Relative energetics of acetyl-histidine protomers with and without Zn²⁺ and a benchmark of energy methods

We studied acetylhistidine (AcH), bare or microsolvated with a zinc cation by simulations in isolation. First, a global search for minima of the potential energy surface combining both, empirical and first-principles methods, is performed individually for either one of five possible protonation states. Comparing the most stable structures between tautomeric forms of negatively charged AcH shows a clear preference for conformers with the neutral imidazole ring protonated at the N-epsilon-2 atom. When adding a zinc cation to the system, the situation is reversed and N-delta-1-protonated structures are energetically more favorable. Obtained minima structures then served as basis for a benchmark study to examine the goodness of commonly applied levels of theory, i.e. force fields, semi-empirical methods, density-functional approximations (DFA), and wavefunction-based methods with respect to high-level coupled-cluster calculations, i.e. the DLPNO-CCSD(T) method. All tested force fields and semi-empirical methods show a poor performance in reproducing the energy hierarchies of conformers, in particular of systems involving the zinc cation. Meta-GGA, hybrid, double hybrid DFAs, and the MP2 method are able to describe the energetics of the reference method within chemical accuracy, i.e. with a mean absolute error of less than 1kcal/mol. Best performance is found for the double hybrid DFA B3LYP+XYG3 with a mean absolute error of 0.7 kcal/mol and a maximum error of 1.8 kcal/mol. While MP2 performs similarly as B3LYP+XYG3, computational costs, i.e. timings, are increased by a factor of 4 in comparison due to the large basis sets required for accurate results

Multiconfigurational Short-Range Density-Functional Theory for Open-Shell Systems

Many chemical systems cannot be described by quantum chemistry methods based on a singlereference wave function. Accurate predictions of energetic and spectroscopic properties require a delicate balance between describing the most important configurations (static correlation) and obtaining dynamical correlation efficiently. The former is most naturally done through a multiconfigurational (MC) wave function, whereas the latter can be done by, e.g., perturbation theory. We have employed a different strategy, namely, a hybrid between multiconfigurational wave functions and density-functional theory (DFT) based on range separation. The method is denoted by MC short-range (sr) DFT and is more efficient than perturbative approaches as it capitalizes on the efficient treatment of the (short-range) dynamical correlation by DFT approximations. In turn, the method also improves DFT with standard approximations through the ability of multiconfigurational wave functions to recover large parts of the static correlation. Until now, our implementation was restricted to closed-shell systems, and to lift this restriction, we present here the generalization of MC-srDFT to open-shell cases. The additional terms required to treat open-shell systems are derived and implemented in the DALTON program. This new method for open-shell systems is illustrated on dioxygen and [Fe(H2O)6]3+.Comment: 37 pages, 3 figures, 4 tables, 1 appendix and 79 references Changes in v2: 1) Appendix B and reference 81 removed 2) Removed dublicated reference and corrected reference 31. 3) Added spin-charge cross terms to GGA (Appendix A). Code changed accordingly and GGA results recalculated. All GGA results are revised -only small modifications observed. Conclusions are unchange

Triplet-Tuning: A Novel Family of Non-Empirical Exchange-Correlation Functionals

In the framework of DFT, the lowest triplet excited state, T$_1$, can be evaluated using multiple formulations, the most straightforward of which are UDFT and TDDFT. Assuming the exact XC functional is applied, UDFT and TDDFT provide identical energies for T$_1$ ($E_{\rm T}$), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T$_1$ and S$_1$. Inspired by the optimal tuning strategy for frontier orbital energies [Stein, Kronik, and Baer, {\it J. Am. Chem. Soc.} {\bf 2009}, 131, 2818], we proposed a novel and non-empirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in $E_{\rm T}$ is strictly enforced. Referred to as "triplet tuning", our procedure allows us to formulate the XC functional on a case-by-case basis using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-$\omega$PBEh, is formulated as a long-range-corrected hybrid of PBE and HF functionals [Rohrdanz, Martins, and Herbert, {\it J. Chem. Phys.} {\bf 2009}, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-$\omega$PBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to $E_{\rm T}$, $E_{\rm S}$, $\Delta E_{\rm ST}$, and $I$, as it adjusts the effective electron-hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging

Density functional theory embedding for correlated wavefunctions: Improved methods for open-shell systems and transition metal complexes

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the accuracy and stability of WFT-in-DFT embedding calculations. In particular, we develop spin-dependent embedding potentials in both restricted and unrestricted orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and we develop an orbital-occupation-freezing technique to improve the convergence of optimized effective potential (OEP) calculations that arise in the evaluation of the embedding potential. The new techniques are demonstrated in applications to the van-der-Waals-bound ethylene-propylene dimer and to the hexaaquairon(II) transition-metal cation. Calculation of the dissociation curve for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating errors in the dispersion interactions due to conventional exchange-correlation (XC) functionals while simultaneously avoiding errors due to subsystem partitioning across covalent bonds. Application of WFT-in-DFT embedding to the calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II) cation reveals that the majority of the dependence on the DFT XC functional can be eliminated by treating only the single transition-metal atom at the WFT level; furthermore, these calculations demonstrate the substantial effects of open-shell contributions to the embedding potential, and they suggest that restricted open-shell WFT-in-DFT embedding provides better accuracy than unrestricted open-shell WFT-in-DFT embedding due to the removal of spin contamination.Comment: 11 pages, 5 figures, 2 table

Quantitative wave function analysis for excited states of transition metal complexes

The character of an electronically excited state is one of the most important descriptors employed to discuss the photophysics and photochemistry of transition metal complexes. In transition metal complexes, the interaction between the metal and the different ligands gives rise to a rich variety of excited states, including metal-centered, intra-ligand, metal-to-ligand charge transfer, ligand-to-metal charge transfer, and ligand-to-ligand charge transfer states. Most often, these excited states are identified by considering the most important wave function excitation coefficients and inspecting visually the involved orbitals. This procedure is tedious, subjective, and imprecise. Instead, automatic and quantitative techniques for excited-state characterization are desirable. In this contribution we review the concept of charge transfer numbers---as implemented in the TheoDORE package---and show its wide applicability to characterize the excited states of transition metal complexes. Charge transfer numbers are a formal way to analyze an excited state in terms of electron transitions between groups of atoms based only on the well-defined transition density matrix. Its advantages are many: it can be fully automatized for many excited states, is objective and reproducible, and provides quantitative data useful for the discussion of trends or patterns. We also introduce a formalism for spin-orbit-mixed states and a method for statistical analysis of charge transfer numbers. The potential of this technique is demonstrated for a number of prototypical transition metal complexes containing Ir, Ru, and Re. Topics discussed include orbital delocalization between metal and carbonyl ligands, nonradiative decay through metal-centered states, effect of spin-orbit couplings on state character, and comparison among results obtained from different electronic structure methods.Comment: 47 pages, 19 figures, including supporting information (7 pages, 1 figure

Development of Novel Density Functionals for Thermochemical Kinetics

A new density functional theory (DFT) exchange-correlation functional for the exploration of reaction mechanisms is proposed. This new functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a general-purpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct `back' the excess exact exchange mixing for ground-state properties, possibly simulating variable exchange.Comment: J. Chem. Phys., in press (303431JCP, scheduled for August 15, 2004 issue); supplementary data available at http://theochem.weizmann.ac.il/web/papers/BMK.htm