Metal-Organic Charge Transfer Can Produce Biradical States and Is Mediated by Conical Intersections

Metal-organic charge transfer can produce biradical INAUGURAL ARTICLE states and is mediated by conical intersections

Oksana Tishchenkoa,1, Ruifang Lia,b, and Donald G. Truhlara,1

aDepartment of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431; and bDepartment of Chemistry, Nankai University, Tianjin 300071, People’s Republic of China

This article is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2009.

Edited by Nicholas J. Turro, Columbia University, New York, NY, and approved September 20, 2010 (received for review July 14, 2010)

The present paper illustrates key features of charge transfer be- theory revealed the presence of two types of equilibrium struc- tween calcium atoms and prototype conjugated hydrocarbons tures: one at a distance R between Ca and the closest carbon (ethylene, benzene, and coronene) as elucidated by electronic of about 3.8 Å with slightly negative charge on the calcium atom, structure calculations. One- and two-electron charge transfer is and another state with a smaller R and with considerable shift of controlled by two sequential conical intersections. The two lowest electrons from Ca to coronene; the latter is metastable. To get a electronic states that undergo a conical intersection have closed- better understanding of the structure of potential energy surfaces shell and open-shell dominant configurations correlating with that govern the charge transfer process and of the nature of the 4s2 and 4s13d1 states of Ca, respectively. Unlike the neutral- electronic states involved, we performed a detailed electronic ionic state crossing in, for example, hydrogen halides or alkali structure study using multiconfigurational wave functions for halides, the path from separated reactants to the conical intersec- the interaction of Ca with the smaller prototype molecules ben- tion region is uphill and the charge-transferred state is a biradical. zene and ethylene as well as coronene. The lowest-energy adiabatic singlet state shows at least two The closed-shell singlet potential energy surfaces of all three minima along a single approach path of Ca to the π system: (i)a systems have been found to possess similar features: an “outer” R “ ”

van der Waals complex with a doubly occupied highest molecular van der Waals minimum at a longer and a metastable inner CHEMISTRY ϕ2 ii orbital, denoted 1, and a small negative charge on Ca and ( )an minimum, characterized by a different dominant electron config- open-shell singlet (biradical) at intermediate approach (Ca⋯C dis- uration, at a shorter R. Furthermore, at intermediate R the lowest ≈ – ϕ ϕ ϕ tance 2.5 2.7 Å) with molecular orbital structure 1 2, where 2 singlet state is open-shell, and the lowest-energy state appears is an orbital showing significant charge transfer form Ca to the to be a triplet state. (Such states could be easily missed if one π-system, leading to a one-electron multicentered bond. A third calculated only closed-shell singlets, as is often done in computa- minimum (iii) at shorter distances along the same path correspond- tional materials research.) ϕ2 ing to a closed-shell state with molecular orbital structure 2 The multiconfigurational calculations of geometries and ener- has also been found; however, it does not necessarily represent gies presented here are multireference Moller–Plesset perturba- the ground state at a given Ca⋯C distance in all three systems. tion theory (MRMP2) (18, 19) calculations. Geometries and The topography of the lowest adiabatic singlet potential energy energies were also found by M06-2X (20) density functional cal- surface is due to the one- and two-electron bonding patterns in culations. Single point coupled-cluster calculations [CCSD(T)] Ca-π complexes. (21) were also performed at M06-2X geometries. We will also show partial sections of the potential energy surfaces calculated metal atom ∣ metastable state ∣ nature of metal-π binding ∣ one- and by MS-CASPT2 (22). (Details of the electronic structure calcula- two-electron multicentered bonds ∣ triplet ground state tions are given in Methods.) These systems present the classic case of two-orbital configura- ϕ2 ϕ ϕ ϕ2 ϕ ϕ he interactions of metal atoms with alkenes, polyenes, tion interaction with 1, 1 2, and 2 singlets and a 1 2 triplet. Taromatics, and graphene-based materials are important for In the notation that we use below for potential energy surfaces applications in catalysis (1, 2), molecular electronics (3–6), optoe- and stationary points, S0 denotes a state with the dominant con- ϕ2 lectronic and sensing devices (7, 8), and hydrogen storage mate- figuration 1,S1 and T1 denote the open-shell singlet and the rials (9–12). Charge transfer from the metal to the organic system corresponding triplet, and S2 denotes a state with the dominant ϕ2 is one of the key features determining adsorption energies, reac- configuration 2. We calculated these states with MRMP2, M06- tivities, electronic structure, conductivities, and optical properties 2X, and CCSD(T) for ethylene and benzene and with M06-2X for (4, 8). Most studies of charge transfer have focused on equili- coronene. Note that the S0,S1,S2, and T1 labels apply to diabatic brium geometries (4, 13–15), but the design of molecular devices (23) states, and due to conical intersections (which become and the understanding of adsorption and reactivity also require avoided crossings along most paths), a given adiabatic state understanding the dependence of charge transfer on molecular can have different labels at different geometries. geometry (16). In this communication we show that charge trans- First we consider the amount of charge transfer as a function of π fer character can change rapidly and suddenly for small changes the distance from Ca to the -system. To ensure that the geome- in geometry, and we explain this phenomenon in terms of conical tries considered are relevant to low-energy structures, we select intersections (CIs). In addition we show that the charge transfer the geometries making a path between the low-energy structures. R state can be a ferromagnetically coupled biradical, which is rele- Let denote the distance from the Ca atom to the closest carbon P vant to the possibility of control of magnetization by an electric atom in a molecular partner denoted . Figs. 1 and 2 show the field in, for example, spintronics applications (17). A fundamen- tal understanding of the interfacial states of metal atoms inter- Author contributions: O.T., R.L., and D.G.T. designed research, performed research, acting with conjugated π-systems is an essential element underly- analyzed data, and wrote the paper. ing rational molecular electronics design. The authors declare no conflict of interest. To model metal-π interactions, we first considered interactions This article is a PNAS Direct Submission. of a calcium atom with the coronene molecule, a small nonper- 1To whom correspondence may be addressed. E-mail: [email protected] or truhlar@ iodic model of graphene. Calculations using density functional umn.edu.

www.pnas.org/cgi/doi/10.1073/pnas.1010287107 PNAS ∣ November 9, 2010 ∣ vol. 107 ∣ no. 45 ∣ 19139–19145 Downloaded by guest on September 23, 2021 ground singlet state energy of all three systems as a function of R along a path constructed as follows: At large R the path is the linear synchronous path (LSP) (24, 25) from the global minimum S0 van der Waals complex, Ca⋯P, to the minimum-energy S1 structure; and at smaller R, it is an LSP from the S1 minimum to an inner local minimum on the S2 surface, and this path is ex- tended linearly beyond the S2 minimum as well. Figs. 1 and 2 also show the partial atomic charge q on Ca along these three paths. The jumps in q along a reaction path together with the multiple minima in potential energy are intriguing. Such jumps have also been observed in chemical reactions involving metal atoms and small electronegative molecules (26–31), but have not been well studied in materials chemistry context. The charge transfer mediated by conical intersections is particularly interesting in the present case because of the negative electron affinity of the hydrocarbon molecules, because of the nonreactive nature of the potential energy surfaces, because the jumps are very sudden, and because of the technological importance of metal- π interactions. Although the acceptor of the transferred electron Fig. 2. Same as Fig. 1 except for CaCor system, using M06-2X/def2-SVP. The has a negative electron affinity when isolated, it binds the electron path has C2v symmetry.

in the presence of the cation produced by the charge transfer, as in the NaH2 system (32). The relative energies of optimized structures corresponding to key minima are given in Table 1, and their molecular geometries are shown in Figs. 3 and 4. In the structural labels, M denotes a local minimum, SP a saddle point, and CI a conical intersection. The semiquantitative agreement between single-reference [M06- 2X and CCSD(T)] and multireference (MRMP2) calculations in Table 1 is encouraging because previous work (33) showed poor agreement between these two kinds of calculations for Sc, V, and Ni complexes with benzene. (Those systems also show a long- range global minimum and a short-range metastable state, some- times with a different spin; experiments (34, 35) are consistent with observation of the long-range state.) Fig. 5, Upper and Low- er, show the energies of the four lowest electronic states of the CaEth and CaBen systems, respectively, as functions of the distance R along the LSP that connects an inner S2-M and an outer S0-M minima. The shapes of the potentials along these paths are similar for the two systems. The ground electronic state, which correlates adiabatically with the 4s2 state of the calcium atom, intersects the first excited singlet state twice: first at R of approxi- mately 3 Å, and then at a smaller R. At large R the first excited singlet state correlates adiabatically to the 4s13p1 state of Ca, and it is dominated by the 4s13d1 configuration of the Ca atom at geometries close to a conical intersection and at medium separations of the reactants in a region before the earliest S0S1 conical intersections due to crossing of the P and D states as the reactants approach. The middle minimum corresponds to a metastable biradical, which is found to have a similar bonding pattern in the Ca-ethylene, Ca-benzene, and Ca-coronene systems. In each case, a one- electron bond is formed between the Ca atom and the π-electron system, in which Ca and the hydrocarbon share one electron in an orbital ϕ2 formed by the interaction of the d-type orbital of Ca and one of the π orbitals of the hydrocarbon molecule. Because interactions between two closed-shell species in the ground electronic state are usually closed-shell singlets, the one-electron bonding in systems considered here is surprising. The origin of this unusual bonding type may be understood as follows: At large R Fig. 1. Cuts through the S0,S1, and S2 states as functions of for CaEth intermolecular separation of the reactants, the Ca atom in its (Upper) and CaB (Lower) systems. The zero of energy corresponds to infinitely ground electronic state has a closed-shell 4s2 dominant configura- separated reactants. The path has C2 symmetry for CaEth and C2v symmetry tion, whereas its 4s13d1 configuration corresponds to the second for CaBen. Dotted lines show the Hirshfeld charge on the Ca atom along the 4s13d1 ground electronic state singlet PES. Two sudden changes in the charge dis- excited state (36). As the reactants approach, the state of tributions along this path occur at two conical intersections. All data shown in Ca is lowered in energy due to the interaction of the 3d orbital this figure are obtained with M06-2X/def2-TZVPP (see Methods). with a π orbital of the hydrocarbon; therefore, this state under-

19140 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1010287107 Tishchenko et al. Downloaded by guest on September 23, 2021 Table 1. Relative energies (kcal∕mol, with respect to the middle minimum for ethylene and benzene, respectively)

† ‡ Structure PG* State ec q MRMP2 M06-2X CCSD(T)//M06-2X INAUGURAL ARTICLE Ethylene 1 2 S2-M C2 A b 0.7 25.5 21.5 22.5 1 2 S0S2-SP C2 A a 0.3 32.5 25.1 1 S1-M C2 B ðabÞS 0.3 3.45 0.87 1.62 1 a a S1-Mip C2v A2 ð 1 2ÞS 0.3 29.0 27.0 30.7 3 T1-M C2 B ðabÞT 0.3 0.0 0.0 0.0 3 a a T1-Mip C2v A2 ð 1 2ÞT 0.3 27.6 28.1 30.1 1 2 S0-M C2v A1 a 0.0 −11.9 −17.4 1 2 S0-M C2v A1 a 0.0 −11.7 −17.2 Benzene 1 2 S2-M C2v A1 a2 0.6 18.9 25.2 1 S1-M C2v A2 ða1a2ÞS 0.2 −0.25 0.68 3 T1-M C2v A2 ða1a2ÞT 0.2 0.0 0.0 3 a a T1-Mip C2v A2 ð 1 2ÞT 0.3 46.1 43.9 1 2 S0-M C2v A1 a1 0.0 −7.2 −15.4 1 a2 − − S0-Mip C2v A1 1 0.0 3.8 13.5 All results in this table are calculated at the optimized molecular structures of the CaEth and CaBen systems. *Point group. †Dominant electron confuguration. ‡Charge on Ca atom.

goes (avoided or actual, depending on the path) intersection with system with a metal atom are within 10–30 kcal∕mol from the 1 1 the state correlating with the 4s 3p state of Ca prior to the S0S1 isolated ground state reactants. conical intersections, and finally it intersects the ground electro- The biradical thus corresponds to a weakly quasibound com- nic state at S0S1-CI. At R smaller than its value at S0S1-CI, the plex of a hydrocarbon molecule with the Ca atom, in which 1 1 1 1 4s 3d configuration becomes the lowest-energy state; it corre- the latter largely preserves its atomic nature with an 4s 3d CHEMISTRY sponds to a biradical. The metastable biradical structure consti- open-shell dominant configuration, bound to the hydrocarbon tutes a middle minimum that is separated from reactants by an molecule by a one-electron multicentered bond. A schematic re- (avoided or actual) intersection of the two lowest singlet states presentation of the orbitals involved in the bonding is given in 2 and is separated from the inner minimum by another (avoided Fig. 6. The CaEth complex is bihapto (η ) with the Ca atom an- or actual) intersection of the S1 and S2 states. The intersections chored to the two carbons by the three-centered one-electron are actual (conical) intersections along the paths shown in Figs. 1 bond formed from the dxy orbital of Ca and π orbital of ethylene, 4 and 2, but they would be (weakly) avoided for most nonsymmetric and the CaBen complex is tetrahapto (η ) with the Ca atom an- paths. When conical intersections with biradical states have been chored to the carbons by the five-centered one-electron bond studied in organic chemistry (37–57), they are often located much formed from the dxz orbital of Ca and one of the π (e2u) orbitals higher in energy relative to the ground electronic state and come of benzene (see Fig. 6). The degeneracy of the two (e2u) orbitals into play only in photochemically induced processes, whereas the of benzene is lifted when the Ca atom approaches the benzene present intersections arising from the interaction of a π-electron ring, favoring the state with the highest orbital overlap. At geometries close to the middle minimum, the lowest-energy state is a ϕ1ϕ2 triplet, whose energy is lower than the corresponding ϕ1ϕ2 singlet. This feature may be viewed as a consequence of the lower energy of the 4s3d 3D state of free Ca atom as com- 1 pared to its 4s3d D state (36). The T1 triplet is close to the S1 singlet both geometrically and energetically. Spin change for the lowest adiabatic state has also been observed in, e.g., interactions of transition metal atoms with benzene (13), in reactions of Mo with CH4 (58), and in more complex organometallic reactions (59, 60).

Fig. 3. Optimized structures of CaEth complex. Bond lengths are given at the best electronic structure level available, namely, MRMP2∕CASSCFð2∕2Þ∕ 2 d – def -TZVPP þ for structures T1-M S1-Minpl (inpl denotes in-plane), CASSCF (4/7)/def2-TZVPP for structure S0S1-CI, and M06-2X/def2-TZVPP for structures Fig. 4. Same as Fig. 3 except for CaBen, for which all geometries are from – S0-SP S0-Minpl. M06-2X/def2-TZVPP calculations.

Tishchenko et al. PNAS ∣ November 9, 2010 ∣ vol. 107 ∣ no. 45 ∣ 19141 Downloaded by guest on September 23, 2021 the minimum on the a~3 B state of the CaEth complex, R is about 2.5 Å. The four carbon atoms involved in the bonding in the CaBen complex are equally distant from the Ca atom by 2.64 Å, and the two remaining carbons are equally distant from the Ca atom by 2.70 Å. The low-lying d orbitals of Ca have also been found (9) to play an important role in Ca binding to sp3 sites in covalent-bonded graphene (an all-graphitic 3D porous material). It is very important to understand the nature of the metal coor- dination because the coupling of a sudden charge transfer to a magnetic state provides an additional degree of freedom relevant to spintronics applications. Structures S2-M of CaEth and CaBen correspond to local minima on the S2 state at small R. At these structures the portion 2 2 of the valence wave function on Ca is dominated by the 3d (ϕ2) electron configuration at Ca atom, corresponding to a two- electron excitation from the 4s orbital of Ca to a hybrid 3d − π orbital of the system. Because of a change from the biradical to the closed-shell bonding pattern, these structures are characterized by shorter R and longer carbon–carbon distances than the structures at the middle minimum. In addition to the three minima, a variety of other critical points have been located on the potential energy surfaces of each of the systems considered. Structure S0 -SP1 is the first order saddle point that connects S2-M with an outer van der Waals complex on the lowest-energy closed-shell adiabatic potential energy surface (PES). Structures T1-Mip and S1-Mip represent local minima on the T1 and S1 potential surfaces analogous to the structures T1-M and S1-M with the only difference being that the Ca atom in the former two cases is placed in the plane of the ethylene molecule. These structures are found to be considerably higher in energy than their out-of-plane counterparts. An analogous T1-Mip structure has also been located on the lowest triplet potential energy surface in the case of CaBen complex. Because of the rather high energy of this structure, no attempt was made to locate a similar structure for an open-shell singlet state. Structure S0S1-CI is a minimum-energy point on the S0S1 conical intersection of the two lowest singlet states. This structure, as Fig. 5. Cuts through four lowest potential energy surfaces for CaEth (Upper) and CaBen (Lower) systems calculated by MS-CASPT2 as functions of R. optimized by complete active space self-consistent (CASSCF) 1 Also shown are the shapes of ϕ2 (the orbital that forms the one-electron (2/2)/def2-TZVPP, exceeds the energy of the E-S -M inner multicentered bond between Ca and the hydrocarbon) in these systems as minimum of the CaEth complex by 13.9 kcal∕mol. Calculations functions of the same distance. Arrows indicate approximate position of including dynamical electron correlation are expected to de- the optimized structures given in Table 1. The zero of energy in each case crease this energy difference. Although the importance of CIs is at the outer minimum. (61–65) in photochemical processes is now widely recognized (66, 67), their role in thermally activated processes is not well Shapes of the bonding orbital along the LSPs in CaEth and studied (68). The effect of a CI on a thermally activated reaction CaBen complexes are shown in Fig. 5. The three-centered depends on the energetic accessibility of the dividing surface and one-electron bond in the CaEth complex leads to an elongation of the seam of intersection. Examples of thermally activated re- of the carbon–carbon distance by about 0.1 Å, and the five- actions where the CI seam is (or can be) accessed under usual centered one-electron bond in the CaBen complex leads to an conditions involve chemiluminescence, energy transfer, reactions elongation of the two opposite carbon–carbon bonds of the four involving metal atoms (29, 32), and hydrogen atom abstractions carbons involved in the bonding by about the same amount. At from phenolic antioxidants (69). The CIs in systems considered here are particularly interesting because of their relevance in nonreactive processes, such as attachment of metal atoms to aromatic systems, which is of utmost importance in organometallic chemistry and materials chemistry. We now return to the coronene–calcium system, which will be abbreviated CaCor. The coronene-Ca cation has been recently studied by photodissociation (70), but we know of no experiment on the neutral. As in the cases of the smaller prototype systems, three kinds of equilibrium structures with dominant electron 2 2 configurations ϕ1,(ϕ1ϕ2), and ϕ2 exist that correspond to the outer, middle, and the inner minima, respectively (optimized molecular structures are shown in Fig. 7, and their energies are given ϕ2 in Table 2). Structure S0-Mcr (cr denotes central ring) ( 1) corresponds to the van der Waals minimum (no change in the elec- Fig. 6. Schematic representation of the key molecular orbitals (one of the Ca tron configurations of the fragments relative to the separated R ≈ 3 8 ϕ ϕ atom, and another on the hydrocaron molecule) involved in bond making for fragments; . Å), structures T1-Mcr [ð 1 2ÞT], and S1-Mcr CaEth (Left) and CaBen (Right) complexes. [ðϕ1ϕ2ÞS] correspond to the middle minima (one-electron bond

19142 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1010287107 Tishchenko et al. Downloaded by guest on September 23, 2021 Structures in which Ca is bound to an outer ring (S1-Mor, T1-Mor, and S2-Mor) are found to be energetically lower than structures in which Ca is bound to the central ring (i.e., than INAUGURAL ARTICLE the corresponding structures S1-Mcr,T1-Mcr, and S2-Mcr). This feature may be rationalized by considering that the geometry dis- tortion accompanying the metal-π bond formation is energetically more favorable for an outer ring than for the central ring. Mo- bility of the metal atom between different rings in both singlet and triplet manifolds represents an interesting question inviting a further study. The electronic state at the T1-Mcr minimum- energy geometry is found to be (nearly) degenerate (with the 3 3 B1 and B2 components in C2v symmetry). Furthermore, the ex- 3 cited A2 state has an energy minimum only ≈12 kcal∕mol above a~3B the ground 1 in the vicinity of the T1-Mcr structure. On the contrary, the excited states above the T1-M minima in the case of CaBen system are appreciably higher in energy. Fig. 8, Lower, depicts the eight lowest electronic states of the CaCor system as a function of R for the perpendicular approach of Ca toward the center of the coronene molecule. Because of the large size of this system, the results are given only at the state-averaged (SA)- CASSCF level. For comparison, Fig. 8, Upper and Middle, show CHEMISTRY

Fig. 7. Optimized (M06-2X/def2-TZVPP) structures of the CaCor system.

between Ca and the coronene molecule; R ≈ 2.7 Å) analogously to structures T1-M and S1-M for the CaEth and the CaBen sys- ϕ2 tems, and structures S2-Mcr ( 2) and S2-Mor (or denotes outer 2 ring) (ϕ2) correspond to the inner minima (two-electron bond between Ca and the coronene molecule; R ≈ 2.4–2.5 Å) analogously to the structures S2-M in the two smaller systems. The no- table distinctions between the CaCor and the CaBen systems are the following: (i) there are more than one attachment site for the metal atom in the former and (ii) due to the lower energy of the first several unoccupied molecular orbitals in the former system, several excited states at medium R become lower in energy as compared to the CaBen system.

Table 2. Relative energies at the optimized molecular structures of the coronene + Ca system* Structure PG State ec q M06-2X 1 b2 S2-Mcr C2v A1 2 0.7 42.8 1 0 a00 S2-Mor Cs A 0.7 18.6 1 00 a0a00 − S1-Mor Cs A ð ÞS0.3 0.2 1 a b S1-Mcr C2v B1 ð 1 1ÞS 0.4 6.1 3 00 a0a00 T1-Mor Cs A ð ÞT 0.3 0.0 3 a b T1-Mcr C2v B2 ð 1 2ÞT 0.4 7.5 3 a b T1-Mcr C2v B1 ð 1 1ÞT 0.4 7.5 3 a a T1-Mcr C2v A2 ð 1 2ÞT 0.3 19.0 1 2 S0-M C2v A a 0.0 −3.3 cr 1 1 Fig. 8. Cuts through the lowest adiabatic potential energy surfaces for The energies in this table are in kcal∕mol, with respect to the inner CaEth (Upper) and CaBen (Middle) and CaCor (Lower) systems calculated minimum, a~ 3A00). by SA-CASSCF as functions of R. In the latter case, additional states are shown *See footnotes to Table 1. because of their low energies.

Tishchenko et al. PNAS ∣ November 9, 2010 ∣ vol. 107 ∣ no. 45 ∣ 19143 Downloaded by guest on September 23, 2021 the SA-CASSCF results for the two smaller prototype systems. on Ca, whereas ϕ2 is a combination of the 3d orbital of Ca and a π orbital of The similarity in shapes of the adiabatic PESs corresponding the hydrocarbon at medium and small R, and it is a pure 3d orbital of Ca at R 3d to the S0,S1,T1, and S2 states in all three cases implies that larger ; the latter orbital is defined (among the set of 5 orbitals) as the the basic features described above must be valid for interactions one that has the largest overlap with a π lowest unoccupied molecular of Ca with a variety of aromatic molecules. orbital of the molecule. In MRMP2 calculations all orbitals were correlated; In summary, we find that approach of a Ca atom to an ex- i.e., no core orbitals were frozen. Molecular geometries were fully optimized tended π-system involves three kinds of minima in the PES: a by MRMP2 with numerical gradients. i Partial atomic charges in Tables 1 and 2 are Hirshfeld charges (74) ob- van der Waals minimum ( ), a biradical formed by partial single tained by density functional theory calculations with the M06-2X density charge transfer (ii), and a closed-shell singlet formed by partial iii functional. (The Hirshfeld charges are about 25% smaller than charges double charge transfer ( ). The shift in charge in moving from obtained by fitting the electrostatic potential.) i to ii or from ii to iii occurs suddenly (over a small range of geo- M06-2X density functional calculations are spin-unrestricted (i.e., spin- metry) because of two sequential (along a path) conical intersec- polarized) for the biradical states and spin-restricted for S0 and S2. 2 tions. In the entrance channel, the ϕ1 and ϕ1ϕ2 states intersect in Cuts through the PESs shown in Fig. 5 are obtained by multistate multi- a region where the energy of the d orbital of the metal atom is reference perturbation theory (MS-CASPT2) based on SA-CASSCF reference lowered by interaction with the π-type lowest unoccupied mole- wave functions with all four states weighted 25%. For the CaEth system, cular orbital of a molecule. The recognition that a sudden redis- the active space used in the reference SA-CASSCF wave function involves four tribution of charge may occur for a small change in geometry active electrons in seven active orbitals. This active space is larger than the provides a computational design handle for molecular electronic active space used in geometry optimizations by MRMP2; in addition to the two above-mentioned orbitals (4s and 3d orbitals of Ca), it also includes the π, switching devices if a conical intersection can be engineered to π orbitals of ethylene, and the 3px , 3py , and 3pz orbitals of Ca; this active occur near a stable or metastable state. In the middle range space is denoted (4∕4)or 4∕ 4s;3d;3px ;3py ;3pz;π;π . For CaBen system, the lowest-energy state overall is a metastable triplet so that ð f gÞ the SA-CASSCF wave function is based on the ð2∕fϕ1;ϕ2gÞ active space as the charge transfer may be coupled to magnetic changes. The described above. singlet-triplet splitting is small. The metastability and the mag- The potential energy curves shown in Fig. 8 are obtained by SA-CASSCF netic moment of the lowest-energy charge-transferred state at calculations. In the case of the CaCor system, the SA-CASSCF wave function is the intermediate approach distance are surprising and also invite constructed using the (2∕4) active space, where the four active orbitals in- exploitation. clude the lowest-energy orbital in each of the four symmetries, in order Organized charge transfer is a key element of photoactive re- to include additional electronic states. In this case, seven states (three lowest ceptors and electronic devices for sensing, signal conversion, and triplets and four lowest singlets) are weighted equally in the state average. memory. The transfer of a significant amount of charge when a For the CaBen system, these additional states are energetically higher and, system parameter is varied a small amount provides a control me- for that reason, the state average includes only four states. The SA-CASSCF chanism for charge transfer. The biradical character of the initial potential curves for CaEth and CaBen systems shown in Fig. 8 are obtained charge transfer state provides a mechanism for a magnetic state using the same active spaces as in the correlated MS-CASPT2 calculations. The change to be coupled to the motion of the metal atom. The para- CASSCF calculations include only nondynamical electron correlation, whereas meter here is a geometrical coordinate, but in a device sensitivity the other methods include both nondynamical and dynamical correlation. The one-electron basis set used in coupled cluster, including all single and to a geometrical coordinate could be replaced by sensitivity to a double excitations and a quasiperturbative treatment of connected triple ex- physical parameter such as pressure, external field, or substrate citations [CCSD(T)], MS-CASPT2, and most M06-2X and SA-CASSCF calcula- (71). The high sensitivity could then be manifested in a large hy- tions is def2-TZVPP (75), and in the MRMP2 calculations it is def2-TZVPP perpolarizability or sensitive control of charge or magnetization plus one s and one p diffuse functions on carbon atoms with the exponents state. The present results show that it is important to consider not 0.04402 (76) and 0.03569 (76), respectively. The exceptions are the M06-2X just equilibrium structures but also nearby features of the poten- calculations for CaCor shown in Fig. 2 and the SA-CASSCF calculations for tial energy surfaces that indicate accessible mechanisms for pro- the same system shown in Fig. 7; these are performed with the def2-SVP cesses that change the charge distribution or magnetic state. (75) basis set. MRMP2 calculations are performed with GAMESS (77), M06-2X and CCSD(T) calculations are performed with GAUSSIAN (78), and SA-CASSCF Methods and MS-CASPT2 calculations are performed with MOLPRO (79). The MRMP2 results in Table 1 are based on CASSCF (72, 73) reference wave functions with two electrons in two active orbitals, ϕ1 and ϕ2; this active ACKNOWLEDGMENTS. The authors are grateful to Doreen Leopold for helpful 2∕ ϕ ;ϕ 2∕ 4s;3d 2∕ ϕ ;ϕ space is denoted here as ð f 1 2gÞ or ð f gÞ. The ð f 1 2gÞ active discussion. This work was supported in part by the National Science Founda- space is the minimal active space required to get a qualitatively correct de- tion under Grant CHE09-56776, by a Molecular Science Computing Facility scription of the shapes of the lowest potential energy surfaces and the three Computational Grand Challenge grant at the Environmental Molecular (middle, M-S1 and M-T1, and inner, M-S2) mechanistically relevant energy Science Laboratory of Pacific Northwest National Laboratory (computer minima. In terms of atomic orbitals, ϕ1 is mainly composed of the 4s orbital time), and by the Minnesota Supercomputing Institute (computer time).

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