Thermodynamic Stability versus Kinetic Stability: Is the Planar

Apr 28, 2014 - ... during Born–Oppenheimer molecular dynamic (BOMD) simulations. ... Juan Andrés , Lourdes Gracia , Patricio González-Navarrete , Vice...
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Thermodynamic Stability versus Kinetic Stability: Is the Planar Hexacoordinate Carbon Species D3h CN3Mg3+ Viable? Chao-Feng Zhang,† Shao-Jin Han,†,‡ Yan-Bo Wu,*,‡ Hai-Gang Lu,‡ and Gang Lu# †

College of Chemistry and Chemical Engineering, Taiyuan University of Technology, Taiyuan, 030024, P.R. China Institute of Molecular Science, the Key Laboratory of Chemical Biology and Molecular Engineering of Education Ministry, Shanxi University, Taiyuan 030006, P.R. China # State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, P. R. China ‡

S Supporting Information *

ABSTRACT: The experimentally observed planar hypercoordinate carbon species were detected in gas phase experiments and characterized by photoelectron spectroscopy. According to the Boltzmann distribution law, the thermodynamically favorable isomers, especially global minima, were relatively easier to detect than other isomers in such an experimental process. Here, we reported a thermodynamically unfavorable case, i.e., D3h CN3Mg3+ (1a), which we think is experimentally viable because all isomers that are energetically lower than 1a show bimolecular assembly type structures consisting of an N2 unit and various types of CNMg3+ units. The natural bond orbital (NBO) analysis suggests that the bonding between N2 and CNMg3+ is rather weak, and we think it is very hard to retain their basic structures when kinetic factors are considered. Consistently, the four lowest isomers in the second group show dissociation (to free N2 molecule and CNMg3+ cations) during Born−Oppenheimer molecular dynamic (BOMD) simulations. In contrast, the structure of 1a can be maintained under temperatures up to 2000 K during the BOMD simulation, and ring-opening reaction studies suggest the barrier to be very high, 46.75 kcal/mol. We think the excellent kinetic stability of 1a will compensate for its thermodynamic instability and it will own its existence in the gas phase synthesis. Although many isomers in the second group are energetically more favorable than 1a, they will be dissociated by the kinetic process. In the magnetic field, the positively charged CNMg3+ units will be separated quickly from N2 molecules in the general gas phase synthesis, and they are therefore undetectable.

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INTRODUCTION Planar tetracoordinate carbon (ptC) was first reported by Monkhorst in 1968 as a transition state of “interconversion of enantiomers containing asymmetric carbon atoms without breaking bonds”.1 Hoffmann, Alder, and Wilcox sponsored in 1970 the project stabilizing the ptC species.2 The quest for ptC originated from the question of whether such nonclassical carbon bonding, previously believed to exist in transition state structure, can be stabilized in equilibrium structure. The ptC arrangement was first realized computationally in 1976 when the Schleyer−Pople joint group proposed 1,1-dilithiocyclopropane.3 Since then, numerous theoretical investigations have been performed,4−9 which eventually led to the experimental detection of ptC species CAl4−, NaCAl4−, CAl3Si−, and CAl3Ge− in gas phase photoelectron detachment spectroscopy in 1999−2002 by the Wang−Boldyrev joint group.10−13 As a conceptual extension to ptC, the planar hypercoordinate carbon, including planar penta- and hexa-, and hepta-coordinate carbon (ppC, phC, and p7C), was also extensively studied. In 2000, the phC bonding, as exemplified by the milestone D6h CB62−, was proven to be viable by Schleyer’s group.14 In 2001, they further proposed that the ppC-containing units, −C3B3−, −C2B4−, and −CB5−, can be used as the building blocks to link © 2014 American Chemical Society

with various aromatic or anti-aromatic hydrocarbons to construct a large family of ppC-containing aromatic species, the so-called “hyperenes”.15 They simultaneously proposed the D7h CB7− minimum with p7C. In 2004, Li’s group proposed a hydrocopper complex Cu5H5C with a ppC in the center.16 In 2007, using the strategy similar to that employed in designing hyperenes, the Li−Schleyer joint group reported a series of species with phC.17 However, in 2007 and 2008, the Wang− Boldyrev joint group proved that the planar hypercoordinate species D7h CB7−,18 D6h CB62−, CB6−, and C2v C2B5−19 were experimentally unviable because they are the high energy isomers on their potential surfaces and their signals will be overwhelmed by those of their low-lying isomers. Such results prompted the theoretical chemists to find thermodynamically stable planar carbon species to facilitate experimental confirmation. In 2006, Schleyer’s group proposed that D4h CCu42+, C2v CCu3Ni+, and D2h CCu2Ni2 were ptC global minima on their potential surfaces.20 Our group found in 2009 that the global minima of hexatomic species C2E4 (E = Al, Received: November 20, 2013 Revised: April 16, 2014 Published: April 28, 2014 3319

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Ga, In, Tl) were rhomboid and had double ptCs in the center.21 Note that C2Al4 was experimentally confirmed by single photon ionization spectroscopy in 2010.22 Our analysis on the electron structure of C2Al4 suggested that each Al atom possesses a 3s lone pair which may lead to high chemical reactivity. We then proposed a bifunctional strategy to stabilize the C2Al4 and simultaneously designed a series ptC species with C2Al4 cores C2Al4E8 (E = CH3, NH2, OH, F, Cl, t-Bu, etc.),23 in which C2Al4E8 (E = CH3, NH2, OH) was employed to design the chains, planar sheets, and tubular nanomolecules with ptC.24,25 In 2010, Ding’s group proposed to use the strategy of localization rather than delocalization to design the pentatomic species with ptC and C-X multiple bonds, and they found that their designed species BCAl32− and NCAl3 are global minima.26 In 2011, the Ding−Merino joint group further found that the global minimum of CB4+ possesses a ptC.27 In 2012, Merino’s group designed CE42− (E = Ga, In, Tl), which are the isoelectronic species of CAl42−.28 In 2008, the first global minimum ppC species D5h CAl5+ was predicted by the Zeng− Schleyer joint group.29 In 2010 and 2012, our group proved that the isoelectronic species of D5h CAl5+, including C2v CAl4Be, C2v CAl3Be2−, C2v CAl2Be32−, and C2v LiCAl2Be3−, were global minima with ppC.30,31 Merino’s group revealed that CBe5E− (E = Al, Ga, In, Tl) were also global minima with ppC and were also isoelectronic with D5h CAl5+.32 As for phC, the crowded positioning of atoms around the central carbon seriously affects the stability of molecules. Global minimum phC species are rare. In 2012, our group reported an ionic bonded global minimum structure D3h CO3Li3+, and we proposed from the “coordination number” point of view that it is a phC species.33 The above species were thought to be viable because they possessed good thermodynamic stability. In this work, we would like to explore the importance of kinetic stability for planar carbon species. We are inspired by our previous findings that the high energy local minimum (D3h CN3Be3+) can be kinetically very stable.33 We wonder whether there exists a component in which the energetically low-lying isomers are kinetically unstable, and thus a kinetically stable high-lying isomer can be viable. The answer turned out to be YES and CN3Mg3+ is proven to be such a component. We will show in the following that a D3h isomer with a phC (1a, see Figure 1 for the structure) in the center is kinetically very stable, whereas those energetically more favorable isomers are kinetically unstable.

Figure 1. MP2/aug-cc-pVTZ optimized structures, point groups, and CCSD(T)/aug-cc-pVTZ corrected relative energies of five lowest isomers in the first group and four lowest isomers in the second group of CN3Mg3+ potential energy surface.

frequencies are restudied at the MP2/aug-cc-pVTZ level. The energies of these isomers are further improved at the CCSD(T)/aug-cc-pVTZ level based on the MP2/aug-ccpVTZ optimized geometries [CCSD(T)//MP2]. The T1 diagnostics of converged CCSD wave functions range from 0.017 to 0.027 and simultaneously the D1 diagnostics are less than 0.1, ranging from 0.043 to 0.094, so the multireference characters are not considered. To assess the kinetic stabilities of concerned isomers, the Born−Oppenheimer molecular dynamic (BOMD)37,38 simulation was performed at B3LYP/6-31G(d) level without the consideration of periodic boundary condition (PBC). The simulations were run at both 298 and 373 K for the isomers concerned, including 1a and 2a−2d, while for 1a only, the simulations were also performed at 1000, 1500, and 2000 K, respectively. The force constant was renewed every five steps during the simulation. The lowest ring-opening barrier was obtained by searching for the transition states of various types of isomerization reactions. Natural bond orbital (NBO) analysis was performed to understand the electron structures of some isomers.39 The nucleus-independent chemical shift (NICS) analysis was carried out to assess the aromaticity of 1a.40,41 The electron affinities (EA) of certain isomers were calculated by the outer-valence Green’s function (OVGF) at the OVGF/aug-cc-pVTZ level.42 The random structures for the exploration of potential energy surface were generated by the GXYZ program,36 while other calculations were carried out using the Gaussian 09 package.43

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COMPUTATIONAL METHODS The potential energy surface (PES) of CN3Mg3+ was probed using the stochastic search algorithm.34,35 The needed random geometries were generated by the GXYZ program21,36 and then subjected to geometry optimization at B3LYP/6-31G(d) level. To guarantee the convergence of PES, we run three sets of PES searches on singlet surface and two sets on triplet surface. It is found that the isomers can be divided into two groups. In the first group, all atoms in the isomer are tightly bound as a whole molecule, whereas in the second group, the isomers can be considered as the weak assemblies of an extremely stable N2 molecule (nitrogen gas) and a CNMg3+ unit. We select 6 and 40 lowest isomers in the first and second groups, respectively, for the reoptimization and harmonic vibrational frequency analysis as the B3LYP/aug-cc-pVTZ level. For the six lowest isomers in the first group and the ten lowest isomers in the second group, the geometries and harmonic vibrational

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RESULTS AND DISCUSSION We start from our previously reported phC species D3h CN3Be3+. By replacing the Be atoms in D3h CN3Be3+ by its heavy congener Mg atoms, a new species D3h CN3Mg3+ can be constructed (see 1a in Figure 1). At both B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels, 1a is an energy minimum with the lowest vibrational frequency at 162 and 156 cm−1, respectively. The C−N and C−Mg interatomic distances are 3320

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(point “c”). As shown in Figure 2, the total NICS values for a, b, and c are 0.61, −13.81, and −50.17 ppm, respectively. With the symmetry of 1a taken into account, more than two-thirds of the molecular regions are aromatic in total, so we consider 1a to be an aromatic molecule. NICS(0)πzz is the most refined NICS index, which extracts the out-of-plane tensor component of the isotropic NICS and includes only the π MO contributions for quantifying aromaticity. The dissected contributions from each π MO are given below the π MO plots in Figure 2. Though one of the degenerate HOMOs contribute negatively (positive values) to the aromaticity at points a and b, other contributions from the π MO to the aromaticity of a, b, c are all positive (negative values). Based on NICS(0)πzz criteria, the aromaticity in 1a is a little weaker than in cyclopentadienyl anion (C5H5−) and benzene (C6H6), whose molecular centers have NICS(0)πzz values of −35.63 and −35.50 ppm, respectively, at the B3LYP/aug-cc-pVTZ level, thus 1a should be an aromatic molecule and we think it is indispensable for the stabilization of such phC structure. 1a is an equilibrium structure with a relatively large HOMO−LUMO gap, but this does not suffice for the experimental realization. For such a small cluster, the thermodynamic stability plays a very important role in the experimental viability. The energetically low-lying isomers, especially the global minima, are strongly favored. Nevertheless, the kinetic persistence is equally important for viability. A large number of higher energy “metastable” molecules can exist due to the large barriers precluding the isomerization to more stable forms and further reaction. To assess the experimental viability of 1a and its isomers, we analyzed the stability both thermodynamically and kinetically. The thermodynamic stability was explored by the stochastic search algorithm. The located isomers can be divided into two groups. In the first group, the atoms in the isomers are tightly bonded as a whole molecule, while in the second group, the isomers can be considered as the assemblies of N2 (nitrogen gas) molecules with various types of CNMg3 units. The five lowest isomers in the first group (1a−1e) and the four lowest isomers in the second group (2a−2d) are shown in Figure 1. 1a is the most stable isomer in the first group, but due to the extreme stability of the N2 molecule, there are 33 isomers in the second group, which turned out to be thermodynamically more favorable than 1a at the B3LYP/aug-cc-pVTZ level. The global minimum (2a, see Figure 3) is located 20.25 kcal/mol lower in energy than 1a. Though the calculations at MP2 diminish the energy difference to 3.95 kcal/mol, the CCSD(T)//MP2 calculations amplify such a difference to 13.96 kcal/mol. Thus, from the thermodynamic consideration, 1a is very hard to observe in the gas phase synthesis as its signals will be overwhelmed by the thermodynamically more favorable isomers. Could this happen in the experiments? To answer the question, we need to examine the kinetic stability of certain isomers because the importance of kinetic stability is equal to that of thermodynamic stability for the viability. Without good kinetic stability, even the global minima cannot be viable experimentally. Before we carried out the kinetic studies, we first analyzed the electron structures of isomers in the second group and we found that the bonding between the N2 part and the CNMg3 part is rather weak. If we take the global minimum (2a, see Figure 1) as the example, the natural charge on the N2 unit is 0.09 |e|, suggesting that the N2 unit almost exists as a neutral nitrogen gas molecule; as a result, the net charge on the

1.391 and 2.212 Å at B3LYP/aug-cc-pVTZ and 1.399 and 2.234 Å at MP2/aug-cc-pVTZ, respectively. The values are well within the normal C−N and C−Mg bond lengths, so D3h CN3Mg3+ can be regarded as a phC species. The HOMO− LUMO gap is relatively large, 2.46 eV at the B3LYP/aug-ccpVTZ level, which suggests good electron structure in this phC species. Why can the phC structure be stabilized in 1a? NBO analysis gives some clues. The total Wiberg bond order for C−N, C− Mg, and N−Mg (WBIC−N, WBIC−Mg, and WBIN−Mg) is 1.33, 0.01, and 0.28, respectively. The natural charges (Q) on C, N, and Mg atoms are 0.35, −1.42, and 1.64 |e|, respectively. The WBIC−N value of 1.33 suggests the typical covalent C−N bonding, the WBIC−Mg value of 0.01 suggests that C−Mg interactions are mainly ionic, and the WBIN−Mg value of 0.28, together with the large charge separation (−1.42 vs 1.64 |e|), suggests the N−Mg interactions are mainly ionic but with substantial covalent properties. According to our previous results, the ionic C−Mg interaction helps to soften the rigidity of directionality of classical carbon bonding, i.e., to benefit the stabilization of nonclassical phC bonding, while the effective N−Mg interactions (both electrovalent and covalent) are crucial to maintaining the phC skeleton. Aromaticity plays an important role in the stabilization of phC in 1a. Like benzene and previously reported phC species, D6h CB62−, D3h C4B3+, CN3Be3+, and CO3Li3+, it possesses three occupied π molecular orbitals. As shown in Figure 2, the

Figure 2. Plots of valence occupied MOs of 1a. The dissected contributions from each occupied π MO to the NICS values are listed below the π MO plots.

symmetries of π orbitals HOMO−3 and degenerate HOMOs are like those of benzene. Consistently, NBO analysis revealed total π electron occupancy of 5.95 |e|, which suggests a typical 6 π electron aromatic system. The NBO analyses also revealed that 5.84 of the total 5.95 |e| for π electron occupancy locate on one C and three N atoms, whereas only 0.11 |e| locate on three Mg atoms. Nevertheless, as shown in Figure 2, the π MOs are delocalized on the whole molecule rather than only on C and N atoms. To further confirm the aromaticity, we calculated the NICS and NICS(0)πzz at the middle points of C−Mg bond (point “a”), the C−N−Mg triangle (point “b”), and C−N bond 3321

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curves for simulation of 2a at 298 and 373 K are shown in Figure 3 as I and II. We can see the irreversible increase for the RMSD values at 9.9 and 33.9 ps, respectively, suggesting the essential structural changes from 2a during the dynamic simulations. Similar situations are met for the simulations of 2b (see Figure 3 III and IV). The RMSD curve for the simulation at 298 K shows a drastic fluctuation after 41.9 ps, and it eventually increases irreversibly at 60.6 ps, whereas that for the simulation at 373 K directly shows the irreversible increase at 9.1 ps. For the simulation of 2c and 2d, the RMSD curves (see Figure 3 V, VI, VII, and VIII) increase irreversibly at 10.1 and 3.5 ps at 298 K and at 5.2 and 3.6 ps at 373 K, respectively. We checked the detailed structural evolution around the time where increase of RMSD curves occurs and found that the variations of RMSD values are all caused by the expected dissociation (to free N2 unit and CNMg3+ moiety). As a comparison, we run the BOMD simulations for 1a at 298 and 373 K. As shown in the upper two RMSD curves in Figure 4, the values have no sharp increase during the 100 ps

Figure 3. RMSD vs time in the BOMD simulation of 2a−2d at 298 and 373 K, respectively.

CNMg3 moiety is 0.91 |e|, suggesting a monocation. The Mg atom that bonds to the N2 unit holds the natural charge of +0.62 |e|, while the N atom that bonds to such a Mg atom holds only −0.09 |e|; the other N atom in the N2 unit holds +0.18 |e|. The charge distribution on the N2 unit shows obviously induced local dipole character, so the electrovalent interaction between the N2 unit and CNMg3 moiety is rather weak. Simultaneously, the Wiberg bond index (WBI) for N−Mg interaction is only 0.18, revealing also the weak covalent interactions between N2 unit and CNMg3 moiety. The NBO results of other isomers in the second group are listed in Table S1 in the Supporting Information. Similar to the situation for 2a, The natural charges of Mg atoms that link to the N2 unit range from 0.22 to 0.93 |e|, that of related N atoms ranges from −0.19 to −0.07 |e|, and that of whole N2 units ranges from −0.20 to 0.11 |e|, respectively, which indicates weak Mg−N2 electrovalent interactions. In addition, the WBIN−Mg values concerning Mg−N2 bonding range from 0.06 to 0.23, revealing the weak Mg−N2 covalent interaction. We think such weak bonding is sufficient for kinetically retaining the basic structures of isomers in the second group. In this work, the kinetic stability of isomers is mainly examined by BOMD simulations at the B3LYP/6-31G(d) level. The evolution of structures during the simulations is evaluated by the root-mean-square deviation (RMSD, in Å) of atomic coordinates to that in B3LYP/6-31G(d) optimized structures. To demonstrate our deduction that the isomers in the second group are kinetically unstable, the four lowest isomers (2a−2d) are taken as the example for BOMD simulations. The RMSD

Figure 4. RMSD vs time in the BOMD simulation of 1a at 298, 373, 1000, 1500, and 2000 K, respectively.

simulations, suggesting that the structure of 1a is wellmaintained at these two temperatures. We further run the simulations at much higher temperatures, i.e., 1000, 1500, and 2000 K, respectively. Remarkably, the RMSD curves also have no sharp increase during the 100 ps simulations, which implies structural rigidity of 1a at the temperature up to 2000 K. Despite the well-maintained structure, the thermal vibrations become intense as the temperature goes up. The RMSD values of simulations at 298, 373, 1000, 1500, and 2000 K range from 0.04, 0.05, 0.07, 0.07, and 0.08 to 0.25, 0.27, 0.30, 0.40, and 0.49 Å, respectively. The average RMSD values for these five sets of simulations are 0.17, 0.16, 0.19, 0.22, and 0.24 Å, respectively. The dynamic simulations suggest excellent kinetic stability of 1a. Why can 1a be kinetically very stable? We studied the ringopening reactions to destroy 1a at the B3LYP/aug-cc-pVTZ level. According to our calculations, the out-of-plane reaction paths are unfeasible because we cannot locate any transition state for such reactions. Only an in-plane path can be feasible, but the barrier for such an isomerization reaction is very high, being 46.75 kcal/mol (see Figure 5) at the CCSD(T)/aug-ccpVTZ//MP2/aug-cc-pVTZ level, which suggests that kineti3322

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Kinetically, since one of the products (H2) is extremely stable, our desired product (1a) may also have the opportunity to be generated and detected in the experiment with precursors having CN3 subunits. To aid the experimental confirmation, we compute the EA for 1a, 2a, and 2b at OVGF/aug-cc-pVTZ level. The EA value of 1a (being 4.35 eV) is differentiable from that of 2a and 2b (being 4.45 and 4.44 eV, respectively). Since 1a has the doubly degenerate HOMOs, the corresponding EA peak will be very intense and can be regarded as the fingerprint in the spectra.

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CONCLUSION In summary, we have proven in this work the important effect of kinetic stability for the viability of planar hypercoordinate carbon species. Though phC species 1a (D3h CN3Mg3+) is thermodynamically unfavorable, our BOMD simulations and ring-opening barrier studies suggest its excellent kinetic stability and we think it will own its existence finally. In contrast, though many isomers with N2−CNMg3+ assembly type structures are thermodynamically more favorable than 1a, they will be dissociated by the kinetic motivation because the bonding interactions between N2 and CNMg3+, which are crucial for maintaining their basic structure, are rather weak. The BOMD simulations for the four lowest such type isomers proved our deduction. Therefore, 1a may be realized as a kinetically stable phC species.

Figure 5. Reaction path to destroy the structure of 1a. The minima nature for the reactant (RE) and the product (PR) and the first-order saddle point nature for the transition state (TS) structure were confirmed at the MP2/aug-cc-pVTZ level. The reaction barrier and reaction heat were reported at the CCSD(T)/aug-cc-pVTZ//MP2/ aug-cc-pVTZ level. The red arrows in the transition state (TS) structure denote the vibrational modes of imaginary frequency.

cally destroying the structure of 1a is very difficult. Note that the initial product for the ring-opening reaction is in a singlet electron state. As the singlet product of the reaction and the isomer 1d are almost identical in structure, the electron state with lower energy will be the real existing form. When the singlet PR is generated, the electron state will change immediately to the triplet state to lower the energy, so the final product should be triplet PR, 1d. We also studied the reaction on the triplet surface, but we cannot locate any triplet TS for the reaction, so the reaction should proceed in the singlet pathway. On the basis of the thermodynamic and kinetic analysis above, we think that 1a is more probable than its energetically more favorable isomers in the second group because of kinetic factors. 1a is kinetically stable at the temperature up to 2000 K, so once it is generated, it is very easy to maintain the basic structure during the annealing process and finally own its existence. It should be noted here that the detection of 1a may need a relatively long time to collect enough signals. In contrast, though many isomers in the second group can be thermodynamically more stable than 1a, they will dissociate during the kinetic process. Since the molecules generated in the gas phase synthesis will generally move in the magnetic field, the positively charged CNMg3+ units will separate quickly from the neutral N2 molecules; thus, these N2−CNMg3+ assemblytype isomers will lose their opportunity to be detected in the following spectroscopic studies. We think one manner of experimental generation of 1a can be laser ablation or arc discharge of the targets with C, N, and Mg atoms and the other manner is to employ the species having a CN3 moiety. For example, a possible precursor is the guanidinium cation, i.e., D3 C(NH2)3+. Substituting the H atoms in D3 C(NH2)3+ by Mg atoms will lead to 1a. We studied the substitution energy at the CCSD(T)/aug-cc-pVTZ//MP2/ aug-cc-pVTZ level, suggesting an endothermic substitution process (by 20.20 kcal/mol). Though it is thermodynamically unfavorable, the very high temperature in the initial moment of gas phase synthesis will easily compensate such energy.

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ASSOCIATED CONTENT

S Supporting Information *

Optimized geometries of structures mentioned in the text, NBO analysis results on N2−CNMg3+ bonding, and full form of ref 43. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86 351 701 8113. Tel: +86 351 701 0699. Author Contributions

Chao-Feng Zhang and Shao-Jin Han contributed equally. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

This work is supported financially by NSFC (Grant Nos. 21273140, 21003086, and 20973197), SXNSF (Grant No. 2009021016), and the Foundation of State Key Laboratory of Theoretical and Computational Chemistry (Grant No. K1104).

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ABBREVIATIONS BOMD, Born−Oppenheimer molecular dynamic; ptC, planar tetra-coordinate carbon; ppC, planar penta-coordinate carbon; phC, planar hexa-coordinate carbon; p7C, planar heptacoordinate carbon; PES, potential energy surface; CCSD(T), coupled-cluster theory with single, double, and perturbative triple excitation; PBC, periodic boundary condition; NBO, natural bond orbital; NICS, nucleus-independent chemical shift; OVGF, outer-valence Green’s function; RE, reactant; TS, transition state; PR, product 3323

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