Quantum Definition of Molecular Structure.

Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics, despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of the molecular structure from fundamental quantum principles.

Theoretical analysis of the long-distance limit of NMR chemical shieldings.

After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland-McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel-Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree-Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin-orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland-McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

A Quantum Chemistry View on Two Archetypical Paramagnetic Pentacoordinate Nickel(II) Complexes Offers a Fresh Look on Their NMR Spectra.

Quantum chemical methods for calculating paramagnetic NMR observables are becoming increasingly accessible and are being included in the inorganic chemistry practice. Here, we test the performance of these methods in the prediction of proton hyperfine shifts of two archetypical high-spin pentacoordinate nickel(II) complexes (NiSAL-MeDPT and NiSAL-HDPT), which, for a variety of reasons, turned out to be perfectly suited to challenge the predictions to the finest level of detail. For NiSAL-MeDPT, new NMR experiments yield an assignment that perfectly matches the calculations. The slightly different hyperfine shifts from the two "halves" of the molecules related by a pseudo-C2 axis, which are experimentally divided into two well-defined spin systems, are also straightforwardly distinguished by the calculations. In the case of NiSAL-HDPT, for which no X-ray structure is available, the quality of the calculations allowed us to refine its structure using as a starting template the structure of NiSAL-MeDPT.

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

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 CrIII 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.

The combination of multipartitioning of the Hamiltonian with canonical Van Vleck perturbation theory leads to a Hermitian variant of quasidegenerate N-electron valence perturbation theory.

Many recent developments in the area of multistate multireference perturbation theories focused on methods that use a state-averaged 0th order Hamiltonian. We recently found that the dynamic correlation dressed complete active space method fails in describing ligand field and charge transfer states in a balanced way precisely because it uses a state-averaged 0th order Hamiltonian [L. Lang and F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioning idea allows the use of state-specific 0th order Hamiltonians in a multistate framework and could therefore alleviate the mentioned problem. However, the effective Hamiltonian is non-Hermitian in the traditional formulation of multipartitioning, which can lead to unphysical behavior, especially for nearly degenerate states. In order to achieve a more balanced treatment of states with different physical character and at the same time have a Hermitian effective Hamiltonian, we combine in this work multipartitioning with canonical Van Vleck perturbation theory. At the 2nd order, the result is a Hermitian variant of multipartitioning quasidegenerate N-electron valence state perturbation theory. The effect of model space noninvariance of the method is discussed and the benefit of a Hermitian formulation is highlighted with numerical examples. The method is shown to give good results for the calculation of electronic transitions of the [CuCl4]2 -complex and for the calculation of electron paramagnetic resonance parameters, which are two examples where the balance between ligand field and charge transfer configurations is of utmost importance.

Spin-dependent properties in the framework of the dynamic correlation dressed complete active space method.

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.

A dynamic correlation dressed complete active space method: Theory, implementation, and preliminary applications.

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.

Tuning the Protein-Induced Absorption Shifts of Retinal in Engineered Rhodopsin Mimics.

Rational design of light-capturing properties requires understanding the molecular and electronic structure of chromophores in their native chemical or biological environment. We employ here large-scale quantum chemical calculations to study the light-capturing properties of retinal in recently designed human cellular retinol binding protein II (hCRBPII) variants (Wang et al. Science, 2012, 338, 1340-1343). Our calculations show that these proteins absorb across a large part of the visible spectrum by combined polarization and electrostatic effects. These effects stabilize the ground or excited state energy levels of the retinal by perturbing the Schiff-base or ß-ionone moieties of the chromophore, which in turn modulates the amount of charge transfer within the molecule. Based on the predicted tuning principles, we design putative in silico mutations that further shift the absorption properties of retinal in hCRBPII towards the ultraviolet and infrared regions of the spectrum.

The DREAM complex represses growth in response to DNA damage in Arabidopsis.

The DNA of all organisms is constantly damaged by physiological processes and environmental conditions. Upon persistent damage, plant growth and cell proliferation are reduced. Based on previous findings that RBR1, the only Arabidopsis homolog of the mammalian tumor suppressor gene retinoblastoma, plays a key role in the DNA damage response in plants, we unravel here the network of RBR1 interactors under DNA stress conditions. This led to the identification of homologs of every DREAM component in Arabidopsis, including previously not recognized homologs of LIN52. Interestingly, we also discovered NAC044, a mediator of DNA damage response in plants and close homolog of the major DNA damage regulator SOG1, to directly interact with RBR1 and the DREAM component LIN37B. Consistently, not only mutants in NAC044 but also the double mutant of the two LIN37 homologs and mutants for the DREAM component E2FB showed reduced sensitivities to DNA-damaging conditions. Our work indicates the existence of multiple DREAM complexes that work in conjunction with NAC044 to mediate growth arrest after DNA damage.

Endoreplication - a means to an end in cell growth and stress response.

Endoreplication, also called endoreduplication or endopolyploidization, is a cell cycle variant in which the genome is re-replicated in the absence of mitosis causing cellular polyploidization. Despite the common occurrence of endoreplication in plants and the tremendous extent in specific tissues and cell types such as the endosperm, the underlying molecular regulation and the physiological consequences have only now started to be understood. Endoreplication is often associated with cell differentiation and withdrawal from mitotic cycles. Recent studies have underlined the importance of endoreplication as a stress response and we summarize here this progress with particular focus on future perspectives offered by the recent advances in genomics and biotechnology.

Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory.

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.

Toward First-Principles-Level Polarization Energies in Force Fields: A Gaussian Basis for the Atom-Condensed Kohn-Sham Method.

The last 20 years of force field development have shown that even well parametrized classical models need to at least approximate the dielectric response of molecular systems-based, e.g., on atomic polarizabilities-in order to correctly render their structural and dynamic properties. Yet, despite great advances most approaches tend to be based on ad hoc assumptions and often insufficiently capture the dielectric response of the system to external perturbations, such as, e.g., charge carriers in semiconducting materials. A possible remedy was recently introduced with the atom-condensed Kohn-Sham density-functional theory approximated to second order (ACKS2), which is fully derived from first principles. Unfortunately, specifically its reliance on first-principles derived parameters so far precluded the widespread adoption of ACKS2. Opening up ACKS2 for general use, we here present a reformulation of the method in terms of Gaussian basis functions, which allows us to determine many of the ACKS2 parameters analytically. Two sets of parameters depending on exchange-correlation interactions are still calculated numerically, but we show that they could be straightforwardly parametrized owing to the smoothness of the new basis. Our approach exhibits three crucial benefits for future applications in force fields: i) efficiency, ii) accuracy, and iii) transferability. We numerically validate our Gaussian augmented ACKS2 model for a set of small hydrocarbons which shows a very good agreement with density-functional theory reference calculations. To further demonstrate the method's accuracy and transferability for realistic systems, we calculate polarization responses and energies of anthracene and tetracene, two major building blocks in organic semiconductors.