A computational approach to the study of magnetism in molecular crystals is outlined, and applications are presented for three purely organic nitronyl nitroxide (NN) crystals: WILVIW (p-N-methylpyridiniumNN + ‚ I -), TOLKEK (R-2-hydroNN), and KAXHAS (β-p-nitrophenylNN). Data from ab initio electronic structure computations are used to parametrize an algebraic Heisenberg Hamiltonian. The magnetic susceptibility as a function of temperature χ(T) is, in turn, obtained directly from the computed energy levels of the algebraic Heisenberg Hamiltonian. The parametrization of the two site interaction parameters J AB requires the identification of the (one-, two-, or three-dimensional) magnetic motifs (e.g., spin ladders, etc.) from a study of the magnetic structure of the crystal. The energy levels of the magnetic motif are then computed as a function of the extension of the constituent magnetic building blocks along the crystallographic axes until convergence on χ(T) can be demonstrated. Rapid convergence has been demonstrated, showing that a simple model (the minimal magnetic model space) can be used as a realistic model of the magnetic motif for an infinite crystal lattice. Applications to the three organic NN crystals have demonstrated the efficacy of this theoretical approach for the simulation of the experimental magnetic susceptibility and heat capacity data.

The complex (2,3-dmpyH)2CuBr4 has been synthesized and its crystal packing determined by single-crystal X-ray diffraction (2,3-dmpyH = 2,3-dimethylpyridinium). The compound crystallizes in the triclinic space group P1. The crystal packing is characterized by the formation of a ladder structure for the CuBr4 anions showing short Br...Br contacts. The rungs of the ladder are formed via a crystallographic inversion center, while the rails are formed via unit cell translations. Variable temperature magnetic susceptibility measurements agree very well with the ladder model [Jrung = -3.10 cm-1 (-4.34 K) and Jrail = -6.02 cm-1 (-8.42 K)]. The assignment as a magnetic ladder is confirmed by first principles bottom-up theoretical calculations which conclude that Jrung = -3.49 cm-1 (-4.89 K) and Jrail = -7.79 cm-1 (-10.9 K), in very good agreement with the experimental values. They also support the absence of additional significant magnetic exchange within the crystals. Thus, (2,3-dmpyH)2CuBr4 represents the second reported example of a weak-exchange limit magnetic ladder (that is, one in which the exchange along the rail is stronger than that across the rung).

The neutral radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) is a prototype of moleculebased bistable materials. TTTA crystals undergo a first-order phase transition between their low-temperature diamagnetic and high-temperature paramagnetic phases, with a large hysteresis loop that encompasses room temperature. Here, based on ab initio molecular dynamics simulations and new X-ray measurements, we uncover that the regular stacking motif of the high-temperature polymorph is the result of a fast intra-stack pair-exchange dynamics, whereby TTTA radicals continually exchange the adjacent TTTA neighbour (upper or lower) with which they form an eclipsed dimer. Such unique dynamics, observed in the paramagnetic phase within the whole hysteresis loop, is the origin of a significant vibrational entropic gain in the low-temperature to high-temperature transition and thereby it plays a key role in driving the phase transition. This finding provides a new key concept that needs to be explored for the rational design of novel molecule-based bistable magnetic materials.

The magnetic bistability present in some molecule-based magnets is investigated theoretically at the microscopic level using the purely organic system TTTA (1,3,5-trithia-2,4,6-triazapentalenyl). The TTTA crystal is selected for being one of the best-studied molecule-based systems presenting magnetic bistability. The magnetic properties of the high- and low-temperature structures (HT and LT phases, respectively) are accurately characterized by performing a First-Principles Bottom-Up study of each phase. The changes that the magnetic exchange coupling constants (J AB) undergo when the temperature is raised (LT → HT) or lowered (HT → LT) are also fully explored in order to unravel the reasons behind the presence of these two different pathways. The triclinic LT phase is diamagnetic due to the fact that the nearly eclipsed π dimer is effectively magnetically silent and not to formation of a covalent bond between two TTTA molecules. It is also shown that bistability in TTTA results from the coexistence of the monoclinic HT and triclinic LT phases in the temperature range studied.

The mechanism of the magnetic interaction in the pyridyl-verdazyl radical:hydroquinone (pyvd:hq) molecular co-crystal is important as it has been suggested to originate by a unique "mediated through-space" magnetic interaction. This interaction was proposed to magnetically connect two nonadjacent pyridyl-verdazyl radicals within a pi stack, where adjacent radicals pile up in a head-over-tail orientation. The connection is made through a third radical sitting between the previous two mediated radicals. Given the relevance of this proposal, we decided to reinvestigate the magnetic properties of this co-crystal by using our recently proposed first-principles "bottom-up" procedure. Based on B3LYP/6-31+G(d) and CASSCF(6,6)/6-31+G(d) calculations (the results of which are identical to those provided by CASSCF(10,10)/6-31+G(d) calculations), we have computed the microscopic J(AB) values for all direct through-space magnetic interactions between nearby pyridyl-verdazyl radicals. The magnetic interactions give rise to two dominant values of similar strength: -56 and -54 cm(-1) at the B3LYP level, which are calculated as -38 and -31 cm(-1) at the CASSCF(6,6) and CAS(10,10) levels (all other interactions being smaller than |1| cm(-1)). The dominant interactions correspond to the direct through-space interaction between two adjacent radicals of a pi stack. The crystal also exhibits a radical-mediated through-space interaction of -0.31 cm(-1) between two nonadjacent radicals of a pi stack. The direct through-space magnetic interactions are two orders of magnitude larger than the mediated through-space interaction. Thus, first-principles calculations do not support a mediated through-space mechanism to explain the magnetism of the pyvd:hq co-crystal. The magnetic topology generated by the two dominant antiferromagnetic interactions in the pyvd:hq co-crystal consists of one-dimensional (1D) alternating chains (interacting very weakly along the b and c axes). By using this topology, the computed macroscopic magnetic susceptibility curve reproduces the experimental one properly. This first-principles bottom-up description of the magnetism in the pyvd:hq co-crystal differs in some fundamental aspects from that previously proposed in the literature.

The state-of-the-art theoretical evaluation and rationalization of the magnetic interactions (J(AB)) in molecule-based magnets is discussed in this critical review, focusing first on isolated radical···radical pair interactions and afterwards on how these interactions cooperate in the solid phase. Concerning isolated radical pairwise magnetic interactions, an initial analysis is done on qualitative grounds, concentrating also on the validity of the most commonly used models to predict their size and angularity (namely, McConnell-I and McConnell-II models, overlap of magnetic orbitals,…). The failure of these models, caused by their oversimplified description of the magnetic interactions, prompted the introduction of quantitative approaches, whose basic principles and relative quality are also evaluated. Concerning the computation of magnetic interactions in solids, we resort to a sum of pairwise magnetic interactions within the Heisenberg Hamiltonian framework, and follow the First-principles Bottom-Up procedure, which allows the accurate study of the magnetic properties of any molecule-based magnet in an unbiased way. The basic principles of this approach are outlined, applied in detail to a model system, and finally demonstrated to properly describe the magnetic properties of molecule-based systems that show a variety of magnetic topologies, which range from 1D to 3D (152 references).

The crystal structure of the spin-canted antiferromagnet beta-p-NCC(6)F(4)CNSSN* at 12 K (reported in this work) was found to adopt the same orthorhombic space group as that previously determined at 160 K. The change in the magnetic properties of these two crystal structures has been rigorously studied by applying a first-principles bottom-up procedure above and below the magnetic transition temperature (36 K). Calculations of the magnetic exchange pathways on the 160 K structure reveal only one significant exchange coupling (J(d1)=-33.8 cm(-1)), which generates a three-dimensional diamond-like magnetic topology within the crystal. The computed magnetic susceptibility, chi(T), which was determined by using this magnetic topology, quantitatively reproduces the experimental features observed above 36 K. Owing to the anisotropic contraction of the crystal lattice, both the geometry of the intermolecular contacts at 12 K and the microscopic J(AB) radical-radical magnetic interactions change: the J(d1) radical-radical interaction becomes even more antiferromagnetic (-43.2 cm(-1)) and two additional ferromagnetic interactions appear (+7.6 and +7.3 cm(-1)). Consequently, the magnetic topologies of the 12 and 160 K structures differ: the 12 K magnetic topology exhibits two ferromagnetic sublattices that are antiferromagnetically coupled. The chi(T) curve, computed below 36 K at the limit of zero magnetic field by using the 12 K magnetic topology, reproduces the shape of the residual magnetic susceptibility (having subtracted the contribution to the magnetization arising from spin canting). The evolution of these two ferromagnetic J(AB) contributions explains the change in the slope of the residual magnetic susceptibility in the low-temperature region.

A complete first-principles bottom-up computational study of the magnetic properties of [Cu(pz)2](ClO4)2 is presented. A remarkable agreement is observed in the whole range of temperatures between simulated and experimental magnetic susceptibility data. Interestingly, the simulated heat capacity values show an anomaly close to the Néel temperature of 4.21 K associated with a transition from a two-dimensional (2D) antiferromagnet to a three-dimensional (3D) ordered state. The antiferromagnetic behavior of [Cu(pz)2](ClO4)2 is due to a 2D magnetic topology owing to two antiferromagnetic J(AB) interactions through pyrazine ligands. Although presenting a very similar molecular arrangement, the numerical values of the two magnetically significant J(AB) couplings differ by 25% (-10.2 vs -7.3 cm(-1)). This difference can be ascribed to three main contributions: (i) the central pyrazine ring shearing-like distortion, (ii) the effect of the orientation of the perchlorate counterions, and (iii) a hitherto unrecognized skeleton-counterion cooperation arising from different hydrogen bonding contributions in the two most significant J(AB) couplings. The impact of the orientation of the perchlorate counterions is disclosed by comparison to J(AB) studies using structurally similar ligands but with different electronegativity (namely, BF4(-), BCl4(-), and BBr4(-)). Pyrazine ligands and perchlorate counterions prove to be noninnocent.