Exploring Chemical Space with Alchemical Derivatives: BN-Simultaneous Substitution Patterns in C₆₀

Abstract

With the idea of using alchemical derivatives to explore in an efficient, computer- and cost-effective way Chemical Space was launched several years ago. In the context of Conceptual DFT response functions, these energies vs nuclear charge derivatives permit the estimatation of the energy of transmutants of a given starting or reference molecule showing different nuclear compositions. After an explorative study on small and planar molecules ( Balawender et al. J. Chem. Theory Comput. 2013 , 9 , 5327 ) by the present authors of this paper, the present study fully exploits the computational advantages of the alchemical derivatives in larger three-dimensional systems. Starting from a single reference calculation on C, the complete BN substitution pattern, from single substituted CBN via the belt (C(BN) and the ball C(BN) structures to the fully substituted (BN), is explored. Successive and simultaneous substitution strategies are followed and compared, indicating that both techniques yield identical results up to 13 substitutions but that for higher substitutions the simultaneous approach needs to be taken. Due to the cost-efficiency of the algorithm this path can indeed be followed as opposed to earlier work in the literature where for each step a full SCF calculation was at stake leading to prohibitively large computational demands for adopting the simultaneous approach. Previously formulated rules governing the substitution pattern by Kar and co-workers are scrutinized in this context and reformulated giving chemical insight in the gradual substitution process and the relative energies of the isomers. In its present form the method offers an interesting venue to study BN substitution patterns in higher fullerenes and graphene and in general paves the way for more efficient exploration of the Chemical Space.

A first step towards quantum energy potentials of electron pairs

“…in a simple manner and starting from chemically meaningful concepts. 48,49 As previously stated, another field on which this energy model may suppose a breakthrough is in Force Field development. In this respect, our model provides useful insight on non-classical terms and further justifies the design of Force Fields transcending the all-atom paradigm.…”

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

“…Second and higher order alchemical estimates were studied in Refs. [27,[47][48][49][50][51]. Insertion of µ I in Eq.…”

New Insights and Horizons from the Linear Response Function in Conceptual DFT

“…The LRF has recently been exploited when investigating Chemical Compound Space [54][55][56]. Chemists are continuously exploring chemical compound space (CCS) [57,58], the space populated by all imaginable chemicals with natural nuclear charges and realistic interatomic distances for which chemical interactions exist.…”

“…The alchemical hardness matrix η thus completely determines the substitution energy and pattern. To summarize the results (for an in-depth discussion see [55]), the study reveals that the correct sequence of stabilization energies for each n is retrieved by adopting an approach in which for each n value the problem is looked upon without prejudice of the n À 1 result (called the 'simultaneous' approach). The other, simpler method (we called it the 'successive' approach) was shown to fail already after n = 13, be it that at some n values identical values were obtained with both approaches, for example, for the Belt structure (n = 20).…”

“…The sequence of substitutions could be interpreted in terms of a number of 'alchemical' rules of which the two most important are when (referring to earlier work by Kar et al [69]): (1 ) hexagon-hexagon junctions are preferably substituted, in a way that minimizes the homonuclear (BB,NN) bonds and (2 ) the higher stability is created by maximizing the number of filled hexagons. For the subsequent, more intricate, rules we refer to [55].…”