Second-order many-body perturbation study on thermal expansion of solid carbon dioxide

An embedded-fragment ab initio second-order many-body perturbation (MP2) method is applied to an infinite three-dimensional crystal of carbon dioxide phase I (CO₂-I), using the aug-cc-pVDZ and aug-cc-pVTZ basis sets, the latter in conjunction with a counterpoise correction for the basis-set superposition error. The equation of state, phonon frequencies, bulk modulus, heat capacity, Grüneisen parameter (including mode Grüneisen parameters for acoustic modes), thermal expansion coefficient (α), and thermal pressure coefficient (β) are computed. Of the factors that enter the expression of α, MP2 reproduces the experimental values of the heat capacity, Grüneisen parameter, and molar volume accurately. However, it proves to be exceedingly difficult to determine the remaining factor, the bulk modulus (B₀), the computed value of which deviates from the observed value by 50-100%. As a result, α calculated by MP2 is systematically too low, while having the correct temperature dependence. The thermal pressure coefficient, β = αB₀, which is independent of B₀, is more accurately reproduced by theory up to 100 K.