Abstract
The electronic structure of transition metal oxides is frequently studied using density functional theory. Nonetheless, the electronic structure of VO3 has been found to be sensitive to the choice of functional. As a consequence, the basic question of whether or not the ground electronic state exhibits a Jahn-Teller distortion has yet to be resolved. Using basis sets of triple zeta quality and multireference configuration interaction wave functions as large as 700 million configuration state functions, we determine that the ground electronic state of VO3 is a 2 A 2 state in C3v symmetry. The first two excited electronic states are also characterized and found to be the components of a degenerate 2 E state, in C3v symmetry, which exhibits a small Jahn-Teller distortion. The Jahn-Teller stabilization energy is only 40 cm−1 and the barrier to pseudo-rotation is 9 cm−1. This 2 E state exhibits some unexpected properties. In the vicinity of the minimum energy conical intersection, the local topography appears almost quadratic, rather than linear, in the Jahn-Teller active coordinates. This gives rise to three symmetry-related seams of conical intersections in addition to the symmetry-required seam and results in the suppression of the geometric phase effect. These features, attributable to small linear Jahn-Teller parameters, are usually found in states characterized by e 2 (or e 3 e ′ ) electron configurations rather than the e 3 configuration found here. In addition to its Jahn-Teller minimum, the first excited state exhibits a second minimum with a structure significantly distorted from C3v. A conical intersection with Cs symmetry connects the two minima and puts an upper limit of 190 cm−1 on the barrier connecting these minima.
The preponderance of this work was performed while E.M.Y.L. was an undergraduate at the Johns Hopkins University. E.M.Y.L. acknowledges helpful conversations with Joseph Dillon. This work was supported by the National Science Foundation Grant No. CHE-1010644 to D.R.Y.
I. INTRODUCTION
II. THEORETICAL APPROACH
A. Description of and VO_{3}
B. Extrema
C. Potential energy surfacetopography
III. CONCLUSIONS
Key Topics
- Jahn Teller effect
- 27.0
- Excited states
- 17.0
- Ground states
- 16.0
- Electronic structure
- 13.0
- Potential energy surfaces
- 13.0
Figures
(a) From left to right, HOMO, HOMO-1, HOMO-2, HOMO-3 of the anion at .(b) From left to right, SOMOs of the ground state wave function at and for the first excited state wave function at , , and . Each state's point group symmetry, bond lengths and bond angles are given.
(a) From left to right, HOMO, HOMO-1, HOMO-2, HOMO-3 of the anion at .(b) From left to right, SOMOs of the ground state wave function at and for the first excited state wave function at , , and . Each state's point group symmetry, bond lengths and bond angles are given.
g and h vectors at (a) and (b) . Each vector has a top (left) and a side (right) view.
g and h vectors at (a) and (b) . Each vector has a top (left) and a side (right) view.
Calculated ab initio MRCI potential energy surfaces along the out-of-plane bending mode for the 2 A 2′, 2 E′, and 2 A 1″ electronic states. The origin is . The out-of-plane angle (θ) is in degrees. The 2 E′ surface (blue and green lines) depicts both the D3h and C3v conical intersections.
Calculated ab initio MRCI potential energy surfaces along the out-of-plane bending mode for the 2 A 2′, 2 E′, and 2 A 1″ electronic states. The origin is . The out-of-plane angle (θ) is in degrees. The 2 E′ surface (blue and green lines) depicts both the D3h and C3v conical intersections.
The vicinity of displaced along its g-direction. The magnitude of displacement is indicated by changes in the V-O(1) bond length. The conical intersection is at R(V-O(1)) = 1.628 Å. Displacements take the C3v point to Cs points.
The vicinity of displaced along its g-direction. The magnitude of displacement is indicated by changes in the V-O(1) bond length. The conical intersection is at R(V-O(1)) = 1.628 Å. Displacements take the C3v point to Cs points.
The vicinity of displaced along its g-direction. The magnitude of displacement is indicated by changes in the V-O(1) bond length. The conical intersection is at R(V-O(1)) = 1.627 Å. Displacements take the D3h point to C2v points.
The vicinity of displaced along its g-direction. The magnitude of displacement is indicated by changes in the V-O(1) bond length. The conical intersection is at R(V-O(1)) = 1.627 Å. Displacements take the D3h point to C2v points.
Linear interpolation path connecting the D3h conical intersection, , and a C2v ground state saddle point, , defined in Table II . Some geometry measurements (bond lengths and angles) are shown for the conical intersection and the ground state saddle point.
Linear interpolation path connecting the D3h conical intersection, , and a C2v ground state saddle point, , defined in Table II . Some geometry measurements (bond lengths and angles) are shown for the conical intersection and the ground state saddle point.
Tables
Comparison of expansion at the D3h ground state saddle point. The number of CSFs is given in Cs symmetry, and the total number of CSFs is the sum of A′ and A′′ CSFs. Relative energy is the energy difference between the ground state and the state of interest.
Comparison of expansion at the D3h ground state saddle point. The number of CSFs is given in Cs symmetry, and the total number of CSFs is the sum of A′ and A′′ CSFs. Relative energy is the energy difference between the ground state and the state of interest.
Anion minimum and critical points for the lowest three electronic states of neutral are reported. Bond lengths are in Å, and the bond angles are in degrees. Energy (cm−1) is relative to E 1( ). Energy of optimized state is in bold italic typeface. Here, is the minimum geometry of state J. The symmetry of the optimized state J is denoted below the symbol Q J . is a saddle point of state J, and is the geometry at the minimum energy crossing (mex) of states I and J. Results from Ref. 15 are in parenthesis.
Anion minimum and critical points for the lowest three electronic states of neutral are reported. Bond lengths are in Å, and the bond angles are in degrees. Energy (cm−1) is relative to E 1( ). Energy of optimized state is in bold italic typeface. Here, is the minimum geometry of state J. The symmetry of the optimized state J is denoted below the symbol Q J . is a saddle point of state J, and is the geometry at the minimum energy crossing (mex) of states I and J. Results from Ref. 15 are in parenthesis.
Harmonic vibrational frequencies (cm−1) of VO3 and VO3 −. The D3h symmetry designations are applicable to and only.
Harmonic vibrational frequencies (cm−1) of VO3 and VO3 −. The D3h symmetry designations are applicable to and only.
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