Article pubs.acs.org/JPCA
Effect of Lone Pairs on Molecular Resonance Energy Croix J. Laconsay, Andrew M. James,† and John Morrison Galbraith* Department of Chemistry, Biochemistry, and Physics, Marist College, 3399 North Road, Poughkeepsie, New York 12601, United States ABSTRACT: In an effort to understand the theoretical parameters of charge-shift bonding, computational experiments have been designed to elucidate the factors effecting molecular resonance energy. Valence bond theory calculations have been used to calculate resonance energies of homonuclear bonds in the series [HnX−XHn]Z, where n = 0−3 and Z = 2n − 6, 2n − 4, 2n − 2, and 2n for X = C, N, O, and F, respectively. It is shown that the resonance energy decreases as the number of lone pairs increases. Calculated orbital contraction coefficients show that this unexpected result is due to the dominance of orbital size over the lone-pair effect. These results are irrespective of the HXX bond angles. It is also shown that the resonance energy increases with decreasing HXX bond angles due to the increase in p character in the bonding orbital.
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INTRODUCTION
electrons such as F−F are CS bonds whereas bonds such as H3C−CH3 are not. Given this situation, one might expect the RE of a molecule with large CS character, such as F2, to decrease as the number of lone pairs decreases in the series F−F, [HF−FH]2+, [H2F− FH2]4+, and [H3F−FH3]6+. Likewise, the RE of a molecule with low charge-shift character, such as C2H6, should increase in the series H3C−CH3, [H2C−CH2]2−, [HC−CH]4−, and [C−C]6− as the number of lone pairs increases.15 Herein we seek to determine the change in RE as the number of lone pairs changes, while the bonding atoms remain constant. To establish trends, we have considered all molecules in the series [HnX−XHn]Z, where n = 0−3 and Z = 2n − 6, 2n − 4, 2n − 2, and 2n for X = C, N, O, and F, respectively.
Chemical bonds are traditionally classified as either covalent, where electrons are shared between bonding partners, or ionic, where there is a complete electron transfer from one bonding partner to the other. However, in recent years, the charge-shift (CS) bonding concept has emerged to establish a unique form of chemical bond that is neither covalent nor ionic in nature but rather due to large covalent-ionic resonance energy (RE).1,2 Considering a bond between two species A and B, in the framework of valence bond theory (VB), a purely covalent bond is represented by a single spin-paired VB structure, A·−·B, whereas an ionic bond is represented as a single VB structure with both electrons on one constituent, A:−B+. The RE is then the energetic stabilization resulting from mixing spin-paired and ionic structures. Although the CS concept was originally formulated by Shaik, Hiberty, and coworkers using VB,3,4 CS bonds arise when using molecular orbital theory (MO) and density functional theory (DFT) as well.5 Additionally, they have been shown to be more than a theoretical artifact and have been experimentally verified.6,7 Furthermore, examples of CS bonding continue to emerge in a variety of bonding situations, thus establishing the ubiquity of the CS concept.1,8−11 The origin and theoretical foundation of the CS concept has been described in detail elsewhere.12,2 In summary, mixing in ionic character results in a lowering of kinetic energy in the bonding region. This mixing is most pronounced (and therefore resonance stabilization is greatest) when the bonding partners have lone pairs of electrons and compact bonding orbitals. Lone-pair electrons repel bonding electrons, leading to the lone-pair bond-weakening effect (LPBWE).13 In addition to destabilizing the spin-paired structure, these repulsions raise the kinetic energy in the bonding region. Compact bonding orbitals, such as those of highly electronegative atoms, also raise the kinetic energy in the bonding region. In both cases, mixing in ionic structures counterbalances this increase in kinetic energy and thereby restores the virial ratio.14 Thus bonds between highly electronegative atoms with lone pairs of © XXXX American Chemical Society
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THEORETICAL METHODS The geometries of C2H6, N2H4, O2H2, and F2 were first optimized at the B3LYP/6-31G(d,p) level of theory using the Gaussian03 suite of programs.16 For all molecules in the [HnX− XHn]Z series, the bonds were held at the B3LYP/6-31G(d,p)optimized length of the neutral species. All H−F bonds were held constant at the B3LYP/6-31G(d,p)-optimized length for the HF molecule (0.925 Å). Unless otherwise specified, all HXX angles were held fixed at the B3LYP/6-31G(d,p) C2H6 HCC value (111.4°) (Table 1). Likewise, all HXXH dihedral angles were held fixed at the B3LYP/6-31G(d,p) C2H6 HCC values to ensure maximum symmetry. Valence bond calculations were then performed using the XMVB17 program with the breathing orbital VB (BOVB)18−20 method. BOVB allows for a separate set of orbitals for each VB structure, thus allowing the orbitals to “breathe”, thereby acquiring some dynamic correlation while retaining the compact VB wave function. All VB wave functions were constructed as in eq 1, where ϕHL is the spin-paired Heitler and Received: August 15, 2016 Revised: October 1, 2016
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DOI: 10.1021/acs.jpca.6b08245 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 1. Optimized B3LYP/6-31G(d,p) Bond Lengths of Molecules Studied Hereina X X X X a
= = = =
C N O F
H−X
X−X
1.095 1.022 0.970 0.925
1.531 1.488 1.455 1.406
All bond lengths in angstroms.
London21 structure, A·−·A, and ϕion are the ionic structures, A:−A+ and A+:A−, where A is the HnXZ/2 fragment. ΨVB = c1ϕHL + 2c 2(ϕion)
(1)
Initial s-type heavy atom basis functions have been shown to be significant in some cases;22 therefore, all basis functions and orbitals have been included in the VB calculations. Lone-pair and HX bonds were included in the VB calculation but forced to remain doubly occupied. Resonance energies, RE, are defined as the difference in energy between the lowest energy VB structure (ϕHL, in all cases herein) and the three-structure BOVB calculation (Figure 1).
Figure 2. Resonance energies of [HnX−XHn]Z molecules (X = C, N, O, F) as a function of the number of lone pairs. Resonance energies in kJ/mol relative to the molecule in each series with no lone pairs (H3C−CH3 = 108.5 kJ/mol, [H3N−NH3]2+ = 202.6 kJ/mol, [H3O− OH3]4+ = 264.0 kJ/mol, [H3F−FH3]6+ = 273.2 kJ/mol).
Figure 1. Three structure VB mixing diagram. Resonance energy (RE) is the energetic stabilization due to mixing the spin-paired structure, A·−·A (ϕHL), and two ionic structures, A:−A+ and A+:A− (ϕion) (A = HnXZ/2).
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Figure 3. Index of contraction, Ic, of the X−X bonding orbitals in the [HnX−XHn]Z series according to eq 2. A smaller value indicates a more compact orbital. Indices of contraction relative to the molecule in each series with no lone pairs (H3C−CH3 = 0.218, [H3N−NH3]2+ = 0.184, [H3O−OH3]4+ = 0.160, [H3F−FH3]6+ = 0.164).
RESULTS AND DISCUSSION Figure 2 shows that the RE actually decreases as the number of lone pairs increases. While this behavior may seem counterintuitive at first, one should recall that RE depends on the degree of compactness of the bonding orbitals as well as the number of lone pairs. The index of compactness of the bonding orbital, Ic, can be measured in a similar manner as Hiberty and coworkers12 according to eq 2, where cso/cpo and csi/cpi are the coefficients of the outermost and innermost s-/p-type contracted basis functions, respectively, and c1s is the coefficient of the initial s-type basis function. Thus, a small value of Ic indicates a more compact orbital. 2 Ic = [(cso2 + c po )/(c1s2 + csi2 + c pi2)]1/2
to the six lone-pair case, [C−C]6−, the high negative charge results in even more diffuse orbitals and thus lower resonance energies. Considering F−F on the other extreme, the zero lonepair case, [H3F−FH3]6+, starts out with very compact orbitals due to the high positive charge. Although the F orbitals in F−F are quite compact, resulting in a high RE compared with other neutral molecules such as H3C−CH3, compared with H3F− FH36+, they are more diffuse, leading to a lower RE. The effect of orbital contraction can be nearly removed23 by using a minimal basis set and freezing the core orbitals at the RHF level while excluding their associated basis functions (initial s-type bsf) from the VB calculation.24 With the effect of contraction minimized in such a manner, the lone-pair effect dominates and RE increases as the number of lone pairs increases as expected (Figure 4). The F−F series does not appear to follow the same trends as the other series in Figure 4. However, this series would fall in line with the others in Figure 4 if the [H3F−FH3]6+ RE was
(2)
A plot of Ic versus the number of lone pairs (Figure 3) shows that the bonding orbitals become more diffuse as the number of lone pairs increases. As the number of lone pairs increases, the VB bonding orbitals become more diffuse, leading to a smaller RE relative to the compound with no lone pairs. In the case of H3C−CH3, the orbitals are fairly diffuse to begin with; however, upon moving B
DOI: 10.1021/acs.jpca.6b08245 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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that orbital compactness is the dominant effect and the lonepair effect is observed only when orbital contraction is effectively removed. Table 2. Resonance Energies of X−X Bonds in the Series [HnX−XHn]Z with Changing HXX Bond Anglea,b 0lp 111.4 105 100 95 90 2lp 111.4 105 100 95 90 4lp 111.4 105 100 95 90 6lp
Figure 4. Resonance energies of [HnX−XHn]Z molecules (X = C, N, O, F) as a function of the number of lone pairs obtained with the STO-3G basis set.25 Resonance energies in kJ/mol relative to the molecule in each series with no lone pairs (H3C−CH3 = 103.8 kJ/mol, [H3N−NH3]2+ = 184.1 kJ/mol, [H3O−OH3]4+ = 263.5 kJ/mol, [H3F−FH3]6+ = 267.5 kJ/mol).
∼20 kJ/mol lower, indicating a potential problem with this single point rather than the whole series. A problem calculating the RE of [H3F−FH3]6+ is not unreasonable considering that the STO-3G basis set is very small and inflexible and that this molecule represents the most extreme case of orbital contraction with the high electronegativity of F and a large positive charge. Therefore, to verify the qualitative trends, we have repeated the calculations comprising Figure 4 with another minimal basis set (Figure 5). Although Figure 5 still
C−C
N−N
O−O
F−F
108.5 116.3 123.9 133.3 144.5
202.6 212.7 221.3 230.8 241.5
264.0 271.2 276.5 281.4 286.4
273.2 274.7 275.0 274.7 273.7
92.6 97.6 102.8 109.8 118.9
189.2 196.3 202.5 209.5 217.7
256.2 262.1 266.4 270.6 274.9
265.9 269.4 271.4 272.7 273.4
75.8 77.2 79.3 82.7 87.7
174.0 177.3 180.4 184.2 189.0
247.0 250.6 253.3 256.0 258.7
262.6 265.7 267.7 269.2 270.3
51.9
145.6
230.6
260.9
a
Molecules are grouped according to number of lone pairs. bAll energies in kJ/mol.
In each case above, the HXX angle was held at the H3C− CH3 HCC optimized value (111.4°). While this angle was held constant to focus on the effect of lone pairs on the bond resonance energy, it is somewhat arbitrary considering that the B3LYP/6-31G(d,p) HNN and HOO angles in H2N−NH2 and HO−OH are 103.4 and 98.3°, respectively. However, when the HXX angles are varied from 111.4 to 90° with the 6-31G(d,p) basis set (Table 2), the same trend discussed above still holds; RE decreases as the number of lone pairs increases. The same data in Table 2 can be viewed in a different way to highlight the effects of bond angle on RE. As the HXX bond angle is decreased with a set number of lone pairs, the RE increases (Figure 6). When the HXX angle is 111.4° the HX and XX bond orbitals are each approximately sp3. However, as the angle decreases to 90°, the HX bond orbitals become sp2hybridized, whereas the XX bond orbitals become completely p in character. This trend is consistent with the previous discussion when considered in light of the different shapes of s and p orbitals. The spherical shape of s-type orbitals makes them inherently more diffuse than the directional p orbitals; therefore, a bond orbital with more s character will be more diffuse and thus have lower RE. Indeed, the RE of the H−H bond determined with a single s-type basis function is 528 and 682.5 kJ/mol when calculated with a single p-type basis function with the same orbital exponent.27
Figure 5. Resonance energies of [HnX−XHn]Z molecules (X = C, N, O, F) as a function of the number of lone pairs obtained with the scaled MINI26 basis set. Resonance energies in kJ/mol relative to the molecule in each series with no lone pairs (H3C−CH3 = 68.2 kJ/mol, [H3N−NH3]2+ = 129.9 kJ/mol, [H3O−OH3]4+ = 157.7 kJ/mol, [H3F−FH3]6+ = 151.2 kJ/mol).
dips for [H2F−FH2]4+, it does so less than in Figure 4, and the [HF−FH]2+ point lies above the [H3F−FH3]6+ point. Thus Figure 5 supports the qualitative trend that RE increases with the number of lone pairs when the effect of orbital contraction is removed. Both orbital compactness and lone-pair/bond-pair repulsion lead to the previously observed tendency for RE (and therefore CS character) to increase from left to right and bottom to top of the periodic table. This trend holds in the current study as well, as can be seen in Table 2. However, Figures 2−4 indicate
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CONCLUSIONS By replacing hydrogen atoms with lone pairs of electrons in the series [HnX−XHn]Z, where n = 0−3 and Z = 2n − 6, 2n − 4, 2n − 2, and 2n for X = C, N, O, and F, respectively, we have determined the effect of lone pairs on molecular resonance energy and thereby charge-shift bonding. The prevailing theory C
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The Journal of Physical Chemistry A
and bonding orbitals become more diffuse. Only when the bonding orbital size fluctuation is restricted by using a minimal basis set does the lone pair effect become evident. The dominance of bond orbital size over the number of lone pairs is irrespective of HXX bond angle. While investigating the effect of the HXX bond angle, we have also shown that RE increases as the bond angle decreases due to increasing bond orbital p character.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: (845) 575-3000, x2264. Fax: (845) 575-3184. Present Address †
A.M.J.: Department of Chemistry, Virginia Tech, Blacksburg, VA 24061, USA. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the School of Science and the office of the Academic Vice President of Academic Affairs at Marist College for continued support of research. C.J.L. and A.M.J. thank the J. Richard LaPietra Chemistry Summer Research Fellowship at Marist College for funding.
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REFERENCES
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Figure 6. Resonance energies of [HnX−XHn]Z molecules (X = C, N, O, F) as a function of HXX bond angle for molecules with (a) zero, (b) two, and (c) four lone pairs of electrons. Resonance energies in kJ/ mol relative to the molecule in each series with HXX = 111.4: (a) H3C−CH3 = 108.5 kJ/mol, [H3N−NH3]2+ = 202.6 kJ/mol, [H3O− OH3]4+ = 264.0 kJ/mol, [H3F−FH3]6+ = 273.3 kJ/mol; (b) [H2C− CH2]2− = 92.6 kJ/mol, H2N−NH2 = 189.2 kJ/mol, [H2O−OH2]2+ = 256.2 kJ/mol, [H2F−FH2]4+ = 265.9 kJ/mol; and (c) [HC−CH]4− = 75.8 kJ/mol, [HN−NH]2− = 174.0 kJ/mol, HO−OH = 247.0 kJ/mol, [HF−FH]2+ = 262.6 kJ/mol.
of charge-shift bonding states that charge-shift character should increase with the number of lone pairs. However, the effect of orbital compactness overrides the lone-pair effect and the resonance energy decreases as the number of lone pairs increases D
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The Journal of Physical Chemistry A (12) Hiberty, P. C.; Ramozzi, R.; Song, L.; Wu, W.; Shaik, S. The Physical Origin of Large Covalent-Ionic Resonance Energies in Some Two-Electron Bonds. Faraday Discuss. 2007, 135, 261−272. (13) Sanderson, R. T. Polar Covalence; Academic Press: New York, 1983. (14) Lauvergnat, D. L.; Maitre, P.; Hiberty, P. C.; Volatron, F. Valence Bond Analysis of the Lone Pair Bond Weakening Effect for the X-H bonds in the Series XHn = CH4, NH3, OH2, FH. J. Phys. Chem. 1996, 100, 6463−6468. (15) This idea was originally proposed by an attendee (identity unknown) at a lecture given by Philippe Hiberty to the group of Raold Hoffmann at Cornell University in the Fall of 2008. (16) Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Rob, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. L.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.02; Gaussian, Inc.: Wallingford, CT, 2003. (17) Somg, L.; Wu, W.; Mo, Y.; Zhang, Q. XMVB-01: An Ab Initio Non-Orthogonal Valance Bond Program; Xiamen University: Xiamen, China, 2003. (18) Hiberty, P. C.; Humbel, S.; Byrman, C. P.; van Lenthe, J. H. Compact Valence Bond Functions with Breathing Orbitals: Application to the Bond Dissociation Energies of F2 and FH. J. Chem. Phys. 1994, 101, 5969−5976. (19) Hiberty, P. C.; Flament, J. P.; Noizet, E. Compact and Accurate Valence-Bond Functions with Different Orbitals for Different Configurations: Application to the Two-Configuration Description of Molecular Fluorine. Chem. Phys. Lett. 1992, 189, 259−265. (20) Hiberty, P. C.; Shaik, S. BOVB - A Valence Bond Method Incorporating Static and Dynamic Correlation Effects. In Theoretical and Computational Chemistry: Valence Bond Theory; Cooper, D. L., Ed.; Elsevier: New York, 2002; Vol. 10, pp 187−225. (21) Heitler, W.; London, F. Interaction of Neutral Atoms and Homopolar Binding According to the Quantum Mechanics. Eur. Phys. J. A 1927, 44, 455−472. (22) Galbraith, J. M.; James, A. J.; Nemes, C. T. The Effect of Diffuse Basis Functions on Valence Bond Structural Weights. Mol. Phys. 2014, 112, 654−660. (23) The effects of orbital contraction cannot be completely removed with a minimal basis set because the s/p hybridization will be altered to attempt to compensate for the lack of basis set flexibility. (24) Additional calculations show that the qualitative trends presented herein remain unchanged when the core orbitals are held frozen at the RHF level as long as the corresponding initial heavy atom s-type basis functions are not included in the VB orbital optimization. Laconsay, C. J.; James, A. J.; Galbraith, J. M., unpublished results. (25) When using the STO-3G basis set, RE is taken as the difference between the HL and 3 structure VBSCF. With the STO-3G basis, BOVB values are meaningless, as VB orbitals do not have any means by which to “breathe”. Instead, separate orbitals for separate structures attempt to mimic the effects of breathing by altering s/p hybridization leading to spurious results. (26) MINI (Scaled) EMSL Basis Set Exchange Library. Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E.; Saka1, Y.; Tatewaka, H. Gaussian Basis Sets for Molecular Calculations; Huzinaga, S., Ed.;
Elsevier: Amsterdam, 1984. Valence scale factors from John Deisz of North Dakota State University. (27) For this computational experiment, three-structure VB resonance energies were obtained at the B3LYP/6-31G(p)-optimized bond length (0.742 A) using a single s- and p-type basis function. In each case, the orbital exponent of the second s-type basis function in the hydrogen 6-31G(p) basis set was used (ζ = 1.16)
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DOI: 10.1021/acs.jpca.6b08245 J. Phys. Chem. A XXXX, XXX, XXX−XXX
