Exploring the Origin of the Generalized Anomeric Effects in the Acyclic

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Exploring the Origin of the Generalized Anomeric Effects in the Acyclic Nonplanar Systems Neda Hasanzadeh, Davood Nori-Shargh, Hooriye Yahyaei, Seiedeh Negar Mousavi, and Sahar Kamrava J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b04447 • Publication Date (Web): 29 Jun 2017 Downloaded from http://pubs.acs.org on June 30, 2017

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The Journal of Physical Chemistry

Exploring the Origin of the Generalized Anomeric Effects in the Acyclic Nonplanar Systems Neda Hasanzadeh1,*, Davood Nori-Shargh2,*, Hooriye Yahyaei3, Seiedeh Negar Mousavi4 and Sahar Kamrava2 1

Department of Chemistry, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran 2 Department of Chemistry, Arak Branch, Islamic Azad University, Arak, Iran 3 Department of Chemistry, Zanjan Branch, Islamic Azad University, Zanjan, Iran 4 Department of Nanochemistry, Faculty of Pharmaceutical Chemistry, Pharmaceutical Science Branch, Islamic Azad University (IAUPS), Tehran, Iran

*Corresponding authors: E-mail address: DNS ([email protected]; [email protected]), NH ([email protected])

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Abstract Contrary to the published conclusions in the literature concerning the origin of the generalized anomeric relationships in open-chain nonplanar systems, its origin has remained an open question. In order to explore the origin of the generalized anomeric relationships in openchain nonplanar systems, we assessed the roles and contributions of the effective factors on the conformational properties of methyl propargyl ether (1), methyl propargyl sulfide (2) and methyl propargyl selenide (3) by means of the G3MP2, CCSD(T), MP2, LC-ωPBE and B3LYP methods and natural bond orbital (NBO) interpretations.

We examined the contributions of the

hyperconjugative interactions on the conformational preferences of compounds 1-3 by the deletions of the orbitals overlapping from the Fock matrices of the gauche- and anticonformations. The trend observed for energy changes in the Fock matrices justify the variations of the gauche-conformations preferences going from compound 1 to compound 3, revealing that the hyperconjugative interactions are solely responsible for the generalized anomeric relationships in compounds 1-3. Accordingly, the conclusions published in the literature concerning the origin of the generalized anomeric effect in the acyclic nonplanar compounds should be revised by these findings. The Pauli exchange type repulsions (PETR) are in favors of the gauche-conformations and the variations of the PETR differences between the gauche- and anti-conformations of compounds 1-3 correlate well with their gauche-conformations preferences, revealing that the generalized anomeric relationships in compounds 1-3 have also the Pauli exchange-type repulsions origin. The resemblance between the pre-orthogonal natural bond orbitals (that are involved in the hyperconjugative interactions) and their corresponding molecular orbitals have been investigated.

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Introduction The anomeric effect which is emerging as a central player in carbohydrate chemistry (as the most dominant conformation-controlling factor) could be defined as the preference of an electronegative substituent to be axially on the chair-type cyclohexane derivatives rather than equatorially oriented which is in opposition to the steric effect that normally leads to a preference for the equatorial conformation.1-15 This concept has now been generalized to open-chain (or acyclic) nonplanar compounds as the preference of a gauche-conformation over an anticonformation for a R-X-C-Y moiety in which X atom possesses one or more non-bonded lone electron pairs (O, S, N…) whereas Y donates as an electronegative group (F, Cl, -C≡C-H, -C≡CR, -C≡N,…).4,16,17 The efficiency of the negative hyperconjugative interactions associated with the LPX→σ*C-Y electron delocalization depends on the orientations of the R and Y groups around the X-C bond. In 2013, Mo and co-worker performed the extended block-localized wavefunction (BLW) method to investigate the origin of the generalized anomeric effect.16 They surmised that the steric effect (more specifically electrostatic) usually is the primary cause for the generalized anomeric effect, with the contributions from the hyperconjugation effect in certain cases. Also, they pointed out that the identification of any molecule of generalized anomeric effect for which the hyperconjugative interaction dominates, would be of significant interest. Interestingly, the results of this work contradict their conclusions concerning the origin of the generalized anomeric effect. The results of the current study revealed that the electrostatic effect contributes to the generalized anomeric effects in the molecular systems studied in the present work but their conformational preferences is dominated by the hyperconjugative interactions. At the same year, Bauerfeldt pointed out that the total energy difference between two anomers correlate very well with the difference in their exchange components, revealing that the anomeric effect has no electrostatic origin.18 In view of the discrepancies between the earlier conclusions concerning the origin of the anomeric effect and its generalization in acyclic compounds,16-20 it was considered worthwhile to undertake a theoretical study of methyl propargyl ether (1), methyl propargyl sulfide (2) and methyl propargyl selenide (3) with the objective of trying to clarify the situation regarding the role and contributions of the hyperconjugative interactions, Pauli exchange-type repulsion and

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the electrostatic model associated with dipole-dipole interactions on the origin of the generalized anomeric relationships in the acyclic nonplanar systems (Scheme 1). Effectively, an efficient way to investigate the impacts of the hyperconjugative interactions on the conformational properties of compounds 1-3 is the deletion of the effective orbitals mixings from their Fock matrices and rediagonalization and comparison of the current Fock matrices with the original ones. This procedure is a sufficient tool to investigate quantitatively the contribution of a specific hyperconjugative interaction on the total energy differences between different conformations of a molecule.12,17,20,21 In this regard, in order to explore the roles and contributions of the hyperconjugative generalized anomeric effects on the anomeric relationships in compounds 1-3, we deleted the orbitals mixings that their overlapping

change with the gauche- ⇌ anti-conformational interconversions from the Fock matrices of the gauche- and anti-conformations. Then, by rediagonalization and comparison of the current Fock

matrices with their original ones, we evaluated the contributions of the hyperconjugative interactions on the anomeric relationships in compounds 1-3. Further, we analyzed the resemblance between the pre-orthogonal natural bond orbitals (that are involved in the hyperconjugative interactions) with their corresponding molecular orbitals. Furthermore, the potential energy surfaces of the conformational interconversion processes in compounds 1-3 have been analyzed by means of the G3MP2,22 the long-range-corrected version of the PerdewBurke-Ernzerhof (PBE) exchange functional (LC-ωPBE),23 second-order Møller-Plesset perturbation theory (MP2)24,25 and hybrid density functional (B3LYP)26 based methods with the 6-311+G** basis set27-30 on all atoms.

Scheme 1. Schematic representation of gauche- and anti-conformations of compounds 1-3 [X=O (1), S (2), Se (3)].

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Computational details G3MP2, LC-ωPBE, MP2, and B3LYP method with the 6-311+G** basis set on all atoms were performed to optimize the structural parameters and also to calculate the electronic energies and thermodynamic functions of the ground and transition state structures compounds 1-3 with the GAMESS US package of programs.31,32 The minimum energy structures of compounds 1-3 were located by minimizing their corresponding energies with respect to all geometrical coordinates without imposing any symmetry constraints. The potential energy surfaces associated with the rotations around the XCH2 bonds were investigated by changing and scanning the dihedral angles CH3-X-CH2-Csp [X=O (1), S (2), Se (3)] (Figure 1). Then, the Saddle Point subroutine was used to locate the structures of the molecular transition state geometries of the conformational interconversion processes in compounds 1-3. In order to verify the localized transition state structures in connection with their corresponding minimum stationary points (reactant and products), intrinsic reaction coordinate (IRC) calculations were performed.33 The nature of the stationary points of the ground and transition state structures of compounds 1-3 has been determined by means of their imaginary frequencies number. The transition state structures were characterized by having only single imaginary vibrational frequency while the minimum energy ground state structures possess only all real frequency values.34-36 In order to assess quantitatively the roles and contributions of the plausible hyperconjugative interactions and Pauli exchange type repulsions on the conformational and structural properties of compounds 1-3, we conducted natural bond orbital analysis37 (NBOB3LYP/6-311+G**) for the gauche- and anti-conformations and also their corresponding interconversional transition state structures. In addition, the NBO-B3LYP/6-311+G** interpretation was performed to investigate the bonding and antibonding orbital occupancies and energies of the gauche- and anti-conformations of compounds 1-3 and also their corresponding interconversional transition state structures by means of the NBO 5.G program.37 It is worth noting that the second order perturbational energies (stabilization energies) associated with the donor (i)→acceptor (j) hyperconjutative interactions are proportional inversely to the energy differences between the donor and acceptor orbitals and directly to the magnitudes of the orbital overlap integrals:38-40 5



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Stabilization or resonance energy α ∆ Accordingly, the stabilization or resonance energy (E2) associated with i→j electron delocalization, is explicitly estimated by the following equation: =

(,)

Eq. (1)

where qi is the ith donor orbital occupancy, ε i , ε j are diagonal elements (orbital energies) and F(i,j) is the off-diagonal natural bond orbital Fock matrix element. The desirable orbital overlapping could be reachable by the substantial adjustments of the off-diagonal terms when going from one compound to the next.41,42 The natural bond orbital interpretations were performed to investigate quantitatively the impacts of the hyperconjugative generalized anomeric effects associated with LP1X→σ*CH2-C, LP2X→σ*CH2-C, H(CH2)→σ*X-CH3, CH2→π*C≡C

LP1X→π*C≡C,

LP2X→π*C≡C,

LP1X→σ*C-H(CH2),

LP2X→σ*C-H(CH2),

σC-

σX-CH3→σ*C-H(CH2), σX-CH3→σ*CH2-C, σCH2-C→σ*X-CH3, σX-CH2→σ*C≡C, σX-

and πC≡C→σ*X-CH2 electron delocalizations (Figures 2-6), Pauli exchange type

repulsion (total steric exchange energy, TSEE) and the electrostatic model associated with dipole-dipole interactions on the structural and conformational properties of compounds 1-3. In order to assess the impacts of the hyperconjugative interactions on the conformational properties of compounds 1-3, we deleted these electron delocaliations from the Fock matrices of their gauche- and anti-conformations. Then, by rediagonalization and comparing the current Fock matrices with their original forms, we estimated the contributions and impacts of the hyperconjugative interactions on the anomeric relationships in compounds 1-3. Further, the correlations between the pre-orthogonal natural bond orbitals associated with the through space LP2X→π*C≡C and the through bond LP2X→σ*CH2-C negative hyperconjugative interactions with their corresponding molecular orbitals (HOMOs and LUMOs+n) have been investigated. Effectively, the natural bond orbital interpretation is a capable and adequate theoretical method to investigate quantitatively the influences of the hyperconjugative and electrostatic interactions and also the steric repulsions on the reactivity and dynamic behaviors of chemical compounds.43

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Results and Discussion Conformational properties Enthalpy, entropy and Gibbs free energy differences between the ground and transition state structures of compounds 1-3, as calculated at the G3MP2,

LC-ωPBE/6-311+G**,

B3LYP/6-311+G** and MP2/6-311+G** levels of theory, are summarized in Table 1. In addition, the electronic energies (as calculated at the CCSD(T)/6-311+G** level), zero point energy (ZPE) and corrected electronic energies (Eo=Eel+ZPE) (as calculated at the MP2/6311+G** and LC-ωPBE/6-311+G** levels) for the ground and transition state structures of compounds 1-3 are given in Table S1 (See Supporting Information). In accordance with the published experimental data,44-49 all levels of theory used in this work showed that the chiral gauche-conformations of compounds 1-3 are their most stable forms. Two distinct transition states (excluding the mirror image pathways) describe the dynamic conformational properties of compounds 1-3 (Figure 1). Since the conformations associated with the gauche→[TS(cis)]→gaucheʹ and gauche→[TS(skew)]→anti interconversion processes are true transition state structures of compounds 1-3, the racemization processes of the chiral gaucheconformations of compounds 1-3 could take place by passing through their TS(cis) or TS(skew) conformations that are shown in Figure 1. The calculated energy barrier for the interconversion process in compound 1 between the gauche-conformation and its mirror image conformation via cis-transition state structures (gauche→[TS(cis)]→gaucheʹ) is higher than passing through the skew transition state structure. Note that the barrier heights of the racemization processes of the chiral gauche-conformations (by passing through the cis-transition state structures) decrease going from compound 1 to compound 3, as calculated at all levels of theory used in this work. On the other hand, the barrier heights of the racemization processes of the gauche-conformations (by passing through the skew-transition state structures) increase slightly from compound 1 to compound 2 but decrease from compound 2 to compound 3. It is worth noting that chiral gauche-conformation preference increases from compound 1 to compound 2 but decreases from compound 2 to compound 3, as calculated at all levels of theory used in this work.

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Table 1. G3MP2, LC-wPBE/6-311+G**, B3LYP/6-311+G** and MP2/6-311+G** calculated thermodynamic parameters [∆H, ∆G (in kcal mol-1) and ∆S (in cal mol-1K-1)] for the gauche- and anti-conformations of compounds 1-3 and their corresponding interconversion processes transition state structures. Geometries 1-g 1-a

∆H 0.00 0.45

G3MP2 ∆Sa 0.000 -1.678

[1-g→1-g′, Cis]‡

3.30

-2.884

4.16

3.39

[1-g→1-a]‡

2.52

-3.153

3.46

2.34

2-gauche 2-anti [2-g→2-g′, Cis]‡ [2-g→2-a]‡

0.00 0.80 2.59 2.56

0.000 -2.046 -3.857 -3.756

0.00 1.41 3.74 3.68

0.00 1.39 2.71 2.25

0.000 0.917 -3.666 -3.662

0.00 1.12 3.80 3.34

0.00 1.13 2.49 1.88

0.000 0.945 -3.638 -3.844

0.00 0.85 3.58 3.03

0.00 1.29 3.11 2.71

0.000 -0.045 -2.228 -3.712

0.00 1.30 3.78 3.81

3-g 3-a [3-g→3-g′, Cis]‡ [3-g→3-a]‡

0.00 0.63 1.62 1.96

0.000 -2.247 -4.360 -4.092

0.00 1.30 2.92 3.18

0.00 1.02 1.76 1.73

0.000 0.744 -4.157 -4.027

0.00 0.80 3.00 2.93

0.00 0.80 1.53 1.33

0.000 0.671 -4.320 -4.328

0.00 0.60 2.82 2.62

0.00 1.45 1.70 2.23

0.000 2.151 -3.564 -3.904

0.00 0.81 2.76 3.40

a

a

a

a

∆G 0.00 0.95

∆H 0.00 1.10

LC-wPBE/6-311+G** ∆Sa ∆Ga 0.000 0.00 -0.583 0.93 (1.021±0.174)b -2.642 4.18 (5.24)b -2.918 3.21 (2.92)b

B3LYP/6-311+G** ∆Ha ∆Sa ∆Ga 0.00 0.000 0.00 0.78 -0.538 0.62

MP2/6-311+G** ∆H ∆Sa ∆Ga 0.00 0.000 0.00 1.19 2.543 0.43

3.32

-2.651

4.11

3.89

-2.164

4.54

2.02

-3.061

3.34

2.65

-2.839

3.49

a

Relative to the most stable form. bFrom vibrational spectrum, Ref. [49].

Importantly, contrary to the electrostatic model associated with the dipole-dipole interactions, the hyperconjugative generalized anomeric effect and Pauli exchange type repulsions succeed to account for the gauche-conformations preferences in compounds 1-3, revealing that the conclusions published in the literature concerning the origin of the generalized anomeric relationships in the acyclic nonplanar systems should be reevaluated and revised by the results of the present work.16 8


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Figure 1: G3MP2 calculated comparative potential energy profiles of the rotations around the X-CH2 bonds in compounds 1-3. ∆G, ∆G‡, ∆TSEE, ∆TSEE‡, ∆HCGAE and ∆HCGAE‡ values are in kcal mol-1. ∆µ values are in debye.

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Examinations of the impacts of the hyperconjugative interactions on the conformational properties of compounds 1-3 One may expect that the LP2X→σ*CH2-C negative hyperconjugative interactions play a determining role one the conformational preferences in compounds 1-3 but the results obtained did not confirm this expectation. The NBO-B3LYP/6-311+G** results showed that the stabilization energies associated with LP2X→σ*CH2-C negative hyperconjugative interactions decrease going from the gauche-conformations of compound 1 to compound 3 (Table 2) while the gauche-conformation preference increases from compound 1 to compound 2 but decreases from compound 2 to compound 3 (Table 1). Obviously, other hyperconjugative interactions should be examined.

Since the gauche-→anti-conformational interconversion processes in

compounds 1-3 take place by the rotations around the X-CH2 bonds [X=O (1), S (2), Se (3)], we examined the contributions of the hyperconjugative interactions (which their corresponding orbitals overlapping change with the rotations around the X-CH2 bonds) on the strengthening and weakening of the X-CH2 bonds. The examination of the bonding orbitals orientations around the X-CH2 bonds revealed that the hyperconjugative interactions associated with the LP1X→σ*CH2-C, LP2X→σ*CH2-C, H(CH2)→σ*X-CH3,

LP1X→π*C≡C,

LP2X→π*C≡C,

LP1X→σ*C-H(CH2),

LP2X→σ*C-H(CH2),

σC-

σX-CH3→σ*C-H(CH2), σX-CH3→σ*CH2-C and σCH2-C→σ*X-CH3 electron delocalizations

tend to increase the X-CH2 bond orders while the hyperconjugative interactions associated with the

σX-CH2→σ*C≡C,

σX-CH2→π*C≡C and

πC≡C→σ*X-CH2

have

opposite

impacts.

The

hyperconjugative interactions which tend to weaken the X-CH2 bonds going from the gaucheconformation of compound 1 to compound 3 controls their corresponding X-CH2 bond orders. Based on the results obtained, the X-CH2 bond orders decrease going from the gaucheconformations of compound 1 to compound 3 while the CH2-C bond orders increase inversely. The decrease of the X-CH2 bond orders and also the increase of the CH2-C bond orders going from the gauche-conformations of compound 1 to compound 3 are in the line with the decrease of their corresponding gauche→anti conformational interconversion process barrier heights.

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1 2 3 Table 2. NBO-B3LYP/6-311+G** calculated stabilization energies (E2, in kcal mol-1), generalized anomeric effect (GAE, in kcal mol-1), off4 diagonal elements(Fij, in a.u.), orbital energies (ε, in a.u.), orbital occupancies (e), bond orders (Wiberg bond index), dipole moments (µ, 5 in Debye) and total steric exchange energies (TSEE, in kcal mol-1) for the ground and transition state structures of compounds 1-3. 6 7 1 2 3 8 anti g→gʹ g→a a g→gʹ g→a a g→gʹ g→a 9 Hyperconjugative interactions g g g 10HCGAE(X-CH strengthening) 2 11 1.00 0.80 4.72 0.85 2.09 0.64 1.38 LP1X→σ*CH2-C 12 13 6.89 4.52 3.96 2.50 2.90 1.93 LP2X→σ*CH2-C 14 0.61 LP1X→π*C≡C 15 16 1.02 1.10 1.07 1.08 0.96 0.97 LP2X→π*C≡C 17 2.74 2.82 0.55 0.67 0.65×2 0.92×2 LP1X→σ*C-H(CH2) 18 5.45 5.80 3.48 3.70 2.45 2.57 19 6.43×2 5.20×2 3.89×2 3.10×2 2.76×2 2.23×2 LP2X→σ*C-H(CH2) 20 3.33 1.81 1.47 1.36 1.02 σC-H(CH2)→σ*X-CH3 21 0.84 0.82 1.10 0.65 0.88 0.54 σX-CH3→σ*C-H(CH2) 22 23 1.57 0.65 1.43 0.66 1.13 0.51 σX-CH3→σ*CH2-C 24 2.09 1.21 σCH2-C→σ*X-CH3 25 26 18.82 21.07 18.83 18.39 9.21 12.37 8.29 9.26 6.65 8.85 5.84 6.52 Σ HCGAE(X-CH2 strengthening) 27 28 29 HCGAE(X-CH2 weakening) 30 2.01 1.96 1.97 1.91 2.85 2.69 2.70 2.66 2.73 2.63 2.61 2.59 σX-CH2→σ*C≡C 31 1.89 1.59 1.40 1.88 6.51 5.88 5.92 6.19 8.64 7.91 8.09 8.12 σX-CH2→π*C≡C 32 33 6.20 6.19 6.74 6.24 4.89 5.19 5.96 5.21 5.24 5.68 6.39 5.71 πC≡C→σ*X-CH2 34 10.10 9.74 10.11 10.03 14.25 13.76 14.58 14.06 16.61 16.22 17.09 16.42 35 ΣHCGAE(X-CH2 weakening) 36 37 28.92 30.81 29.94 28.42 23.46 26.13 22.87 23.32 23.26 25.07 22.93 22.94 ΣHCGAE 38 -1.89 -2.67 -1.81 HCGAE(a)-HCGAE(g) 39 40 HCGAE(g→gʹ)-HCGAE(g) -1.02 -3.26 -2.14 41 -2.39 -2.81 -2.13 42 HCGAE(g→a)-HCGAE(g) 43 44 11 45 46 ACS Paragon Plus Environment 47 48


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The differences between the hyperconjugative generalized anomeric effect (HCGAE) values in the anti- and gauche-conformations are used to calculate the total hyperconjugative generalized anomeric effect (HCGAEtotal):10,17 HCGAEtotal= HCGAEanti – HCGAEgauche (Eq. 2)

The calculated HCGAEtotal value associated with LP1X→σ*CH2-C, LP2X→σ*CH2-C, LP1X→π*C≡C, LP2X→π*C≡C, LP1X→σ*C-H(CH2), LP2X→σ*C-H(CH2), σC-H(CH2)→σ*X-CH3, σX-CH3→σ*C-H(CH2), σXCH3→σ*CH2-C,

σCH2-C→σ*X-CH3,

σX-CH2→σ*C≡C,

σX-CH2→π*C≡C

and

πC≡C→σ*X-CH2

hyperconjugative interactions increases going from compound 1 to compound 2 but decreases from compound 2 to compound 3. The HCGAEtotal are in favor of the gauche-conformations and solely succeeds to account for the rationalization of the gauche-conformations preferences in compounds 1-3 (Table 2). In order to estimate quantitatively the impacts of the hyperconjugative interactions on the conformational preferences in compounds 1-3, we deleted the LP1X→σ*CH2-C, LP2X→σ*CH2-C, LP1X→π*C≡C, LP2X→π*C≡C, σC-H(CH2)→σ*X-CH3, σX-CH3→σ*C-H(CH2), C→σ*X-CH3,

LP1X→σ*C-H(CH2)

σX-CH3→σ*CH2-C, σCH2-

and LP2X→σ*C-H(CH2) hyperconjugative interactions from the

Fock matrices of the gauche- and anti-conformations. Then, by rediagonalization and comparison of the current Fock matrices with their original forms, we found that the anticonformations of compounds 1-3 became more stable than their corresponding chiral gaucheconformations, revealing the anomeric relationships in compounds 1-3 have hyperconjugative interactions origin (Table 3). This fact clearly shows that conclusion published in the literature concerning the origin of the generalized anomeric relationships in the acyclic nonplanar systems should be revaluated and reexamined.16

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1 2 3 4 5 Table 3. B3LYP/6-311++G** calculated total SCF energies, energies of deletions associated with the 6 deletion of LP1X→σ*CH2-C, LP2X→σ*CH2-C LP1X→π*C≡C, LP2X→π*C≡C, σC-H(CH2)→σ*X-CH3, 7 σX-CH3→σ*C-H(CH2), σX-CH3→σ*CH2-C, σCH2-C→σ*X-CH3, LP1X→σ*C-H(CH2) and LP2X→σ*C8 9 H(CH2) electron delocalizations and their corresponding energy changes (EC, in a.u.) in the 10 gauche- and anti-conformations of compounds 1-3. 11 Deletion of LPM1→π*C≡N electron delocalizations 12 1 2 3 13 14 Geometries gauche anti gauche anti gauche anti 15 -231.236311 -231.199442 -554.225523 -554.223590 -2557.559981 -2557.558645 16Total SCF energies 17 -231.234773 -554.201924 -554.206268 -2557.543161 -2557.545985 Energies of deletions -231.198516 18 a a a a a Energy changes (EC) 0.037795(23.72) 0.035331(22.17) 0.023598(14.81) 0.017322(10.87) 0.016820(10.55) 0.012660(7.94)a 19 20 ∆(EC 1.55a 4.26a 2.61a gauche-ECanti) 21 22 23 Since the hyperconjugative interactions associated with LP2X→σ*CH2-C, LP2X→σ*C24 25 H(CH2), σX-CH2→π*C≡C and πC≡C→σ*X-CH2 electron delocalizations have the most impacts on the 26 27 strengthening and weakening of the X-CH2 bonds in the chiral gauche-conformations of 28 29 compounds 1-3 via affecting their bond orders, we analyzed their corresponding donor and 30 acceptor profiles of the orbital amplitudes (or electron densities) (Figures 2-6). 31 32 33 34 35 36 37 38 39 σX-CH2→π*C≡C 40 41 H 42 C 43 44 C 45 *C-C 46 Se C 47 48 49 50 Se-CH2 51 σO-CH2→π*C≡C; E2=1.59 σS-CH2→π*C≡C; E2=5.88 σSe-CH2→π*C≡C; E2=7.91 52 53 Figure 2: The calculated profiles of the orbital amplitudes (electron densities) for the through-bond 54 55 σX-CH2→π*C≡C [X=O (1), S (2), Se (3)] negative hyperconjugations in the gauche56 conformations of compounds 1-3. E2 values are in kcal mol-1. 57 58 59 13 60 ACS Paragon Plus Environment


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H

H

C C

H3C

H X

C

Page 14 of 32

C C

H3C

H X

C

H

H

πC≡C→σ*X-CH2

πC≡C→σ*O-CH2; E2=6.19

πC≡C→σ*S-CH2; E2=5.19

πC≡C→σ*O-CH2; E2=5.68

Figure 3: The calculated profiles of the orbital amplitudes (electron densities) for the through-bond πC≡C→σ*X-CH2 [M=O (1), S (2), Se (3)] negative hyperconjugations in the gaucheconformations of compounds 1-3. E2 values are in kcal mol-1. Based on the profiles of the orbital amplitudes (which are in accordance with their corresponding second order perturbative energies), the mixing of the doubly occupied orbitals of the σX-CH2 bonds [X=O (1), S (2), Se (3)] with the adjacent unoccupied antibonding orbitals of πC≡C triple bonds (σX-CH2 + π*C≡C) increases going from the gauche-conformations of compound 1 to compound 3, tending to increase of the σX-CH2 bond lengths via the depletions of their corresponding electronic populations (Figure 2) while there are no significant differences between the mixing of the doubly occupied orbitals of the πC≡C triple bonds with the adjacent unoccupied σ*X-CH2 antibonding orbitals (πC≡C + σ*X-CH2) (Figure 3). This trend is also observed for the variations of the orbital amplitudes associated with the through-space LP2X→π*C≡C negative hyperconjugations in the gauche-conformations of compounds 1-3 (Figure 4).

14


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LP2X→π*C≡C

LP2O→π*C≡C; E2=1.02

LP2S→π*C≡C; E2=1.07

LP2Se→π*C≡C; E2=0.96

Figure 4: The calculated profiles of the orbital amplitudes (electron densities) for the throughspace LP2X→π*C≡C [M=O (1), S (2), Se (3)] negative hyperconjugations in the gauche-conformations of compounds 1-3. E2 values are in kcal mol-1. One may expect that the increase of the lone pairs’ energies of the heteroatoms [LP2X, X=O (1), S (2), Se (3)] going from the chiral gauche-conformations of compound 1 to compound 3 leads to the decrease of their corresponding energy differences between the donor LP2X nonbonding and acceptor σ*CH2-C antibonding orbitals [ε(σ*CH2-C)-ε(LP2X)] but the result obtained did not confirm this expectation (Figure 5).

LP2X→σ*C-H(CH2)

LP2O→σ*C-H; E2=5.45

LP2S→σ*C-H; E2=3.48

LP2Se→σ*C-H; E2=2.45

Figure 5: The calculated profiles of the orbital amplitudes (electron densities) for the through-bond LP2X→σ*C-H(CH2) [M=O (1), S (2), Se (3)] negative hyperconjugations in the gaucheconformations of compounds 1-3. E2 values are in kcal mol-1. 15



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Page 16 of 32

This exception is also observed for the through-bond LP2X→σ*C-H(CH2) [X=O (1), S (2), Se (3)] negative hyperconjugations (Figure 6). Based on the results obtained, the energy differences between the donor LP2X nonbonding and acceptor σ*CH2-C and σ*C-H(CH2) antibonding orbitals (∆[ε (σ*CH2-C)-ε (LP2X)] and ∆[ε (σ*C-H(CH2)) - ε (LP2X)] parameters, respectively) decrease significantly from the gauche-conformations of compound 1 to compound 2 but increases slightly from compound 2 to compound 3 (Table S2). Accordingly, the variations of ∆[ε (σ*CH2C)-ε

(LP2X)] parameter do not explain the decrease of the mixings between the donor LP2X

nonbonding and acceptor σ*CH2-C antibonding orbitals. This fact has been reflected in their corresponding donor and acceptor orbital amplitude profiles (electron densities) (Figure 6). Figure 6 shows that the mixings between the donor LP2X nonbonding and acceptor σ*CH2-C antibonding orbitals lobes decrease going from the chiral gauche-conformations of compound 1 to compound 3, revealing that the variations of the off-diagonal elements (Fij) control the variations of the mixing of the doubly occupied orbitals of LP2M [M=O (1), S (2), Se (3)] with the adjacent unoccupied orbitals of CH2-C bonds (LP2M + σ*CH2-C). Based on the Mulliken (or Wolfberg-Helmholtz) approximation,41,42 the substantial desirable orbital overlapping between the donor and acceptor orbitals are reachable by the adjustments of their off-diagonal terms.

LP2X→σ*CH2-Csp

LP2O→σ*CH2-Csp; E2=6.89

LP2S→σ*CH2-Csp; E2=3.96

LP2Se→σ*CH2-Csp; E2=2.90

Figure 6: The calculated profiles of the orbital amplitudes (electron densities) for the throughbond LP2X→σ*CH2-Csp [M=O (1), S (2), Se (3)] negative hyperconjugations in the gauche-conformations of compounds 1-3. E2 values are in kcal mol-1. 16


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Pauli exchange-type repulsion The Pauli exchange type repulsion (or steric exchange energy) includes effects from all occupied orbitals and therefore typically contains contributions from covalent (intrabond) groups. Accordingly, the natural steric analysis which states the steric exchange repulsion as the energy difference due to orbital orthogonalization express the well-established physical picture of steric repulsions.50-54 The NBO-B3LYP/6-311+G** analysis was used to calculate the steric repulsion contributions in the gauche- and anti-conformations of compounds 1-3 and their corresponding interconversion transition state structures. The results obtained showed that the total steric exchange energies of the anti-conformations of compounds 1-3 are greater than those in their corresponding gauche-conformations, revealing that the Pauli exchange type repulsions are in favor of the gauche-conformations of compounds 1-3 (Table 4). The calculated total steric exchange energy differences between the anti- and gauche-conformations [∆(TSEEantiTSEEgauche)] increase from compound 1 to compound 2 but decrease from compound 2 to compound 3, correlating well with the variations of their corresponding gauche-conformations preferences. This fact reveals that the gauche-conformation preferences in compounds 1-3 have also the exchange component origin. Therefore, the variations of the gauche-conformation preferences in compounds 1-3 results from the cooperative impacts of the hyperconjugative interactions and Pauli exchange type repulsion.

Assessing the impacts of the electrostatic model associated with the dipole-dipole interactions on the generalized anomeric relationships in compounds 1-3 The greater electronegativity differences between the adjacent atoms lead to the larger polarizability and dipole moments. Molecular conformations with the greater polarizabilities (in the gas phase or in the nonpolar media) may possess greater overall energies than those with the smaller charge distributions.5 Dipole moments of the gauche- and anti-conformations of compounds 1-3 and their corresponding interconversion transition state structures which results from the orientations of the dipole moments of the bonds and lone pair electrons are given in Table 4. The dipole moments of the gauche-configurations of compounds 1-3 are smaller than those in their

17



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Page 18 of 32

corresponding anti-configurations. Therefore, the pronounced dipole-dipole interaction (electrostatic model) is in favor of the gauche-conformations of compounds 1-3 (Scheme 2).

gauche

anti

Scheme 2. Schematic representation of the local dipoles orientations in the gauche- and anticonformations of compounds 1-3 [X=O (1), S (2), Se (3)].

It is worth noting that the energy differences between the conformations of a molecule attribute to their corresponding electrostatic, electronic and steric effect differences. Based on the results obtained, the dipole moment differences between the anti- and gauche-conformations of compounds 1-3 [∆(µanti-µgauche)] increase from compound 1 to compound 3 (Table 4). Although the electrostatic model associated with the dipole-dipole interactions is in favor of the gaucheconformations of compounds 1-3, the variations of [∆(µanti-µgauche) parameter do not explain the variations of their corresponding gauche-conformations preferences. This evidence reveals that the anomeric relationships in acyclic molecular systems could not be solely explained by the electrostatic model associated with the diploe-dipole interactions. Clearly, the contributions of the hyperconjugative interactions and Pauli exchange type repulsions on the conformational preferences in compounds 1-3 are greater than that of the electrostatic model.

18


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1 2 3 4 5 Table 4. NBO-B3LYP/6-311+G** calculated dipole moments (µ, in Debye), total natural resonance 6 (natural bond orders, nbo) and total steric exchange energies (TSEE, in kcal mol-1) for the 7 structures of compounds 1-3. 8 2 1 9 10 a g→gʹ g→a a g→gʹ g→a g g 11 1.719 1.307 1.225 1.665 1.895 1.355 1.242 1.827 µ 12 a 13 (1.171±0.013) 14 1.170(±0.018)b 15 0.412 0.540 ∆[µ (a)-µ (g)] 16 17 -0.082 -0.113 ∆[µ (g→gʹ)-µ (g)] 18 0.358 0.472 ∆[µ (g→a)-µ (g)] 19 20 21 nbo 22 23 1.0066 1.0091 1.0089 1.0000 0.9887 0.9858 1.0089 1.0000 X-CH2 24 1.0391 1.0310 1.0399 1.0370 1.0456 1.0422 1.0399 1.0370 CH2-C 25 26 27 119.53 118.12 115.29 116.86 114.56 111.10 106.47 110.98 TSEE 28 1.41 3.46 ∆[TSEE(a) - TSEE(g)] 29 30 ∆[TSEE(g→gʹ) - TSEE(g)] -2.83 -4.63 31 -1.26 -0.12 ∆[TSEE(g→a) - TSEE(g)] 32 a b 33 From microwave spectroscopy, Ref. [45]. From Microwave spectroscopy, Ref. [47]. 34 35 36 37 38 39 40 41 42 43 44 45 46 ACS Paragon Plus Environment 47 48

theory (NRT) bond orders ground and transition state 3 a

g

g→gʹ

g→a

1.7620

1.189

1.048

1.660

0.573 -0.141 0.471

0.9790

0.9778

0.9705

0.9715

1.0523

1.0529

1.0609

1.0558

117.30

114.53

111.82

113.54

2.77 -2.71 -0.99

19


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Assesing the resemblance between the pre-orthogonal natural bond orbitals and their corresponding molecular orbitals The resemblance between the pre-orthogonal natural bond orbitals associated with the through space LP2X→π*C≡C and the through bond LP2X→σ*CH2-C negative hyperconjugative interactions and their corresponding highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) have been analyzed. Based on the results obtained, the through space LP2F→π*C≡C, LP2Cl→π*C≡C and LP2Br→π*C≡C negative hyperconjugative interactions in the gauche-conformations correspond to the HOMO→LUMO+12, HOMO→LUMO+5 and HOMO→LUMO+2 symmetry-allowed transitions, respectively. Although the energy gaps between HOMO→LUMO+12, HOMO→LUMO+5 and HOMO→LUMO+2 decrease going from the gauche-conformations of compound 1 to compound 3, their corresponding stabilization energies

associated

with

LP2F→π*C≡C,

LP2Cl→π*C≡C

and

LP2Br→π*C≡C

negative

hyperconjugative interactions do not change significantly (Figure 7). This fact could be justified by the variations of their corresponding off-diagonal Fock matrix elements. Contrary to the trend observed for the variations of the HOMOs and LUMOs of the gauche-conformations of compounds 1-3 which are involved in the through space LP2X→π*C≡C symmetry-allowed transitions, their corresponding through bond LP2F→σ*CH2-C, LP2Cl→σ*CH2-C and LP2Br→σ*CH2-C negative hyperconjugative interactions correspond to HOMO→LUMO+27, HOMO→LUMO+29 and HOMO→LUMO+30 symmetry-allowed transitions, respectively (Figure 7). Based on the results obtained, with the increase of the HOMO-LUMO+n gap (n=27→30), the stabilization energies associated with the through bond LP2F→σ*CH2-C, LP2Cl→σ*CH2-C and LP2Br→σ*CH2-C negative hyperconjugative interactions decrease going from the gauche-conformations od compound 1 to compound 3, revealing the determining impacts of the energy differences between the donor and acceptor orbitals on the magnitudes of the stabilization energies associated with these negative hyperconjugative interactions. Figure S1 (see Supporting Information) reveals that the HOMO→LUMO transitions in the gaucheconformations of compounds 1-3 are symmetry-forbidden.

20


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H C

2-Gauche: LUMO+29, = 0.29677

C

LP2S

S

C

*CH2-Csp

LP2S

*CH2-Csp; E2=3.96

2-Gauche:LUMO, = -0.23431

Figure 7. Resemblance between the pre-orthogonal natural bond orbitals associated with LP2X→π*C≡C and LP2X→σ*CH2-Csp [M=O (1), S (2), Se (3)] negative hyperconjugations and their corresponding molecular orbitals. 21



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Figure 7 continued.

H C 3-Gauche: LUMO+2, = -0.00332

C *C-C

Se LP 2Se

LP2Se

C

*C C; E2=0.96

3-Gauche: HOMO, = -0.22263

22


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Bond orders The hyperconjugative interactions affect the structural parameters of the gauche- and anti-conformations of compounds 1-3 via changing their corresponding bond orders. We may expect that the decrease of the LP2X→σ*CH2-C, LP2X→σ*C-H(CH2) and σC-H(CH2)→σ*X-CH3 hyperconjugative interactions going from the gauche-conformations of compound 1 to compound 3 may decrease the X-CH2 bond orders. The results obtained confirmed this expectation. Based on the results obtained, the calculated total natural resonance theory (NRT) bond orders (natural bond orders, nbo) of X-CH2 bonds of the gauche-configurations decrease going from compound 1 to compound 3 while the bond orders of the CH2-C bonds increase inversely (Table 4). This fact shows the determining impacts of the hyperconjugative interactions mentioned above on the structural parameters of the molecular systems which reveal that the electrostatic model associated with the dipole-dipole interactions could not control solely structural parameters of the chemical compounds.5

Structural parameters B3LYP/6-311+G**, LC-ωPBE/6-311+G** and MP26-311+G** calculated structural parameters (bond lengths, bond angles and torsion angles) for the gauche- and anticonformations of compounds 1-3 and also for the transition state structures of the gauche-→ gaucheʹ-conformations

and

gauche-→anti-conformations

interconversion

processes

are

summarized in Table S3. Although we do not expect to reproduce exactly the experimental values by means of the theoretical methods, it is possible to perform theoretical calculations to obtain many properties and also structural parameters with an accuracy that is competitive with experiments. The smaller X-CH2 bond lengths in the gauche-conformations of compounds 1-3 compared to those in their corresponding anti-conformations results from the significant LP2X→σ*CH2-C negative hyperconjugative interactions which tends to decrease the X-CH2 bond lengths via increasing their bond orders. Using the structural parameters obtained, “∆” parameters could be found as ∆[rXCH2(anti)-rX-CH2(gauche)].

∆[rX-CH2(anti)-rX-CH2(gauche)

parameter

increases

going

from

compound 1 to compound 2 but decreases from compound 2 to compound 3. The variations of the LP2X→σ*CH2-C negative hyperconjugative interactions going from compound 1 to compound


23


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3 are not similar to the variations of ∆[rX-CH2(anti)-rX-CH2(gauche) parameters. This fact could only be rationalized by variations of their corresponding HCGAE(a)-HCGAE(g) parameters. Importantly, the variations of the calculated total dipole moment differences between those in the anti- and gauche-conformations going from compound 1 to compound 3 do not correlate with the variations of ∆[rX-CH2(anti)-rX-CH2(gauche) parameters, implying that the hyperconjugative interactions play a determining role on the variations of the structural parameters of the different configurations or configurations of chemical compounds compared with the impacts of the electrostatic interactions associated with the dipole-dipole interactions.5

Assesing the applicability of the maximum hardness principle for the conformational properties of compounds 1-3 Based on the Principle of Maximum hardness, the harder conformations of molecules could be more stable than their soft forms.54 Global hardness (η) in chemical species are defined as the energy gaps between their first unoccupied (LUMO) and the first occupied molecular orbitals (HOMO)54-59:

η =0.5 (ε LUMO-ε HOMO)

(eq. 3)

By considering the validity of Koopmans’ theorem, the hardness (η) can be written as (eq. 4):

η = 0.5 (I – A)

(eq. 4)

where I and A are ionization potential (-ε HOMO) and electron affinity (ε

LUMO)

of the molecules,

respectively. It is worth noting that the B3LYP kernel often underestimates the energies of the HOMOs and LUMOs of some molecular systems (due to its inherent self-interaction errors) (Table S4) whereas the range-separated density functional theories such as long range-corrected (LRC) hybrids (e.g. LC-ωPBE) are expected to give more accurate results.60-62 LC-wPBE/6311+G** results showed that the gauche-conformations of compounds 1-3 are harder than their corresponding anti-conformations (Table S5) but the calculated global hardness (η) differences between the anti- and gauche-conformations [∆(ηanti-ηgauche)] do not correlate with the trend 24


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observed for the variations of their gauche-conformations preferences [∆(Ganti-Ggauche)]. -∆(ηantiηgauche) parameter decreases from compound 1 to compound 2 but increases from compound 2 to compound 3, revealing that there are opposite relationships between the variations of ∆(GantiGgauche) and -∆(ηanti-ηgauche) parameters. It is worth noting that the Maximum hardness principle justifies the gauche-conformation preferences in compounds 1-3 but this principle fails to account for the variations of the energy difference between their gauche- and anti-conformations [∆(Ganti-Ggauche)]. Conclusions The results obtained at the G3MP2, CCSD(T), MP2, LC-ωPBE and B3LYP methods and natural bond orbital (NBO) interpretations provided a reasonable picture from energetic, structural, bonding and stereoelectronic points of view to explore the real origin of the generalized anomeric relationships in the acyclic nonplanar systems [e.g. methyl propargyl ether (1), methyl propargyl sulfide (2) and methyl propargyl selenide (3)]. The trend observed for the gauche-conformations preferences in compounds 1-3 could be justified by means of the hyperconjugative interactions. Importantly, the deletion of the orbitals mixings from the Fock matrices of the gauche- and anti-conformations leads to the anti-conformations preferences and the variations of the energy changes in their Fock matrices correlate significantly with the variations of the anti-conformations preferences going from compound 1 to compound 3, revealing that the generalized anomeric relationships in compounds 1-3 have the hyperconjugative origin. Therefore, the hyperconjugative interactions have determining impacts on the origin of the generalized anomeric effect in these acyclic nonplanar compounds, contradicting the conclusions published in the literature concerning the origin of the generalized anomeric effect.16 Although the gauche-conformations of compounds 1-3 possess smaller dipole moments (µ) compared with their corresponding anti-conformation, the variations of ∆(µanti-

µgauche) parameters do not correlate with the variations of their corresponding Gibbs free energy (G) differences [∆(Ganti-Ggauche)], demonstrating that the electrostatic model associated with the dipole-dipole interactions are not solely responsible for the generalized anomeric relationships in these acyclic nonplanar systems. It is worth noting that the Pauli exchange type repulsions (PETR) are in favors of the gauche-conformations of compounds 1-3 and the variations of the PETR differences between the gauche- and anti-conformations [PETRanti-PETRgauche] succeed to 25



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Page 26 of 32

account quantitatively for their conformational preferences. Accordingly, the variations of the gauche-conformations preferences going from compound 1 to compound 3 result mainly from the cooperative contributions of the hyperconjugative and exchange components.

Supporting Information Additional information concerning the electronic energies of the ground and transition state structures of compounds 1-3 (calculated at the CCSD(T)/6-311+G**//B3LYP/6-311+G** level) and their corresponding natural atomic charges (calculated at the NBO-B3LYP/6311+G** level), structural parameters, global hardness (η) and ∆η parameters (calculated at the LC-wPBE/6-311+G**, B3LYP/6-311+G** and

CCSD(T)/6-311+G**//B3LYP/6-311+G**

levels of theory) and the Cartesian coordinates of the optimized structures are given in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgment This work was partially supported by the research council of Ahvaz Branch of Islamic Azad University.

References (1) Deslongchamps, P. Stereoelectronic Effects in Organic Chemistry; Pergamon Press: Maxwell House, Fairview Park, Elmsford, NY, 1983. (2) Kirby, J. The Anomeric Effect and Related Stereoelectronic Effects at Oxygen; Springer Verlag: New York, 1983. (3) Praly, J. -P.; Lemieux, R. U. Influence of Solvent on the Magnitude of the Anomeric Effect. Can. J. Chem. 1987, 65, 213-223. (4) Cramer, C. J. Anomeric and Reverse Anomeric Effects in the Gas Phase and Aqueous Solution. J. Org. Chem. 1992, 57, 7034-7043. (5) Perrin, C. L.; Armstrong K. B.; Fabian, M. A. The Origin of the Anomeric Effect: Conformational Analysis of 2-Methoxy-1,3-Dimethylhexahydropyrimidine. J. Am. Chem. Soc. 1994, 116, 715-722. (6) Juaristi, E.; Cuevas, G. The Anomeric Effect; CRC Press: Boca Raton, FL, 1995. 26


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TOC Graphic

H

H C

C C

H C

C H

H3C

C CC

O

LP2O

O

C

C

O

C

H

*O-CH2

LP2X→σ*CH2-C

versus

πC≡C→σ*X-CH2

32


Exploring the Origin of the Generalized Anomeric Effects in the Acyclic

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