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

Table 1

The values of relaxed lattice constants (in Å), ambient volume (in ų), and total energy, 𝐸 (in a.u.), for rutile 𝑇𝑖𝑂₂. The computations used Hartree-Fock, DFT LDA, PWGGA, BLYP, B3LYP, and B3PW potentials using basis sets 1 and 2 (even numbered rows represent computational values obtained with basis set 2). The numbers within parentheses are percent differences from experiment. (See Sections 2, 3, 5, and 7).

	𝑎(Å)	𝑐(Å)	Vol.(Å^3)
HF	4.568 (−.54)	2.980 (.74)	62.11 (0)
	4.561 (−.70)	2.991 (1.10)	62.24 (0)
LDA	4.559 (.74)	2.932 (.87)	60.98 (2)
	4.539 (−1.18)	2.904 (−1.85)	59.84 (4)
PWGGA	4.640 (1)	2.976 (.33)	64.08 (2)
	4.619 (.56)	2.946 (−.40)	62.82 (1)
PBE	4.647 (1.17)	2.978 (.67)	64.32 (3)
	4.625 (.69)	2.949 (−.30)	63.05 (1.03)
BLYP	4.66 (1.45)	3.01 (1.75)	65.67 (5)
	4.657 (1.37)	2.971 (.43)	64.41 (3.12)
B3LYP	4.629 (.78)	2.976 (.60)	63.78 (2)
	4.607 (.21)	2.957 (−.03)	62.75 (.55)
B3PW	4.599 (.13)	2.961 (.10)	62.63 (0)
	4.583 (−.21)	2.942 (-.54)	61.81 (.95)
PBE0	4.627 (.73)	2.973 (.50)	63.69 (2)
	4.571 (−.48)	2.940 (−.61)	61.46 (1.52)
Exps. [2, 4, 10, 32]	4.593	2.958	62.40