Generalized Valence Bond Description of ChalcogenâNitrogen

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Generalized Valence Bond Description of Chalcogen-Nitrogen Compounds. III. Why the NO–OH and NS–OH Bonds Are So Different Tyler Y. Takeshita, and Thom H. Dunning J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06283 • Publication Date (Web): 08 Aug 2016 Downloaded from http://pubs.acs.org on August 15, 2016

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The Journal of Physical Chemistry

Generalized Valence Bond Description of Chalcogen-Nitrogen Compounds. III. Why the NO–OH and NS–OH Bonds Are So Different Tyler Y. Takeshita and Thom H. Dunning, Jr.* Department of Chemistry, 600 S. Mathews Avenue, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 ABSTRACT: Crabtree et al. recently reported the microwave spectrum of nitrosyl-O-hydroxide (transNOOH), an isomer of nitrous acid, and found that this molecule has the longest O–O bond ever observed: 1.9149 Å ± 0.0005 Å. This is in marked contrast to the structure of the valence isoelectronic trans-NSOH molecule, which has a normal NS–OH bond length and strength. Generalized valence bond calculations show that the long bond in trans-NOOH is the result of a weak through-pair interaction that singlet couples the spins of the electrons in singly occupied orbitals on the hydroxyl radical and nitrogen atom, an interaction that is enhanced by the intervening lone pair of the oxygen atom in NO. The NS–OH bond is the result of the formation of a stable recoupled pair bond dyad, which accounts for both its length and strength.

Keywords: chemical bonding, through-pair interactions, recoupled pair bonding, generalized valence bond theory, spin-coupled valence bond theory, valence isoelectronic molecules

1. Introduction In a recent article in Science, Crabtree et al.1 reported the Fourier transform microwave spectrum of an isomer of nitrous acid, nitrosyl-O-hydroxide (trans-NOOH). They found that trans-NOOH has an unusually long NO–OH bond, 1.9149 Å ± 0.0005 Å, far longer (0.45 Å) than the O–O single bond in H2O2. An earlier computational study by Talipov et al.2 predicted that trans-NOOH would have an unusually long (1.89 Å) and weak (6.5 kcal/mol) NO–OH bond. Talipov et al.2 carried out a topological analysis of the electron density to better understand the nature of the bonding in trans-NOOH and concluded that its electronic structure was a complicated mixture of a radical pair, nitrene, and ion-pair structure. The unusual structure and energetics of trans-NOOH are even more puzzling given the structure and 1

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Why Are the NO–OH and NS–OH Bonds So Different? energetics of the sulfur-substituted analogue, trans-NSOH. Calculations by Méndez et al.3 predicted a NS–OH bond length of 1.667 Å, only 0.005 Å longer than the HS–OH single bond2,4 (see also Refs. 5 and 6). Further, Méndez et al.3 and Grant et al.7 reported nearly identical NS–OH and HS–OH dissociation energies of 68.4 and 70.7 kcal/mol, respectively. In the current paper we show that the structures and energetics of these two valence isoelectronic molecules, trans-NOOH and trans-NSOH, are so different because of a dramatic difference in the bonding in these two species. In Section 2 we briefly review the theoretical methods used in the current study. In Sections 3 and 4 we discuss the results of GVB and more accurate calculations on the transNOOH and trans-NSOH molecules, respectively. We conclude in Section 5.

2. Theoretical and Computational Methods Generalized valence bond (GVB) theory 8,9 can describe the electronic structure of a number of molecular species that are only poorly described by HF theory. 10-12 The GVB wavefunction is more accurate than the corresponding HF wavefunction, including most (if not all) of the non-dynamical correlation included in a valence “n electrons in n orbitals” Complete Active Space Self Consistent Field (CASSCF) wavefunction.13,14 As a result, the GVB wavefunction can describe the bonding in molecules that otherwise require multiconfiguration wavefunctions. Since the omission of dynamical correlation leads to errors in the quantitative predictions from GVB theory, two high-level electronic structure methods were used to accurately characterize the structures and dissociation energies of NOOH and NSOH: (i) the single-reference, singles and doubles coupled cluster with perturbative triples, CCSD(T), method 15 - 17 and (ii) the multireference configuration interaction18,19 (MRCI) method with single and double excitations from a CASSCF wavefunction20 with an approximate quadruples (+Q) correction.21,22 The MRCI+Q method was used for trans-NOOH since this molecule was found to have significant diradical character and, thus, may not be well described by the single configuration wavefunction used in the CCSD(T) calculations. The full valence orbital space, H(1s)∪N(2s, 2p)∪O(2s, 2p), was used for the CASSCF wavefunction for trans-NOOH. The GVB calculations were performed using the CASVB methodology developed by Thorsteinnson and Cooper23-25 as implemented in the Molpro computational chemistry program suite.26,27 The CCSD(T) and MRCI calculations were also performed with Molpro. Augmented correlation consistent basis sets of quadruple zeta quality (aug-cc-pVQZ) were used for hydrogen, oxygen and nitrogen;28 the corresponding 2


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T. Y. Takeshita and T. H. Dunning, Jr. d-augmented basis set, aug-cc-pV(Q+d)Z, was used for the sulfur atom.29

3. Characterization of the trans-NOOH Molecule The results of GVB calculations on the electronic structure of NO are described in Ref. 30, with the GVB description of NO summarized in Figures 2 (orbitals) and 4 (orbital diagram) of Ref. 30. In the inplane πy system of NO, the NO molecule has a singly occupied orbital centered on the nitrogen atom ( ϕ a7 ) and a lone pair centered on the oxygen atom ( ϕ a5 , ϕ a6 ). It is thus clear how nitrous acid (HO–NO) is formed. On the other hand, the formation NOOH is not at all obvious. To bond to the oxygen atom of NO, the hydroxyl radical would have recouple the spins of the electrons in the oxygen lone pair of NO and previous work has shown that this can only be done by the most electronegative of elements (e.g., F) and, even then, the binding is small.31 Nonetheless, NOOH is bound. The geometry obtained for trans-NOOH in the present calculations is listed in Table 1 where our results are compared with those from Talipov et al.2 and Crabtree et al.1 All three studies are in good agreement on the length of the unusually long NO– OH bond, giving values ranging from 1.89-1.91 Å. The calculated energies of the trans-NO–OH bond, which is found to be very weak (6.5–7.4 kcal/mol), are also listed in Table 1.

Table 1.

Calculated and experimental geometries of nitrosyl-O-hydroxide, trans-NOOH, and

calculated NO–OH dissociation energies. Distances in angstroms and angles in degrees; energies in kcal/mol. Geometry Method

Re(NO)

Re(OO)

Re(OH)

θNOO

θOOH

De(NO–OH)

Ref.

CCSD(T)

1.122

1.894

0.966

114.9

98.4

CASPT2

1.132

1.886

0.969

116.7

96.4

6.5

2

CCSD(T)

1.126

1.901

0.968

115.0

98.2

6.5

present

MRCI+Q

1.132

1.896

0.968

116.2

96.3

7.4

present

Expt’l

1.1264

1.9149

0.9698

115.65

97.21

1

1

To gain a better understanding of the nature of the unusually long, weak NO–OH bond, we carried out GVB calculations at the trans-NOOH geometry from the MRCI+Q calculations. Only four orbitals and 3



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Why Are the NO–OH and NS–OH Bonds So Different? four electrons were considered in the GVB calculation: ϕ a5 – ϕ a7 , the three orbitals in the πy system of NO,40 and, ϕ a8 , the singly occupied hydroxyl radical orbital (for continuity, we use the same notation as in Ref. 30). These orbital are shown in Figure 1. The GVB calculations indicate that the oxygen lone pair is not recoupled and that NO–OH binding results from a weak, yet attractive interaction between the electrons in the singly occupied orbitals localized on the nitrogen atom, ϕ a7 , and hydroxyl radical, ϕ a8 , the spins of which are essentially singlet coupled. The spins of electrons in the lone pair orbitals on the central oxygen, ( ϕ a5 , ϕ a6 ), are also largely singlet coupled. The weight of the perfect pairing spin coupling is 0.97. There are important changes in the orbitals in Figure 1 that contribute to the strength of the NO–OH bond, small though it is. In NO, the most diffuse oxygen orbital in the oxygen lone pair, ϕ a6 , delocalizes in a bonding fashion onto the nitrogen atom, thereby strengthening the NO bond.30 Upon addition of OH to the oxygen atom in NO, ϕ a6 also delocalizes in a bonding fashion onto the oxygen atom of the hydroxyl radical, strengthening the NO–OH bond. Delocalization of ϕ a6 onto the nitrogen and hydroxyl oxygen atoms is accompanied by a complementary delocalization of ϕ a7 and ϕ a8 onto the central oxygen atom, which increases the Sa7a8 overlap, leading to an enhancement in the associated NO–OH binding. The overlap of orbitals ( ϕ a7 , ϕ a8 ), which would be spatially well separated without these delocalization tails, is Sa7a8 = 0.19. The delocalization of ( ϕ a7 , ϕ a8 ) onto the central oxygen atom is facilitated by the delocalization of ϕ a6 onto the nitrogen and hydroxyl oxygen atoms since these simultaneous delocalizations minimize charge transfer between the atoms.

Figure 1. GVB active orbitals for the equilibrium geometry of trans-NOOH. Singlet coupled pairs 4


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T. Y. Takeshita and T. H. Dunning, Jr. are separated by dashed lines, with the overlaps of the two orbitals in the singlet coupled pair (Saiaj) given in the upper left. The GVB orbital diagram for trans-NOOH is given in Figure 2. The weak interaction between the electrons in orbitals ( ϕ a7 , ϕ a8 ) is denoted by the red line drawn from ϕ a8 to ϕ a7 through ( ϕ a5 , ϕ a6 ) to reflect the fact that the interaction between the electrons in orbitals ϕ a7 and ϕ a8 is enhanced by their interaction with the central oxygen lone pair. We found this same type on interaction in NOF,30 where we referred to it as a through-pair interaction. Because the overlap between the two orbitals involved in the through-pair interaction is small, the trans-NOOH isomer has substantial diradical character and, thus, is not expected to be well described by single configuration-based methods, although in this case the differences between the results from the single reference CCSD(T) and multireference MRCI+Q calculations is modest (see Table 1). The through-pair interaction is closely related to, and may be considered a generalization of, the through-bond interaction first identified and characterized by Hoffmann32 and others.33,34 The difference is that, in the present case, the intervening pair is a lone pair, rather than a bond pair. Although throughpair interactions are expected to be relatively rare, we also encountered this type of interaction in SOCl;35 the (CH3)2SFF intermediate in the (CH3)2S + F2 reaction; 36 and the ozone molecule.37 So, the through-pair bonding in trans-NOOH, as unusual as it is, is not an isolated case.

Figure

2.

GVB

orbital

diagram

at

the

5



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Why Are the NO–OH and NS–OH Bonds So Different? equilibrium geometry of trans-NOOH. Orbitals participating in the through-pair interaction are shaded red and connected by red lines.

4. Characterization of the trans-NSOH Molecule The results of GVB calculations on the electronic structure of NS are described in Ref. 38 and the results are summarized in Figures 2 (orbitals) and 3 (orbital diagram) in that article. Unlike NO, The πy system of NS has a recoupled pair bond involving orbitals ( ϕ a5 , ϕ a6 ) and an unpaired, singly occupied orbital centered on the sulfur atom ( ϕ a7 ), using the same orbital notation as in Ref. 38. Thus, it is not at all surprising that the OH radical forms a bond with the sulfur atom in NS. The switch in the location of the singly occupied orbital is a result of the ability of the sulfur atom to form recoupled pair bonds with more electronegative ligands.39-41 The GVB orbital diagram for the equilibrium geometry of trans-NSOH is given in Figure 3.

Figure

3.

GVB orbital diagram for the

equilibrium geometry of trans-NSOH. The bond pairs, (ϕ a5 , ϕ a6 ) and (ϕ a7 , ϕ a8 ) , constitute a recoupled pair bond dyad with each bond connected by lines.

The geometry of trans-NSOH obtained from the present calculations is given in Table 2 and 6


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T. Y. Takeshita and T. H. Dunning, Jr. compared with those from the calculations of Chi et al.,5 Bharatam et al.6 and the cis-isomer studied by Méndez et al.3 All four results are in good agreement. In Table 2 we also list the calculated bond energies for the trans-NS–OH bond.

Table 2. Calculated geometries of trans-SOOH. Distances in angstroms, angles in degrees. MP2(full) basis set: 6-31+G* and MP2 basis set:6-311+G(d,p). Geometry Method

Re(NS)

Re(SO)

Re(OH)

MP2(full)

1.449

1.732

0.984

115.7

116.6

6

MP2

1.442

1.731

0.970

116.5

109.0

5

FPD

1.464

1.667

CCSD(T)

1.454

1.671

0.968

θNSO

114.0

θSOH

108.0

De(NS–OH)

Ref.

68.4

3

66.8

present

The active orbitals for the (four-electron, four orbital) GVB calculation at the geometry obtained from the CCSD(T) calculations on trans-NSOH are shown in Figure 4. These orbitals clearly show the formation of the recoupled pair bond dyad involving the N–SOH and NS–OH bonds in the πy plane—the orbital pair (ϕ a5 , ϕ a6 ) is the original NS recoupled pair bond and (ϕ a7 , ϕ a8 ) is the newly formed NS–OH bond that completes the recoupled pair bond dyad. Addition of the electronegative OH radical to NS results in ϕ a7 localizing in the NS–OH bonding region, which reduces the energetically unfavorable (i.e., Pauli repulsion) overlaps between the orbitals in the two bond pairs—the two unfavorable overlaps in NS, Sa7a5 = 0.12 and S a7a6 = 0.63,38 are reduced to 0.08 and 0.14, respectively, in NSOH. As a result, the length of the NS–OH bond is calculated to be 1.671 Å, just 0.004 Å longer than that of HS–OH, 1.667 Å, the XOH angle increases from 98˚ in trans-NOOH to 108˚ in trans-NSOH, and the calculated dissociation energy, 66.82 kcal/mol, is just 6.55 kcal/mol smaller than in HS–OH. The N–SOH bond length is 1.454 Å, 0.043 Å shorter than the ground state NS bond length. Shortening of recoupled pair bonds after recoupled pair bond dyad formation is common and is a direct result of the reduction in the Pauli repulsions.41, 42 As we have shown in earlier work, recoupled pair bonds and recoupled pair bond dyads are common in molecules containing the late main group elements beyond the first row. These bonds account for the

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Why Are the NO–OH and NS–OH Bonds So Different? stability of hypervalent molecules such as PF5,43 SF4/SF6,42 and ClF3/ClF544 as well as the presence of lowlying excited states in the early members of these series, e.g., the 3,1B1 and 3,1A2 states of SF2.42,45 Recoupled pair bond dyads are also responsible for the T-shaped transition states for inversion in heavily fluorinated phosphines46 as well as the formation of the asymmetric FSSF3 molecule resulting from the dimerization of SF2.47 Recoupled pair bonding is involved in the critical points on the potential energy surface for the (CH3)2S + F2 reaction—the bound (CH3)2SFF intermediate as well as the primary products of the reaction: CH2S(F)CH3 and (CH3)2SF, the former possessing a recoupled pair bond dyad and the latter a recoupled pair bond.36

Figure

4.

GVB

active

orbitals

for

the

equilibrium geometry of trans-NSOH. Singlet coupled pairs are separated by dashed lines, with the overlaps of the two orbitals in the singlet coupled pair (Saiaj) given in the upper left.

5. Conclusions GVB calculations on trans-NOOH show that this molecule is stabilized by an unusual, weakly attractive through-pair interaction involving the electrons in singly occupied orbitals centered on the nitrogen atom and hydroxyl radical that is enhanced by the presence of the lone pair on the central oxygen atom. The presence of the lone pair results in an increase in the overlap of the two orbitals and a 8


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T. Y. Takeshita and T. H. Dunning, Jr. strengthening of the NO–OH bond, but the overlap is still small (0.19) and the NO–OH bond is weak (6.57.4 kcal/mol) and long (1.90 Å). A similar through-pair interaction was found in earlier GVB calculations on NOF30 and is closely related to the through-bond interaction first put forward by Hoffmann32 nearly forty-five years ago. In contrast, formation of the trans-NSOH molecule results in the formation of a recoupled pair bond dyad and, as a result, the NS–OH bond is strong, 68 kcal/mol, comparable to that in HS–OH (73 kcal/mol). In addition, the calculated NS–OH bond length in trans-NSOH is essentially the same as that of the HS–OH single bond, 1.67 Å. The present studies provide a clear rationale for the dramatic differences in the structures and energetics of two valence isoelectronic molecules, trans-NOOH and trans-NSOH, illustrating the important role played by two new bond types in chemistry—weak through-pair interactions in transNOOH and a strong recoupled pair bond dyad in trans-NSOH—in determining molecular structures and energetics.

n AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]; 206-616-1439. Present Addresses T.Y.T, Department of Chemistry, University of California, Berkeley, CA 94720-1460 USA. T.H.D., Jr.: Northwest Institute for Advanced Computing, Pacific Northwest National Laboratory & University of Washington, Seattle Washington 98195-2500 and Department of Chemistry, University of Washington, Seattle, Washington 98195-1700 USA. Notes The authors declare no competing financial interests.

n ACKNOWLEDGEMENT Support for this work was provided by the Distinguished Chair for Research Excellence in Chemistry at the University of Illinois at Urbana-Champaign. 9



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Why Are the NO–OH and NS–OH Bonds So Different?

n Table of Contents Graphic

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T. Y. Takeshita and T. H. Dunning, Jr.

(8) Goddard III, W.A. Improved Quantum Theory of Many-Electron Systems. I. Construction of Eigenfunctions of Sˆ2 Which Satisfy Pauli’s Principle. Phys. Rev. 1967, 157, 73-79. Goddard III, W.A. Improved Quantum Theory of Many-Electron Systems. II. The Basic Method. Phys. Rev. 1967, 157, 81-93. Ladner, R. C.; Goddard III, W. A. Improved Quantum Theory of Many-Electron Systems. IV. The SpinCoupling Optimized GI Method. J. Chem. Phys. 1969, 51, 1073-1087. (9) Gerratt, J.; Lipscomb, W. N. Spin-Coupled Wave Functions for Atoms and Molecules. Proc. Natl. Acad. Sci. 1968, 59, 332-335. (10) Goddard, W. A., III. Publications of William A. Goddard III. J. Phys. Chem. A 2000, 104, 21542167. (11)

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Why Are the NO–OH and NS–OH Bonds So Different?

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T. Y. Takeshita and T. H. Dunning, Jr.

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Generalized Valence Bond Description of ChalcogenâNitrogen

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