Although the quasi-harmonic approximation (QHA) method applies to many materials, it is necessary to study the anharmonic interaction for extremely anharmonic materials. In this work, the unusual negative thermal expansion (NTE) property of CaTiF 6 is studied by combing QHA and anharmonic interaction. The improved self-consistent phonon approximation (ISCPA), which treats anharmonic effects in solids nonperturbatively, is employed. The agreement of NTE behavior between the calculation and the experiment can be further promoted from qualitative consistency by QHA to quantitative consistency by the ISCPA. From mode Grüneisen parameters, it is found that the low-frequency phonons, especially acoustic phonons, contribute greatly to the NTE behavior of CaTiF 6 . The rigid unit modes (RUMs) of low-frequency optical phonons can be identified. The phonon lifetime of CaTiF 6 is calculated from three-phonon interactions; thereby, the NTE mechanism can be further explored by phonon lifetimes of phonons with different frequencies on heating. The anomalous lattice thermal conductivity (LTC) is predicted using the Boltzmann transport equation within the relaxation time approximation. The glasslike LTC can occur in crystal CaTiF 6 .
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