## Improvement of Ab Initio Ligand Field Theory by Means of Multistate Perturbation Theory

journal contribution

posted on 24.01.2020 by Lucas Lang, Mihail Atanasov, Frank Neese#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

Over
the last few years, ab initio ligand field theory (AILFT)
has evolved into an important tool for the extraction of ligand field
models from ab initio calculations. The inclusion of dynamic correlation
on top of complete active space self-consistent field (CASSCF) reference
functions, which is important for accurate results, was so far realized
at the level of second-order N-electron valence state perturbation
theory (NEVPT2). In this work, we introduce two alternative methods
for the inclusion of dynamic correlation into AILFT calculations,
the second-order dynamic correlation dressed complete active space
method (DCD-CAS(2)) and the Hermitian quasi-degenerate NEVPT2 (HQD-NEVPT2).
These methods belong to the class of multistate perturbation theory
approaches, which allow for the mixing of CASSCF states under the
effect of dynamic correlation (state-mixing). The two new versions
of AILFT were tested for a diverse set of transition-metal complexes.
It was found that the multistate methods have, compared to NEVPT2,
an AILFT fit with smaller root mean square deviations (rmsds) between
ab initio and AILFT energies. A comparison of AILFT excitation energies
with the experiment shows that for some systems, the agreement gets
better at the multistate level because of the smaller rmsds. However,
for some systems, the agreement gets worse, which could be attributed
to a cancellation of errors at the NEVPT2 level that is partly removed
at the multistate level. An investigation of trends in the extracted
ligand field parameters shows that at the multistate level, the ligand
field splitting Δ gets larger, whereas the Racah parameters

*B*and*C*get smaller and larger, respectively. An investigation of the reasons for the observed improvement for octahedral Cr^{III}halide complexes shows that the possibility of state-mixing relaxes constraints that are present at the NEVPT2 level and that keep Δ and*B*from following their individual preferences.#### Read the peer-reviewed publication

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HQD-NEVPTHermitian quasi-degenerate NEVPT 2AILFT excitation energiesCASSCFN-electron valence state perturbation theoryligand field splitting Δmethodmultistate perturbation theory approachesmultistate leveloctahedral Cr III halide complexesRacah parameters Bab initio ligand field theoryab initio calculationsNEVPT 2 levelligand field parametersMultistate Perturbation Theoryligand field modelsDCD-CASAb Initio Ligand Field Theorycorrelation

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#### Read the peer-reviewed publication

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### Keyword(s)

HQD-NEVPTHermitian quasi-degenerate NEVPT 2AILFT excitation energiesCASSCFN-electron valence state perturbation theoryligand field splitting Δmethodmultistate perturbation theory approachesmultistate leveloctahedral Cr III halide complexesRacah parameters Bab initio ligand field theoryab initio calculationsNEVPT 2 levelligand field parametersMultistate Perturbation Theoryligand field modelsDCD-CASAb Initio Ligand Field Theorycorrelation