Correction to Spin-Free CC2 Implementation of Induced Transitions

Erratum pubs.acs.org/JCTC

Correction to Spin-Free CC2 Implementation of Induced Transitions between Singlet Ground and Triplet Excited States Benjamin Helmich-Paris,* Christof Haẗ tig,* and Christoph van Wüllen* J. Chem. Theory Comput. 2016, 12 (4), 1892−1904. DOI: 10.1021/acs.jctc.5b01197

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All other SOC-PT-based results reported in the article were obtained as described therein with the full SOMF operator.

ur work reported in Table 2 lifetimes for the lowest excited triplet states of XH with X = F, Cl, and Br calculated at the CC2 level using the perturbative SOC-PT and the exact two-component (X2C) approach. We have realized that for the calculation of SOC-PT-based lifetimes in columns 4 and 7 the SOMF operator accidentally lacked all Coulomb (or direct) two-electron contributions. The SOC-PT CC2/aug-ccpVTZ lifetimes based on the full SOMF operator from eq 51 are provided in Table 1 of the present erratum. In the original

Table 1. Phosphorescence Lifetimes τP,f (ms) of the Two Lowest Excited 3Σ+ and 3Π States for Halogen Hydridesa τP,f SOMF state

NR

SR

X2C

2.3 × 10−3 4.0 × 10−1 8.0 × 10−4 1.4

1.8 × 10−3 2.8 × 10−1 4.4 × 10−4 2.4

HF Π Σ 3 Π 3 + Σ

2.3 × 10−3 4.0 × 10−1 7.9 × 10−4 1.5

3

Π 3 + Σ 3 Π 3 + Σ

2.5 1.6 4.8 1.4

× × × ×

10−3 10−2 10−4 10−2

1 3Π 1 3Σ+ 2 3Π 23Σ+

3.2 1.5 2.1 9.5

× × × ×

10−4 10−4 10−5 10−3

1 1 2 2

3

1 1 2 2

3 +

HCl 2.5 1.5 4.8 1.4

× × × ×

10−3 10−2 10−4 10−2

2.4 1.7 4.7 1.2

× × × ×

10−3 10−2 10−4 10−2

3.1 8.2 2.4 6.0

× × × ×

10−4 10−5 10−5 10−3

5.1 1.2 4.4 6.6

× × × ×

10−4 10−4 10−5 10−4

HBr

a

τP,f were calculated with the RI-CC2/aug-cc-pVTZ method by using either the exact two-component (X2C) Hamiltonian or spin−orbit coupling perturbation theory (SOC-PT) with (SR) or without (NR) scalar-relativistic effects from the spin-free X2C Hamiltonian.

article we have shown that without the Coulomb contribution SOC-PT lifetimes of XH were always shorter than with X2C. With the complete SOMF operatorsone-electron and mean field Coulomb and exchange partwe observe for SOC-PT a longer T1 → S0 lifetime for FH, roughly the same lifetime for ClH, and a shorter lifetime for BrH compared to X2C. The increase of the SOC-PT lifetimes is caused by a reduction of the induced spin−orbit coupling and can be attributed to a more effective screening of nuclear charges due to the mean field Coulomb term. We expect that for molecules with only light elements (such as FH and ClH) the mean field-based SOC-PT lifetimes are more accurate than our current X2C lifetimes, which do not include any picture-change effects from the two-electron integrals. © 2016 American Chemical Society

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DOI: 10.1021/acs.jctc.7b00653 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX