Occupied-Virtual Orbitals for Chemical Valence with Applications to Charge Transfer in Energy Decomposition Analysis.

In this article, we introduce the occupied-virtual orbitals for chemical valence (OVOCV). The OVOCVs can replace or complement the closely related idea of the natural orbitals for chemical valence (NOCV). The input is a difference density matrix connecting any initial single determinant to any final determinant, at a given molecular geometry, and a given one-particle basis. This arises in problems such as orbital rearrangement or charge transfer (CT) in energy decomposition analysis (EDA). The OVOCVs block-diagonalize the density difference operator into 2 × 2 blocks, which are spanned by one level that is filled in the initial state (the occupied OVOCV) and one that is empty (the virtual OVOCV). By contrast, the NOCVs fully diagonalize the density difference matrix and therefore are orbitals with mixed occupied-virtual character. Use of the OVOCVs makes it much easier to identify the donor and acceptor orbitals. We also introduce two different types of EDA methods with the OVOCVs and, most importantly, a charge decomposition analysis method that fixes the unreasonably large CT amount obtained directly from NOCV analysis. The square of the CT amount associated with each NOCV pair emerges as the appropriate value from the OVOCV analysis. When connecting the same initial and final states, this value is identical to the CT amount obtained from the independent absolutely localized molecular orbital (ALMO) complementary occupied-virtual orbital pair (COVP) analysis. The total, summed over all pairs, is also exactly the same as the independently suggested excitation number, as proved herein. Several examples are presented to compare NOCVs and OVOCVs: stretched H2+, a strong halogen bond between tetramethylthiourea and iodine, coordination of ethene in Zeise's salt, and binding in the Cp3La···C≡NCy complex.

Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges.

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

Exactly Fragment Additive Breakdown of Polarization for Energy Decomposition Analysis Based on the Self-Consistent Field for Molecular Interactions.

Energy decomposition analysis (EDA) is a useful method to unravel intermolecular interaction energy into chemically meaningful components such as geometric distortion, frozen interactions, polarization, and charge transfer. A further decomposition of the polarization (POL) and charge transfer (CT) energy into fragment-wise contributions would be useful to understand the significance of each fragment during these two processes. To complement the existing exact pairwise decomposition of the CT term, this work describes the formulation and implementation of a nonperturbative polarization analysis that decomposes the POL energy into an exactly fragment-wise additive sum based on the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA). These fragment-wise contributions can be further decomposed into chemically intuitive molecular orbital pairs using complementary occupied-virtual pair (COVP) analysis. A very useful phase convention is established for each COVP such that constructive interference of occupied and virtual corresponds to electron flow into that region, while destructive interference corresponds to electron outflow. A range of model problems are used to demonstrate that the polarization process is typically a collective behavior of the electrons that is quite different from the charge transfer process. This provides another reason in addition to their different distance dependence on fragment separation for separating these two processes in EDA.

A Free Energy Decomposition Analysis: Insight into Binding Thermodynamics from Absolutely Localized Molecular Orbitals.

Traditional energy decomposition analysis (EDA) methods can provide an interpretive decomposition of non-covalent electronic binding energies. However, by definition, they neglect entropic effects and nuclear contributions to the enthalpy. With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a Gibbs decomposition analysis (GDA) by coupling the absolutely localized molecular orbital treatment of electrons in non-covalent interactions with the simplest possible quantum rigid rotor-harmonic oscillator treatment of nuclear motion at finite temperature. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and water binding to an open metal site in the metal-organic framework Cu(I)-MFU-4l. The results show enthalpic trends that generally track the electronic binding energy and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature.

Generalization of ETS-NOCV and ALMO-COVP Energy Decomposition Analysis to Connect Any Two Electronic States and Comparative Assessment.

Energy decomposition analysis (EDA) is a useful tool for obtaining chemically meaningful insights into molecular interactions. The extended transition-state method with natural orbitals for chemical valence (ETS-NOCV) and the absolutely localized molecular orbital-based method with complementary occupied-virtual pairs (ALMO-COVP) are two successful EDA schemes. Working within ground-state generalized Kohn-Sham density functional theory (DFT), we extend these methods to perform EDA between any two electronic states that can be connected by a unitary transformation of density matrices. A direct proof that the NOCV eigenvalues are symmetric pairs is given, and we also prove that the charge and energy difference defined by ALMO are invariant under certain orbital rotations, allowing us to define COVPs. We point out that ETS is actually a 1-point quadrature to obtain the effective Fock matrix, and though it is reasonably accurate, it can be systematically further improved by adding more quadrature points. We explain why the calculated amount of transferred charge measured by ALMO-COVP is typically much smaller than that of ETS-NOCV and explain why the ALMO-COVP values should be preferred. While the two schemes are independent, ETS-NOCV and ALMO-COVP in fact give a very similar chemical picture for a variety of chemical interactions, including H-H+, the transition structure for the Diels-Alder reaction between ethene and butadiene, and two hydrogen-bonded complexes, H2O···F- and H2O···HF.