The Reactivity of Ambident Nucleophiles: Marcus Theory or Hard and Soft Acids and Bases Principle?

The model reactions CH3 X + (NH-CH=O)M ➔ CH3 -NH-NH═O or NH═CH-O-CH3 + MX (M = none, Li, Na, K, Ag, Cu; X = F, Cl, Br) are investigated to demonstrate the feasibility of Marcus theory and the hard and soft acids and bases (HSAB) principle in predicting the reactivity of ambident nucleophiles. The delocalization indices (DI) are defined in the framework of the quantum theory of atoms in molecules (QT-AIM), and are used as the scale of softness in the HSAB principle. To react with the ambident nucleophile NH═CH-O- , the carbocation H3 C+ from CH3 X (F, Cl, Br) is actually a borderline acid according to the DI values of the forming C…N and C…O bonds in the transition states (between 0.25 and 0.49), while the counter ions are divided into three groups according to the DI values of weak interactions involving M (M…X, M…N, and M…O): group I (M = none, and Me4 N) basically show zero DI values; group II species (M = Li, Na, and K) have noticeable DI values but the magnitudes are usually less than 0.15; and group III species (M = Ag and Cu(I)) have significant DI values (0.30-0.61). On a relative basis, H3 C+ is a soft acid with respect to group I and group II counter ions, and a hard acid with respect to group III counter ions. Therefore, N-regioselectivity is found in the presence of group I and group II counter ions (M = Me4 N, Li, Na, K), while O-regioselectivity is observed in the presence of the group III counter ions (M = Ag, and Cu(I)). The hardness of atoms, groups, and molecules is also calculated with new functions that depend on ionization potential (I) and electron affinity (A) and use the atomic charges obtained from localization indices (LI), so that the regioselectivity is explained by the atomic hardness of reactive nitrogen atoms in the transition states according to the maximum hardness principle (MHP). The exact Marcus equation is derived from the simple harmonic potential energy parabola, so that the concepts of activation free energy, intrinsic activation barrier, and reaction energy are completely connected. The required intrinsic activation barriers can be either estimated from ab initio calculations on reactant, transition state, and product of the model reactions, or calculated from identity reactions. The counter ions stabilize the reactant through bridging N- and O-site of reactant of identity reactions, so that the intrinsic barriers for the salts are higher than those for free ambident anions, which is explained by the increased reorganization parameter Δr. The proper application of Marcus theory should quantitatively consider all three terms of Marcus equation, and reliably represent the results with potential energy parabolas for reactants and all products. For the model reactions, both Marcus theory and HSAB principle/MHP principle predict the N-regioselectivity when M = none, Me4 N, Li, Na, K, and the O-regioselectivity when M = Ag and Cu(I). © 2019 Wiley Periodicals, Inc.

O-Regioselective Synthesis with the Silver Salt Method.

The excellent O-regioselectivity of the glycosidation of the ambident 2-O-substituted 5-fluorouracil (5-FU) via the silver salt method is computationally investigated at the MP2/6-311++G(2d,p):DZP//B3LYP/6-31+G(d):DZP level of theory. The reactions studied are those between 1-bromo-1-deoxy-2,3,4,6-tetra-O-acetyl-α-d-glucopyranose and the silver salts of 5-FU, 2-O-butyl-5-FU, and 2-O-benzyl-5-FU. Two pathways are considered as follows: (A) one where the silver and bromide ion do not interact, and (B) another where the silver and bromide ion interact in the transition states. Because the O-reaction barriers are much lower (by 13.3-22.2 kcal/mol) than N-reaction barriers in both pathways, the O-regioselectivity of the silver salt method can be satisfactorily explained by either path A or path B. Furthermore, path B, where Ag and Br interact consistently, has lower activation barriers than the corresponding path A (by 6.8-17.4 kcal/mol) in both N- and O-reactions. This computational result can be attributed to the following reasons: (1) the speeding-up effect in Koenigs-Knorr reactions due to the addition of silver carbonate into the reaction mixture; (2) the halogens being pulled away by silver ions from halides, as proposed by Kornblum and co-workers; and (3) the oxocarbenium ion involvement in the glycosidation reactions. The large energy difference between N- and O-transition states originates from the association between Ag and N-(O-) of the ambident unit (-N3-C4=O4) that shows significant covalent character so that the O-reaction transition states of the silver salt method benefit from favorable ionic interaction (C+···O-) and favorable covalent interaction (Ag···N). These two favorable interactions are in agreement with the hard and soft acids and bases principle; the former is a hard-hard interaction and the latter is a soft-soft interaction.

Theoretical Studies of the Glycosidation of 2-O-Substituted 5-Fluorouracil: N-Regioselective Synthesis with the Phase-Transfer-Catalysis Method.

The observed N-regioselective glycosidation of 2-O-substituted 5-fluorouracil (5-FU) via the phase-transfer-catalysis (PTC) method was investigated computationally. The Gibbs free energy reaction barrier of the N-reaction between the 5-FU anion and 1-bromo-1-deoxy-2,3,4,6-tetra-O-acetyl-α-d-glucopyranose was computed at the MP2/6-311++G(2d,p)//B3LYP/6-31+G* level. The calculated transition states were, in general, quite "loose", with the ambident reaction sites at the N3- or O4-positions on 5-FU located approximately 2.0 Å from the anomeric carbon. With the SN2 mechanism, the formation of ß-glycosides was explained by the characteristics of transition states, and the N-regioselectivity was explained by three considerations: (1) the conformations of initial complexes and the structural requirement of the reactions; (2) the formation of an ionic pair between nBu4N+ and 2-O-substituted 5-FU anions; and (3) the thermodynamic conversion of O-glycosides to N-glycosides. The reactions between the oxocarbenium ion and the 2-O-substituted 5-FU anions (the fast step of SN1 mechanism) were also examined at the same level of theory. Because there were no "promoters" to extract Br in the PTC method, the SN1 mechanism might have an unfavorably high barrier to produce oxocarbenium ion. However, both the formation of ß-glycosides and the experimentally observed N-regioselectivity could also be explained by the SN1 mechanism: The former was explained by the neighboring group participation, and the latter was explained by the formation of ionic pairs between nBu4N+ and 2-O-substituted 5-FU anions. The formation of ionic pairs possibly changed the diffusion-controlled mechanism into an activation-controlled mechanism. Two factors were demonstrated by Marcus theory to play an important role for the experimentally observed N-resioselectivity in the PTC method: (1) the thermodynamic stability of N-products over O-products; (2) the formation of ionic pair between nBu4N+ and 2-O-substituted 5-FU anions.

An efficient extrapolation to the (T)/CBS limit.

We extrapolate to the perturbative triples (T)/complete basis set (CBS) limit using double ζ basis sets without polarization functions (Wesleyan-1-Triples-2ζ or "Wes1T-2Z") and triple ζ basis sets with a single level of polarization functions (Wesleyan-1-Triples-3ζ or "Wes1T-3Z"). These basis sets were optimized for 102 species representing the first two rows of the Periodic Table. The species include the entire set of neutral atoms, positive and negative atomic ions, as well as several homonuclear diatomic molecules, hydrides, rare gas dimers, polar molecules, such as oxides and fluorides, and a few transition states. The extrapolated Wes1T-(2,3)Z triples energies agree with (T)/CBS benchmarks to within ±0.65 mEh, while the rms deviations of comparable model chemistries W1, CBS-APNO, and CBS-QB3 for the same test set are ±0.23 mEh, ±2.37 mEh, and ±5.80 mEh, respectively. The Wes1T-(2,3)Z triples calculation time for the largest hydrocarbon in the G2/97 test set, C6H5Me(+), is reduced by a factor of 25 when compared to W1. The cost-effectiveness of the Wes1T-(2,3)Z extrapolation validates the usefulness of the Wes1T-2Z and Wes1T-3Z basis sets which are now available for a more efficient extrapolation of the (T) component of any composite model chemistry.

MP2/CBS atomic and molecular benchmarks for H through Ar.

We extrapolate to the MP2/CBS limit with a sequence of optimized n-tuple-zeta augmented polarized basis sets (n=4, 5, 6, and 7) for the entire set of 72 atoms, positive and negative atomic ions, homonuclear diatomic molecules, and hydrides representing the first two rows of the Periodic Table. The second-order correlation energies agree with accurate (+/-0.01 mE(h)) numerical values (He, Be, Ne, Mg, Ar, Zn(+2), and Kr) to within +/-0.1%. These MP2/CBS limits of the 72 species can now be used as benchmarks to calibrate more approximate calculations using smaller basis sets.

Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory.

Unrestricted coupled cluster spin contamination corrected [UCCSD(T)] and unrestricted Brueckner doubles [UBD(T)] variations of the Weizmann-1 theory (W1), denoted as W1U, W1Usc, and W1BD, respectively, are compared with the restricted open-shell W1 theory [W1(RO)]. The performances of the four W1 variants are assessed with 220 total atomization energies, electron affinities, ionization potentials, and proton affinities in the G2/97 test set, for consistency with the error analysis of the original W1(RO) study. The root-mean-square deviations from the experiment of W1U (0.65 ± 0.48 kcal/mol), W1Usc (0.57 ± 0.48 kcal/mol), W1BD (0.62 ± 0.48 kcal/mol), and W1(RO) (0.57 ± 0.48 kcal/mol) show that the four methods are virtually indistinguishable. This error analysis excludes the "singlet biradicals," C2 and O3, since single determinantal methods are not really adequate for these strongly multireference systems. The unrestricted W1 variants perform poorly for such highly spin-contaminated and multireference species (the largest deviation from experiment for W1Usc is -4.2 ± 0.1 kcal/mol for the O3 EA). W1(RO) performs much better than its unrestricted counterparts for these pathological cases (the deviation from experiment is reduced to -1.5 ± 0.1 kcal/mol for the O3 EA), though the errors are significantly larger than those for the overall test set. The examples of C2, O3, and the F2 potential energy curve indicate that an advantage to using W1BD is that the error in ⟨S(2)⟩ correlates with the magnitude of the error in energy, whereas W1(RO) loses accuracy without such a warning.

Uniformly convergent n-tuple-zeta augmented polarized (nZaP) basis sets for complete basis set extrapolations. I. Self-consistent field energies.

We present a sequence of n-tuple-zeta augmented polarized (nZaP) basis sets designed for extrapolations of both self-consistent field (SCF) and correlation energies to the complete basis set (CBS) limit. These nZaP basis sets (n=2-6) are formulated to give consistent errors throughout the Periodic Table (e.g., a consistent of approximately 1 mhartree/electron error for the 2ZaP SCF energy and a consistent of approximately 1.4 muhartree/electron error for the 6ZaP SCF energy). The SCF energy exhibits systematic convergence to the CBS limit: E(SCF)(nZaP) approximately E(SCF)(CBS)+Ae(-an). A single parameter, a=6.30, describes the 2ZaP through 6ZaP errors of H through Xe within 10%. The SCF rms basis set truncation errors of H through Xe are 33.5mE(h), 4.58mE(h), 0.82mE(h), 0.18mE(h), and 0.047mE(h) for 2ZaP, 3ZaP, 4ZaP, 5ZaP, and 6ZaP, respectively. Linear extrapolations of the (2,3)ZaP, (3,4)ZaP, (4,5)ZaP, and (5,6)ZaP calculations (all with a=6.30) reduce these errors by an order of magnitude to 0.24mE(h), 0.056mE(h), 0.020mE(h), and 0.005mE(h), respectively. A test set of 34 atoms, ions, and molecules gives similar results, and the associated test set of 25 chemical energy differences also gives comparable absolute accuracy. However, the cancellation of errors between reactant and product is lost by extrapolation. As a result, these chemical energy differences show a more modest two-to-fourfold improvement with extrapolation.

The CCSD(T) complete basis set limit for Ne revisited.

Recent estimates of the CCSD(T)(FC) limit for the neon atom (-128.8690+/-0.001 and -128.8687+/-0.0005 hartree) are refined. Re-examination of the basis set convergence of the separate self-consistent field, MP2-alphabeta, MP2-alphaalpha, CCSD-MP2, and (T) components of the valence CCSD(T) energy gives a complete basis set limit of -128.869 236+/-0.000 02 hartree. This can now be used as an improved benchmark to calibrate more approximate calculations.

A restricted-open-shell complete-basis-set model chemistry.

A restricted-open-shell model chemistry based on the complete basis set-quadratic Becke3 (CBS-QB3) model is formulated and denoted ROCBS-QB3. As the name implies, this method uses spin-restricted wave functions, both for the direct calculations of the various components of the electronic energy and for extrapolating the correlation energy to the complete-basis-set limit. These modifications eliminate the need for empirical corrections that are incorporated in standard CBS-QB3 to compensate for spin contamination when spin-unrestricted wave functions are used. We employ an initial test set of 19 severely spin-contaminated species including doublet radicals and both singlet and triplet biradicals. The mean absolute deviation (MAD) from experiment for the new ROCBS-QB3 model (3.6+/-1.5 kJ mol(-1)) is slightly smaller than that of the standard unrestricted CBS-QB3 version (4.8+/-1.5 kJ mol(-1)) and substantially smaller than the MAD for the unrestricted CBS-QB3 before inclusion of the spin correction (16.1+/-1.5 kJ mol(-1)). However, when applied to calculate the heats of formation at 298 K for the moderately spin-contaminated radicals in the G2/97 test set, ROCBS-QB3 does not perform quite as well as the standard unrestricted CBS-QB3, with a MAD from experiment of 3.8+/-1.6 kJ mol(-1) (compared with 2.9+/-1.6 kJ mol(-1) for standard CBS-QB3). ROCBS-QB3 performs marginally better than standard CBS-QB3 for the G2/97 set of ionization energies with a MAD of 4.1+/-0.1 kJ mol(-1) (compared with 4.4+/-0.1 kJ mol(-1)) and electron affinities with a MAD of 3.9+/-0.2 kJ mol(-1) (compared with 4.3+/-0.2 kJ mol(-1)), but the differences in MAD values are comparable to the experimental uncertainties. Our overall conclusion is that ROCBS-QB3 eliminates the spin correction in standard CBS-QB3 with no loss in accuracy.