spectra of solid formic acid, all at the level of second-order Møller-Plesset perturbation theory or higher.

Despite its terrestrial abundance and astrochemical significance, many aspects of the phase diagram of solid carbon dioxide remain uncertain or unknown. The observed transition pressures from cubic to orthorhombic phase range widely from 2.5 GPa at 80 K to above 18 GPa at room temperature. The vibrational Raman bands that appear at higher pressure and serve as a decisive proof of the existence of the orthorhombic phase have never been assigned. Here we introduce a general ab initio computational method that can predict the Gibbs free energies and thus phase diagrams of molecular crystals. Using this with secondorder Møller-Plesset perturbation theory, we obtain the transition pressure of 13 GPa at 0 K with small temperature dependence, which is in line with many experiments. We also computationally reproduce the vibrational Raman bands and explain the pressure dependence of the structure parameters and Raman band positions of both phases quantitatively.

ABSTRACT:A linear-scaling electron-correlation method based on a truncated many-body expansion of the energies of molecular crystals has been applied to solid hydrogen fluoride. The energies, structures, harmonic, and anharmonic frequencies of the infrared-and/or Raman-active vibrations, phonon dispersions, and inelastic neutron scattering (INS) of the solid have been simulated employing an infinite, periodic, onedimensional zigzag hydrogen-bonded chain model. The Hartree-Fock, second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with a noniterative triples correction [CCSD(T)] methods have been combined with the aug-ccpVDZ and aug-cc-pVTZ basis sets and, in some instances, the counterpoise corrections of the basis-set superposition errors. The computed structural parameters agree with the observed within 0.1-0.2 Å and a few degrees, and the anharmonic frequencies obtained by vibrational MP2 allowing two-phonon couplings reproduce the observed frequencies