Gas separations with porous materials are economically important and provide a unique challenge to fundamental materials design, as adsorbent properties can be altered to achieve selective gas adsorption. Metal−organic frameworks represent a rapidly expanding new class of porous adsorbents with a large range of possibilities for designing materials with desired functionalities. Given the large number of possible framework structures, quantum mechanical computations can provide useful guidance in prioritizing the synthesis of the most useful materials for a given application. Here, we show that such calculations can predict a new metal− organic framework of potential utility for separation of dinitrogen from methane, a particularly challenging separation of critical value for utilizing natural gas. An open V(II) site incorporated into a metal−organic framework can provide a material with a considerably higher enthalpy of adsorption for dinitrogen than for methane, based on strong selective back bonding with the former but not the latter. ■ INTRODUCTIONCoordination of dinitrogen to transition-metal cations is important both fundamentally and industrially. Dinitrogen is highly inert and generally considered to be a poor ligand. In 1965, however, it was shown that a simple coordination complex, [Ru(NH 3 ) 5 ] 2+ , could reversibly bind N 2 . 1 In subsequent years, a number of dinitrogen−transition-metal complexes have been isolated for metals in varying oxidation states with various coordination numbers. 2,3 These complexes typically feature low-valent, relatively reducing metal cations coordinated to dinitrogen in an end-on binding mode. Activating dinitrogen at a metal center to promote its reduction by hydrogen to ammonia under moderate conditions remains a critical goal for homogeneous catalysis. Somewhat weaker metal−dinitrogen binding, however, may be useful for adsorptive separation of gas mixtures. An example is provided by the need to remove dinitrogen (an omnipresent but noncombustible contaminant) from natural gas or other methane-rich gases. This is an extraordinarily difficult separation based on physical properties alone, as both gases lack a permanent dipole and have similar polarizabilities, boiling points, and kinetic diameters. Although cryogenic distillation is currently utilized for separation of these gases, the cost-and capital-intensive nature of this separation has led to development of a number of competing processes, such as membraneor kinetics-based separations, which generally suffer from low selectivities. 4

Catalytic processes are crucially important for many practical chemical applications. Heterogeneous catalysts are especially appealing because of their high stability and the relative ease with which they may be recovered and reused. Computational modeling can play an important role in the design of more catalytically active materials through the identification of reaction mechanisms and the opportunity to assess hypothetical catalysts in silico prior to experimental verification. Kohn–Sham density functional theory (KS-DFT) is the most commonly used method in computational catalysis because it is affordable and it gives results of reasonable accuracy in many instances. Furthermore, it can be employed in a “black-box” mode that does not require significant a priori knowledge of the system. However, KS-DFT has some limitations: it suffers from self-interaction error (sometime referred to as delocalization error), but a greater concern is that it provides an intrinsically single-reference description of the electronic structure, and this can be especially problematic for modeling catalysis when transition metals are involved. In this Perspective, we highlight some noteworthy applications of KS-DFT to heterogeneous computational catalysis, as well as cases where KS-DFT fails to describe accurately electronic structures and intermediate spin states in open-shell transition metal systems. We next provide an introduction to state-of-the-art multiconfigurational (MC; also referred to as multireference (MR)) methods and their advantages and limitations for modeling heterogeneous catalysis. We focus on specific examples to which MC methods have been applied and discuss the challenges associated with these calculations. We conclude by offering our vision for how the community can make further progress in the development of MC methods for application to heterogeneous catalysis.

The applicability and accuracy of the generalized active space self-consistent field, (GASSCF), and (SplitGAS) methods are presented. The GASSCF method enables the exploration of larger active spaces than with the conventional complete active space SCF, (CASSCF), by fragmentation of a large space into subspaces and by controlling the interspace excitations. In the SplitGAS method, the GAS configuration interaction, CI, expansion is further partitioned in two parts: the principal, which includes the most important configuration state functions, and an extended, containing less relevant but not negligible ones. An effective Hamiltonian is then generated, with the extended part acting as a perturbation to the principal space. Excitation energies of ozone, furan, pyrrole, nickel dioxide, and copper tetrachloride dianion are reported. Various partitioning schemes of the GASSCF and SplitGAS CI expansions are considered and compared with the complete active space followed by second-order perturbation theory, (CASPT2), and multireference CI method, (MRCI), or available experimental data. General guidelines for the optimum applicability of these methods are discussed together with their current limitations.

Predicting and understanding the chemical bond is one of the major challenges of computational quantum chemistry. Kohn−Sham density functional theory (KS-DFT) is the most common method, but approximate density functionals may not be able to describe systems where multiple electronic configurations are equally important. Multiconfigurational wave functions, on the other hand, can provide a detailed understanding of the electronic structure and chemical bond of such systems. In the complete-active-space self-consistent field (CASSCF) method one performs a full configuration interaction calculation in an active space consisting of active electrons and active orbitals. However, CASSCF and its variants require the selection of these active spaces. This choice is not black-box; it requires significant experience and testing by the user, and thus active space methods are not considered particularly user-friendly and are employed only by a minority of quantum chemists. Our goal is to popularize these methods by making it easier to make good active space choices. We present a machine learning protocol that performs an automated selection of active spaces for chemical bond dissociation calculations of main group diatomic molecules. The protocol shows high prediction performance for a given target system as long as a properly correlated system is chosen for training. Good active spaces are correctly predicted with a considerably better success rate than random guess (larger than 80% precision for most systems studied). Our automated machine learning protocol shows that a "black-box" mode is possible for facilitating and accelerating the large-scale calculations on multireference systems where single-reference methods such as KS-DFT cannot be applied.

The singlet-triplet splittings of a set of diradical organic molecules are calculated using multiconfiguration pair-density functional theory (MC-PDFT), and the results are compared with those obtained by Kohn-Sham density functional theory (KS-DFT) and complete active space second-order perturbation theory (CASPT2) calculations. We found that MC-PDFT, even with small and systematically defined active spaces, is competitive in accuracy with CASPT2, and it yields results with greater accuracy and precision than Kohn-Sham DFT with the parent functional. MC-PDFT also avoids the challenges associated with spin contamination in KS-DFT. It is also shown that MC-PDFT is much less computationally expensive than CASPT2 when applied to larger active spaces, and this illustrates the promise of this method for larger diradical organic systems.