A recently popularized approach for the calculation of pseudocontact shifts (PCSs) based on first-principles quantum chemistry (QC) leads to different results than the classic “semiempirical” equation involving the susceptibility tensor. Studies that attempted a comparison of theory and experiment led to conflicting conclusions with respect to the preferred theoretical approach. In this Letter, we show that after inclusion of previously neglected terms in the full Hamiltonian, one can deduce the semiempirical equations from a rigorous QC-based treatment. It also turns out that in the long-distance limit, one can approximate the complete A tensor in terms of the g tensor. By means of Kohn–Sham density functional theory calculations, we numerically confirm the long-distance expression for the A tensor and the theoretically predicted scaling behavior of the different terms. Our derivation suggests a computational strategy in which one calculates the susceptibility tensor and inserts it into the classic equation for the PCS.

Complete Active Space SCF (CASSCF) theory may provide poor 0th order descriptions due to the lack of dynamic correlation. The most popular post-CASSCF approaches for recovering dynamic correlation are methods which keep the configuration interaction coefficients fixed at the CASSCF level and use internal contraction. This may result in severe inaccuracies where the wavefunction changes considerably under the influence of dynamic correlation. In this paper, we propose and compare several variants of a straightforward method of the "perturb-then-diagonalize" type that is aimed at keeping this balance while remaining computationally tractable and numerically stable. The method is loosely based on the theory of intermediate Hamiltonians and has been given the acronym "dynamic correlation dressed CAS" (DCD-CAS), with the second-order treatment, DCD-CAS(2), being the most practically useful member of the family. The dynamic correlation energy is treated to second order with a 0th order Hamiltonian based on Dyall's Hamiltonian. The method is orbitally invariant with respect to unitary transformations in the occupied, active, and virtual subspaces. It yields the ground- and low-lying excited states at the same time. Detailed numerical evaluations show that DCD-CAS(2) is superior to NEVPT2 for the difficult situations mentioned above while being very close to it when CASSCF provides a good 0th order description.

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.

We report an extension of the recently proposed 2nd order dynamic correlation dressed complete active space method [S. Pathak et al., J. Chem. Phys. 147, 234109 (2017)] to incorporate spin-dependent relativistic effects into the Hamiltonian. The result is an effective Hamiltonian that contains the effects of static correlation, dynamic correlation, and relativistic effects on an equal footing. All contributions necessary for the description of magnetic phenomena and electron paramagnetic resonance (EPR) spectroscopy, namely, spin-orbit coupling, magnetic hyperfine coupling, Zeeman interaction, and direct electronic spin-spin coupling, are incorporated. We also suggest a novel analysis of g-matrices and A-matrices based on the singular value decomposition, which can provide not only the magnitude but also the sign of the principal components and allows for a transparent decomposition into different physical contributions. The new method was tested for excitation energies of first-row transition metal ions as well as D-tensors and g-shifts of first-row transition metal complexes using minimal active spaces. It was observed that state-mixing effects are usually small in these cases and that the results are comparable to nondegenerate N-electron valence state perturbation theory (NEVPT2) in conjunction with quasi-degenerate perturbation theory (QDPT). Results on EPR parameters of pseudo-square-planar Cu(ii) complexes show that state-mixing with a ligand-to-metal-charge-transfer configuration greatly improves results compared with NEVPT2/QDPT but also demonstrate that future modifications of the 0th order Hamiltonian or more elaborate electron correlation treatments will be necessary in order to achieve better agreement with the experiment.

Rational design of light-capturing properties requires understanding the molecular and electronic structure of chromophoresi nt heir native chemical or biological environment. We employ here large-scale quantumc hemical calculations to study the light-capturing properties of retinal in recently designedh uman cellular retinol binding protein II (hCRBPII) variants (Wang et al. Science, 2012, 338,1 340-1343. Our calculations show that these proteins absorb across al arge part of the visible spectrum by combined polarization and electrostatic effects. These effectss tabilizet he ground or excited state energy levels of the retinalb yp erturbing the Schiff-base or b-iononem oieties of the chromophore, which in turn modulates the amount of charget ransfer within the molecule. Based on the predicted tuning principles,w ed esign putative in silico mutationst hat further shift the absorption properties of retinal in hCRBPII towards the ultravioleta nd infrared regions of the spectrum.