First Principles Computations of Second-Order Elastic Constants (SOEC) and Equations of State of Rutile TiO₂

Table 4

Equation of state results for rutile TiO₂ with the Birch Murnaghan third-order equation. The energy-volume curve was fitted with eleven points, and the range of volume around equilibrium was chosen as ±10% using basis sets 1 and 2 (computational results with basis 2 shown in even-numbered rows). (See Sections 2, 3, 5, and 7). The value of the bulk modulus, 𝐵_EL, calculated separately, is given in the last column for comparison.

	𝐵EOS (GPa)	𝑉𝑜(Å^3)	𝐵EL (GPa)
HF	267.	62.29	270.
	293.	62.31	295.
LDA	241.	60.98	243.
	279.	59.84	283.
PWGGA	206.	64.09	208.
	239.	62.87	237.
PBE	202.	64.33	205.
	236.	63.10	235.
BLYP	191.	65.93	188.
	229.	64.45	231.
B3LYP	217.	63.81	220.
	252.	62.81	255.
B3PW	226.	62.66	229.
	256.	61.83	257.
PBE0	232.36	62.24	217.12
	263.	61.49	263.
Exps.[10, 29, 30, 33]	—	—	212.00, 230.00