. 2016 Mar 10;144(10):104304. doi: 10.1063/1.4942019

TABLE III.

Orbital occupations of the dominant spin-adapted determinants of the CASSCF(18,12)/cc–pVTZ wave functions for the 1¹A₁ and 2¹A₁ states of O₃.^a

	Active orbitals^d^,^e^,^f^,^g^,^h
Spin adapted determinant^b^,^c	5a₁	3b₁	1b₂	6a₁	1a₂	4b₁	2b₂	7a₁	5b₁	Excitation with respect to $\|D_{1}〉$ or $\|D_{2}〉$
$\|D_{1}〉$	2	2	2	2	2	2				…
$\|D_{2}〉$	2	2	2	2	2		2			…
$\|D_{3}〉$	2	2	2	2		2	2			$\|D_{1}, {(1 a_{2})}^{2} \to {(2 b_{2})}^{2}〉$
$\|D_{4}〉$	2	2	2		2	2	2			$\|D_{2}, {(6 a_{1})}^{2} \to {(4 b_{1})}^{2}〉$
$\|D_{5}〉$		2	2	2	2		2	2		$\|D_{2}, {(5 a_{1})}^{2} \to {(7 a_{1})}^{2}〉$
$\|D_{6}〉$	2	2	2	2			2		2	$\|D_{2}, {(1 a_{2})}^{2} \to {(5 b_{1})}^{2}〉$
$\|D_{7}〉$	2		2	2	2		2		2	$\|D_{2}, {(3 b_{1})}^{2} \to {(5 b_{1})}^{2}〉$
$\|D_{8}〉$	2	2	1	2	2	2	1			$\|D_{1}, {(1 b_{2})}^{2} \to {(1 b_{2})}^{1} {(2 b_{2})}^{1}〉$
$\|D_{9}〉$	2	1	2	2	2		2		1	$\|D_{2}, {(3 b_{1})}^{2} \to {(3 b_{1})}^{1} {(5 b_{1})}^{1}〉$
$\|D_{10}〉$	1	2	2	1	2	2	2			$\|D_{1}, {(5 a_{1})}^{2} {(6 a_{1})}^{2} \to {(5 a_{1})}^{1} {(6 a_{1})}^{1} {(2 b_{2})}^{2}〉$
$\|D_{11}〉$	1	2	2	2	2		2	1		$\|D_{2}, {(5 a_{1})}^{2} \to {(5 a_{1})}^{1} {(7 a_{1})}^{1}〉$
$\|D_{12}〉$	2	2	2	1	2		2	1		$\|D_{2}, {(6 a_{1})}^{2} \to {(6 a_{1})}^{1} {(7 a_{1})}^{1}〉$

^{^a}

Listed are the orbital occupations of the ¹A₁ spin-adapted determinants that occur in Table II. The spin-adapted determinants with singly occupied orbitals are normalized combinations of two Slater-determinants.

^{^b}

Indicated in bold font are the configurations, $|D_{1}〉$ and $|D_{2}〉$ , that span the ¹A₁ subspace of the CAS(2,2).

^{^c}

Also indicated in bold are the configurations, $|D_{3}〉$ and $|D_{4}〉$ , that, together with shaded $|D_{1}〉$ and $|D_{2}〉$ , span the ¹A₁ subspace of the CAS(6,4).

^{^d}

The doubly occupied core orbitals 1a₁, 1b₁, and 2a₁ are not listed.

^{^e}

For each of the dominant spin-adapted determinants that contribute to the 1¹A₁ and 2¹A₁ wave functions of O₃, the valence orbitals 3a₁, 2b₁, and 4a₁ are all doubly occupied and therefore not listed. However, the full CAS(18,12) space also contains determinants that involve excitations from orbitals 3a₁, 2b₁, and 4a₁.

^{^f}

Indicated as shaded part are the active orbitals, 4b₁ and 2b₂, that have different occupations in $|D_{1}〉$ and $|D_{2}〉$ .

^{^g}

Indicated in bold are the active orbitals, 6a₁ and 1a₂, that have different occupations in $|D_{3}〉$ and $|D_{4}〉$ .

^{^h}

Orbitals of a₁ and b₁ symmetry are σ-type orbitals. Orbitals of a₂ and b₂ symmetry are π-type orbitals.

	Active orbitals^d^,^e^,^f^,^g^,^h
Spin adapted determinant^b^,^c	5a₁	3b₁	1b₂	6a₁	1a₂	4b₁	2b₂	7a₁	5b₁	Excitation with respect to $\|D_{1}〉$ or $\|D_{2}〉$
$\|D_{1}〉$	2	2	2	2	2	2				…
$\|D_{2}〉$	2	2	2	2	2		2			…
$\|D_{3}〉$	2	2	2	2		2	2			$\|D_{1}, {(1 a_{2})}^{2} \to {(2 b_{2})}^{2}〉$
$\|D_{4}〉$	2	2	2		2	2	2			$\|D_{2}, {(6 a_{1})}^{2} \to {(4 b_{1})}^{2}〉$
$\|D_{5}〉$		2	2	2	2		2	2		$\|D_{2}, {(5 a_{1})}^{2} \to {(7 a_{1})}^{2}〉$
$\|D_{6}〉$	2	2	2	2			2		2	$\|D_{2}, {(1 a_{2})}^{2} \to {(5 b_{1})}^{2}〉$
$\|D_{7}〉$	2		2	2	2		2		2	$\|D_{2}, {(3 b_{1})}^{2} \to {(5 b_{1})}^{2}〉$
$\|D_{8}〉$	2	2	1	2	2	2	1			$\|D_{1}, {(1 b_{2})}^{2} \to {(1 b_{2})}^{1} {(2 b_{2})}^{1}〉$
$\|D_{9}〉$	2	1	2	2	2		2		1	$\|D_{2}, {(3 b_{1})}^{2} \to {(3 b_{1})}^{1} {(5 b_{1})}^{1}〉$
$\|D_{10}〉$	1	2	2	1	2	2	2			$\|D_{1}, {(5 a_{1})}^{2} {(6 a_{1})}^{2} \to {(5 a_{1})}^{1} {(6 a_{1})}^{1} {(2 b_{2})}^{2}〉$
$\|D_{11}〉$	1	2	2	2	2		2	1		$\|D_{2}, {(5 a_{1})}^{2} \to {(5 a_{1})}^{1} {(7 a_{1})}^{1}〉$
$\|D_{12}〉$	2	2	2	1	2		2	1		$\|D_{2}, {(6 a_{1})}^{2} \to {(6 a_{1})}^{1} {(7 a_{1})}^{1}〉$