Fast electron-correlation methods for molecular crystals: An application to the α, β1, and β2 modifications of solid formic acid

A method for the routine first-principles determination of energies, structures, and phonons of molecular crystals by high-accuracy electron-correlation theories has been proposed. It approximates the energy per unit cell of a crystal by a sum of monomer and dimer energies in an embedding field of self-consistent (and, therefore, polarizable) atomic charges and dipole moments. First and second energy derivatives with respect to atom positions and lattice constants (useful for characterizing structures and phonons) have also been computed efficiently with a long-range electrostatic correction. The method has been applied to solid formic acid modeled as infinite one-dimensional hydrogen-bonded chains. Accurate energies (with corrections for basis-set superposition errors), structural parameters, and frequencies have been obtained for three polymorphic structures (beta(1), beta(2), and alpha) with second-order perturbation theory or higher. On this basis, reliable assignments of their infrared, Raman, and inelastic neutron scattering spectral bands have been proposed. The diffraction and spectroscopic data are shown to be consistent with the pristine beta(1) form and the hitherto-inexplicable infrared band splitting can be assigned to the in-phase and out-of-phase vibrations of adjacent hydrogen-bonded molecules rather than speculated polymorphism. Spectral features expected from the beta(2) and alpha forms have also been predicted and are found to be incompatible with the observed Raman and inelastic neutron scattering spectra in the low-frequency region.