Structure and stability of HSNO, the simplest S-nitrosothiolw

Qadir K. Timerghazin,z Gilles H. Peslherbe* and Ann M. English*

Received 1st October 2007, Accepted 19th December 2007

First published as an Advance Article on the web 30th January 2008

DOI: 10.1039/b715025c

High-level ab initio calculations employing the CCSD and CCSD(T) coupled cluster methods with

a series of systematically convergent correlation-consistent basis sets have been performed to

obtain accurate molecular geometry and energetic properties of the simplest S-nitrosothiol

(RSNO), HSNO. The properties of the S–N bond, which are central to the physiological role of

RSNOs in the storage and transport of nitric oxide, are highlighted. Following corrections for

quadruple excitations, core-valence correlation and relativistic effects, the CCSD(T) method

extrapolated to the complete basis set (CBS) limit yielded values of 1.85 A and 29.2 kcal mol�1

for the S–N bond length and the dissociation energy for homolysis of the S–N bond, respectively,

in the energetically most stable trans-conformer of HSNO. The properties of the S–N bond

strongly depend on the basis-set size and the inclusion of triple, and, to a lesser extent, quadruple

excitations in the coupled cluster expansion. CCSD calculations systematically underestimate the

S–N equilibrium distance and S–N bond dissociation energy by 0.05–0.07 A and 6–7 kcal mol�1,

respectively. The significant differences between the CCSD(T) and CCSD descriptions of HSNO,

the high values of the coupled cluster T1 (0.027) and D1 (0.076) diagnostics, as well as the

instability of the reference restricted Hartree–Fock (RHF) wavefunction indicate that the

electronic structure of the SNO group possesses multireference character. Previous quantum-

chemical data on RSNOs are reexamined based on the new insight into the SNO electronic

structure obtained from the present high-level calculations on HSNO.

Introduction

S-Nitrosothiols (RSNOs, where R is an organic substituent or

hydrogen)1,2 are of considerable interest due to their crucial

role in the storage and transport of nitric oxide, an important

biological signaling molecule. The reactivity of RSNOs in the

presence of light or trace metal ions3,4 has led to contradictory

reports of their stability and their ability to function as NO

donors. The S–NO bond is central in these processes, so

characterization of this bond is important in our understand-

ing of the biological chemistry of RSNOs.

There is a paucity of structural data on RSNOs. The

crystallographic results to date5–13 reveal that RSNOs possess

an elongated S–N bond (1.7–1.85 A, Table 1 and Fig. 1) and

can exist as cis (syn) and trans (anti) conformers.5–7,9,14 Based

on NMR studies,9 the conformers are nearly isoenergetic and

are separated by a relatively high interconversion barrier of

B11 kcal mol�1.

Primary and secondary RSNOs favor the cis-conformation

whereas tertiary RSNOs adopt the trans-conformation,

although the energy difference between the cis and trans

conformers is small (B1 kcal mol�1).6,9 The reported activa-

tion energies for RSNO thermal decomposition vary from 20

to 31 kcal mol�1.15,16 Calorimetric measurements by Lu

et al.17 suggest that the homolytic S–N bond dissociation

energy [(D0(S–N)] is B20 kcal mol�1 for aromatic RSNOs

and B25 kcal mol�1 for aliphatic RSNOs.

Reported ab initio studies on RSNOs16,18,19 include calcula-

tions with second-order Møller–Plesset perturbation theory

(MP2) and quadratic configuration interaction with single and

double excitations (QCISD) methods, used in combination

with various double- and triple-zeta quality basis sets. Also,

Table 1 S–N bond lengths in organic RSNOs from X-ray crystal-lographic data

Compounda Conformation r(S–N)/A Reference

1 trans 1.763 5trans 1.762 6trans 1.771 7

2 trans 1.755 83 trans 1.792 64 cis 1.766 95 cis 1.769b 10

cis 1.728b

6 trans 1.744 117 trans 1.703 118 trans 1.781 129 trans 1.85 13

a The RSNO structures are shown in Fig. 1. b Two different rotamers.

Centre for Research in Molecular Modeling, and Department ofChemistry and Biochemistry, Concordia University, 7141 SherbrookeStreet West, Montreal, Quebec, Canada H4B 1R6w Electronic supplementary information (ESI) available: Cartesiancoordinates and total energies of molecules calculated. See DOI:10.1039/b715025cz Present address: Department of Chemistry, University of Alberta,11227 Saskatchewan Drive, Edmonton, Alberta, Canada T6G 2G2.

1532 | Phys. Chem. Chem. Phys., 2008, 10, 1532–1539 This journal is �c the Owner Societies 2008

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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several composite schemes such as G3 and CBS-QB3 have

been applied to RSNOs. MP2 calculations with triple-zeta

basis sets as well as G3 and CBS-QB3 composite methodolo-

gies16,18,19 suggest D0(S–N) in the range of 29–34 kcal mol�1,

in acceptable agreement with experimental values derived

from the thermolysis activation energies.16 QCISD calcula-

tions with triple-zeta basis sets19 yield D0(S–N) values more

than 10 kcal mol�1 lower. Density-functional theory (DFT)

calculations with the popular B3LYP hybrid functional yield

intermediate values (26–29 kcal mol�1)17,29 that are close to

the calorimetric data reported by Lu et al.17 The S–N bond

length calculated with ab inito and DFT methods varies from

1.82 to 1.94 A, with B3LYP calculations generally yielding a

longer S–N bond.19

Experimental D0(S–N) values are only available for rela-

tively large substituted RSNOs and were obtained from

indirect measurements. To the best of our knowledge, no

experimental data on the structure and stability of HSNO,

the simplest RSNO, are available. Moreover, only a few high-

level quantum-chemistry calculations of RSNOs have been

reported to date. Although the S–N bond length [r(S–N)] and

D0(S–N) were found to be highly sensitive to basis-set size,

calculations using larger than triple-zeta basis sets have not

been reported. Compared to molecules containing only first-

row elements, high-accuracy calculations of sulfur-containing

compounds present additional problems due to the greater

role of core-valence correlation,20 as well as relativistic (scalar

and spin–orbit) effects.21 Specially developed correlation-con-

sistent basis sets with additional tight d-functions are recom-

mended22 for calculating thermochemical values with chemical

accuracy for compounds containing second-row elements.

In this paper, we report a systematic study of the geometry

of singlet ground-state (X1A0) HSNO, the trans-HSNO/cis-

HSNO energy difference and the D0(S–N) using high-level

CCSD and CCSD(T) coupled cluster calculations with com-

plete basis-set (CBS) extrapolations21,23,24 and corrections for

core-valence (CV) correlation, scalar-relativistic (SR) and

spin–orbit (SO) effects. The resulting r(S–N) and D0(S–N)

were further corrected by accounting for quadruple excitations

in the coupled cluster expansion. Published quantum-chemical

data on HSNO are reexamined based on the new insights into

the SNO electronic structure obtained from the present high-

level calculations. The applicability of various post-Har-

tree–Fock methods for RSNO calculations is also discussed.

Computational details

The electronic structure calculations were performed with the

Molpro,25 DALTON26 and PSI327 program packages. Geo-

metries were optimized using coupled cluster methods with

single and double excitations with [CCSD(T)] and without

(CCSD) perturbative triples correction28–30 within the frozen-

core approximation. The spin-restricted open-shell coupled

cluster approach as implemented in Molpro31 was used for

calculations of the open-shell SH and NO radicals. To assess

the quality of the single-reference description of the wavefunc-

tion, in addition to the standard T1 diagnostic,32 the D1

coupled cluster diagnostic33 was calculated as implemented

in the PSI3 code.

A series of Dunning’s augmented correlation-consistent

basis sets,34 aug-cc-pVxZ (x = D, T, Q and 5) was used for

all elements except sulfur. Correlation-consistent basis sets

augmented with additional tight d-functions, aug-cc-pV-

(x+d)Z, were employed for this second-row element,35 and

the combination of these basis sets are abbreviated as AVxZ.

For complete basis-set (CBS) extrapolations of the molecular

geometry and energetic properties, mixed Gaussian/exponen-

tial24,36 and two-parameter extrapolation23 formulae were

employed:

E(n) = ECBS + Be�(n�1) + Ce�(n�1)2

E(n) = ECBS + B/n3

Values calculated with AVTZ, AVQZ and AV5Z basis sets

(n = 3, 4, 5) were used for the mixed Gaussian/exponential

extrapolation, while AVQZ and AV5Z (n=4, 5) values served

as input for the two-parameter extrapolation. The CBS limit is

taken as the average of the CBSTQ5 and CBSQ5 values

(denoted as CBS) and their difference is used to estimate

the corresponding uncertainty (given in parentheses,

Tables 2–4).21

The effects of including higher excitations in the coupled

cluster expansion were investigated using coupled cluster with

single, double, triple, and perturbative quadruple excitations

[CCSDT(Q)],37 and coupled cluster with single, double, triple

and quadruple excitations38–40 (CCSDTQ), as implemented in

the MRCC program.41 The steep scaling of the computational

cost in terms of calculation time and memory requirements for

coupled cluster methods beyond CCSD(T) dictates the use of

small basis sets, even for a molecule as small as HSNO.

Therefore, Ahlrichs’ polarized valence double-zeta basis set42

(Ahlrichs pVDZ) was used in combination with these methods

(Ahlrichs’ VDZ42 basis set was used for the oxygen and

hydrogen atoms).

Fig. 1 Organic RSNOs for which X-ray crystal data have been

reported in the literature (Table 1).

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Scalar-relativistic (SR) effects were estimated with the Dou-

glas–Kroll–Hess43,44 approach using the cc-VQZ_DK basis set

specifically designed for relativistic calculations.25 SR correc-

tions for the energies and geometries were determined from the

CCSD(T)/cc-VQZ_DK values obtained with and without the

inclusion of SR effects.

The energy correction for spin–orbit (SO) coupling in the 2PSH radical was explicitly computed by the interacting states

method using the Breit–Pauli operator45 (as implemented in

Molpro) at the internally contracted multireference configura-

tion interaction (MRCI) level46,47 using the AVQZ basis set.

Two 2P states and one 2S state were included and the

CCSD(T)/AVQZ geometry was used for the SO calculation.

Corrections for CV correlation were estimated at the

CCSD(T) level using the weighted CV basis set, aug-cc-

pwCVQZ,20 for geometries optimized at the CCSD(T)/aug-

cc-pwCVTZ level. CV corrections were determined as the

difference between the values obtained with full-electron cor-

relation (excluding the sulfur 1s electrons) and those from

frozen-core calculations.

Zero-point vibrational energies (ZPEs) were calculated from

CCSD/AVTZ and CCSD(T)/AVTZ harmonic vibrational fre-

quencies without scaling factors. HSNO frequencies were

calculated numerically using analytical CCSD and CCSD(T)

energy gradients (as implemented in DALTON26) in an ‘‘em-

barrassingly parallel’’ fashion where all 24 analytical gradient

Table 2 Calculated S–N and N–O bond lengths and S–N–O angles of trans-HSNO and cis-HSNOa

trans-HSNO cis-HSNO

Method r(S–N)/A r(N–O)/A +S–N–O/1 r(S–N)/A r(N–O)/A +S–N–O/1

CCSD AVDZ 1.856 1.187 113.95 1.846 1.189 115.53AVTZ 1.816 1.180 114.11 1.803 1.183 115.92AVQZ 1.805 1.177 114.13 1.790 1.180 116.07AV5Z 1.800 1.177 114.11 1.785 1.180 116.08CBS 1.797 (�0.001) 1.177 114.08 (�0.01) 1.782 (�0.001) 1.179 116.08

CCSD(T) AVDZ 1.903 1.189 114.50 1.894 1.192 115.49AVTZ 1.860 1.183 114.55 1.847 1.187 115.76AVQZ 1.846 1.181 114.54 1.830 1.184 115.88AV5Z 1.841 1.181 114.50 1.825 1.184 115.87CBS 1.838 (�0.001) 1.180 114.45 (�0.01) 1.820 (�0.001) 1.184 115.86

DCV �0.007 �0.001 0.01 �0.008 �0.001 0.07DSR �0.005 0.001 �0.07 �0.005 0.001 �0.04

CBS + CV 1.831 1.179 114.46 1.813 1.183 115.93CBS + CV + SR 1.826 1.180 114.39 1.807 1.184 115.90

DQ B0.02CBS + Q 1.86CBS + Q + CV + SR 1.85

a CBS—complete basis set extrapolated values, DCV—core-valence correlation correction, DSR—scalar-relativistic correction, DQ—correction

for the inclusion of quadruple excitations into the coupled cluster expansion.

Table 3 Calculated S–H bond lengths and H–S–N angles of trans-HSNO and cis-HSNOa

trans-HSNO cis-HSNO

Method S–H/A +H–S–N/1 S–H/A +H–S–N/1

CCSD AVDZ 1.348 90.81 1.353 95.26AVTZ 1.336 91.28 1.343 95.79AVQZ 1.335 91.50 1.342 96.10AV5Z 1.335 91.56 1.342 96.15CBS 1.335 91.61 (�0.02) 1.342 96.19 (�0.01)

CCSD(T) AVDZ 1.350 89.66 1.356 94.28AVTZ 1.339 90.18 1.345 94.88AVQZ 1.338 90.46 1.345 95.28AV5Z 1.338 90.54 1.345 95.35CBS 1.338 90.59 (�0.02) 1.344 95.42 (�0.01)

DCV �0.002 0.06 �0.002 0.08

DSR 0.003 �0.07 0.002 �0.15

CBS + CV 1.336 90.66 1.343 95.48CBS + CV + SR 1.338 90.59 1.345 95.33

a CBS—complete basis set extrapolated values, DCV—core-valence correlation correction, DSR—scalar-relativistic correction.

1534 | Phys. Chem. Chem. Phys., 2008, 10, 1532–1539 This journal is �c the Owner Societies 2008

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calculations were executed simultaneously on different nodes

of a computer cluster. The vibrational frequencies of the SH and

NO radicals were calculated by double numerical differentiation.

Results and discussion

The S–N bond, which is central to NO release, is the weakest

bond in RSNOs. An accurate description of this bond is a

challenge for quantum chemistry since various methods yield

inconsistent results, as discussed above. Therefore, the proper-

ties of the SNO group in HSNO are the focus of this work.

Tables 2 and 3 present the calculated molecular geometries of

the SNO and HSN moieties, respectively, and Table 4 sum-

marizes the calculated energy differences between trans-HSNO

and cis-HSNO, as well as the D0(S–N) calculated for

trans-HSNO.

HSNO molecular geometry

The calculated r(S–N) of HSNO smoothly decreases with basis

set size, with the AVTZ values being 0.02–0.03 A greater than

those at the CBS limit (Table 2, Fig. 2). More significantly,

r(S–N) calculated at the CCSD level exceeds the CCSD(T)

value calculated with the same basis set by B0.04 A, which is

the largest difference between the CCSD and CCSD(T) de-

scriptions of the HSNO molecular geometry that we found.

CV and SR effects each shorten r(S–N) by 0.005–0.007 A, and

the r(S–N) values estimated at the CCSD(T)/CBS level with

ZPE, CV and SR corrections are 1.826 A and 1.807 A for

trans-HSNO and cis-HSNO, respectively.

The large difference in r(S–N) values calculated with the

CCSD and CCSD(T) methods suggests that inclusion of

higher excitations into coupled cluster calculations may be

necessary. To test the sensitivity of the calculated r(S–N) to

inclusion of quadruple excitations, we performed a series of

constrained S–N bond length optimizations using the CCSD,

CCSD(T), and CCSDT(Q) methods. Table 5 summarizes the

Fig. 2 Calculated trans-HSNO S–N bond length [r(S–N)] and homo-

lytic dissociation energy [D0(S–N)] vs. AVxZ basis set size. The

methodology is described in the text under Computational details.

The values plotted do not include corrections for core–valence corre-

lation, relativistic effects and zero-point vibrational energy. The bold

horizontal lines show the respective CBS limits, with the thickness of

the lines representing the uncertainty in these limits.

Table 4 Calculated energy difference between trans-HSNO and cis-HSNO, and homolytic S–N bond dissociation energy [D0(S–N)] of trans-HSNO (kcal mol�1)a

CCSD CCSD(T)

DE(trans � cis) D0(S–N) DE(trans � cis) D0(S–N)

AVDZ �0.99 22.55 �1.05 27.74AVTZ �0.88 24.44 �0.97 29.97AVQZ �0.84 25.42 �0.93 31.03AV5Z �0.82 25.77 �0.91 31.41CBS �0.81 (�0.01) 26.06 (�0.08) �0.89 (�0.01) 31.72 (�0.09)

DZPE 0.12 �2.14 0.15 �2.71

DCV 0.01 0.05DSR �0.002 �0.35DSO �0.48

CBS + ZPE �0.69 23.92 �0.75 29.01

CBS + ZPE + CV �0.74 29.06CBS + ZPE + CV + SR + SO �0.74 28.23

DQ B1.0CBS + Q + ZPE 30.0CBS + Q + ZPE + CV + SR + SO 29.2

a CBS—complete basis set extrapolated values, DZPE—difference in zero-point vibrational energies, DCV—core-valence correlation correction,

DSR—scalar-relativistic correction, DSO—spin–orbit interaction energy correction, DQ—correction for the inclusion of quadruple excitations into

the coupled cluster expansion.

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effects of including triple and quadruple excitations on r(S–N)

in trans-HSNO, calculated using the Ahlrichs pVDZ basis set.

The differences in the CCSD and CCSD(T) values calculated

with the AVDZ basis set and CBS are also shown for

comparison. The effect of including perturbative triple excita-

tions D[SD(T) � SD] is practically the same in the calculations

with the Ahlrichs pVDZ and AVDZ basis sets (B0.05 A,

Table 5), and is slightly larger than at the CBS limit (B0.04

A). Including perturbative quadruple excitations at the

CCSDT(Q) level increases r(S–N) by B0.02 A (Table 5),

and thus the effect of including quadruple excitations (DQ)

on the S–N bond length is estimated to be B0.02 A. Our best

value for r(S–N) in trans-HSNO is then 1.85 A. The CV and

SR corrections, which decrease r(S–N) by 0.012 A, partially

cancel the effect of including quadruple excitations, which

increases r(S–N) by B0.02 A. As a result, the uncorrected

CCSD(T)/CBS value for r(S–N) (1.838 A) is close to our final

1.85 A value. Possible reasons for the sensitivity of the

calculated S–N bond properties to inclusion of triple and

quadruple excitations are discussed later.

As for the S–N bond, r(N–O) smoothly decreases with

basis-set size (Table 2), but exhibits negligible conformational

sensitivity, being just 0.002–0.004 A shorter in trans-HSNO vs.

cis-HSNO. The inclusion of triple excitations has little effect

since r(N–O) is only 0.004 A longer at the CCSD(T) vs. CCSD

level. The effect of including quadruple excitations is expected

to be negligible, since it is normally an order of magnitude

smaller than the effect of including triple excitations,21 and

therefore was not investigated here for r(N–O). The CV and

SR corrections alter r(N–O) by only 0.001 A and work in

opposite directions. Our final corrected CCSD(T)/CBS + CV

+ SR r(N–O)s are 1.180 and 1.184 A for trans-HSNO and cis-

HSNO, respectively (Table 2). The predicted final values of

+S–N–O are similar in both conformations (trans/cis: 114.41/

115.91, Table 2), whereas the final r(S–H) is slightly smaller in

cis-HSNO (trans/cis: 1.338/1.345 A, Table 3).

Energetic properties of HSNO

Our calculations consistently predict that trans-HSNO is more

stable than cis-HSNO but the energy difference is o1 kcal

mol�1 and decreases with increasing basis-set size. Inclusion of

triple excitations increases the energy difference between the

conformers by B0.1 kcal mol�1, and the effect of quadruple

excitations is expected to be even less.21 The ZPE correction

significantly decreases the energy difference by B1.2 kcal

mol�1, and the CV and SR effects are almost negligible

(o0.01 kcal mol�1). Our final estimate of the energy difference

between trans-HSNO and cis-HSNO is 0.74 kcal mol�1. The

dipole moment of trans-HSNO calculated with CCSD(T)/

AVQZ is larger than that of cis-HSNO (1.31 vs. 1.03 D).

As shown in Fig. 2 and Table 4, the D0(S–N) of trans-

HSNO smoothly increases towards the CBS limit, although

the basis-set convergence is relatively slow. The values ob-

tained with the AVTZ basis set are B1.63 and B1.75 kcal

mol�1 lower than the CBS limit in the CCSD and CCSD(T)

calculations, respectively. Clearly, CCSD underestimates

D0(S–N) relative to CCSD(T), the former predicting values

5.2–5.7 kcal mol�1 lower. The relative effect of including

perturbative triple excitations obtained with the Ahlrichs

pVDZ basis set is slightly smaller (D[SD(T) � SD] B4.3 kcal

mol�1, Table 5), although the absolute values of D0(S–N) are

underestimated by B5 kcal mol�1. The effect of including

perturbative quadruple excitations estimated with CCSDTQ/

Ahlrichs pVDZ//CCSDT(Q)/Ahlrichs pVDZ is B1 kcal

mol�1 (Table 5), which we use as an estimate of the correction

for quadruple excitations (DQ) to D0(S–N). However, since

calculations with the Ahlrichs pVDZ basis set tend to under-

estimate the effect of triple excitations (Table 5), this estimated

DQ should be considered a lower limit and the effect of

including quadruple excitations can be expected to yield a

slightly larger correction at the CBS limit.

The ZPE correction decreases the CCSD and CCSD(T)

D0(S–N) by 2.1 and 2.7 kcal mol�1, respectively. The CV

correlation effect is relatively small (0.05 kcal mol�1), perhaps

due to the unusually long S–N bond, whereas the SR correc-

tion (B0.35 kcal mol�1) is 7-fold larger. The SO coupling

constant of a free sulfur atom is 1.13 kcal mol�1,48 indicating

that the ground-state (3P1) is 0.57 kcal mol�1 lower in energy

than the average non-SO-coupled (3P) state. The SH radical,

formed upon homolysis of the S–N bond, has a doubly-

degenerate 2P ground state. Calculations with MRCI/AVQZ,

including the two lowest 2P states and one 2S state, indicate

that the SH 2 P3/2 ground SO state is 0.48 kcal mol�1 lower in

energy than the average non-SO-coupled 2P state, while the

energetic effect of SO interaction is negligibly small in the

closed-shell HSNO molecule. Additional stabilization of the

Table 5 Coupled cluster S–N bond length and homolytic S–N bond dissociation energy of trans-HSNO with and without inclusion of triple andquadruple excitationsa

r(S–N)/A D(S–N)/kcal mol�1

Ahlrichs pVDZb,c AVDZ CBS Ahlrichs pVDZb,c AVDZ CBS

CCSD 1.859 1.856 1.797 17.9 22.55 26.06CCSD(T) 1.906 1.903 1.838 22.1 27.74 31.72CCSDT(Q) 1.926CCSDTQ//CCSDT(Q) 23.1

D[SD(T) � SD] 0.047 0.047 0.041 4.27 5.19 5.66D[SDT(Q) � SD(T)] 0.020D[SDTQ � SD(T)] 1.02

a The effect of quadruple excitations was estimated with CCSDT(Q)/Ahlrichs-pVDZ for r(S–N), and with CCSDTQ/Ahlrichs-pVDZ//

CCSDT(Q)/Ahlrichs-pVDZ for D(S–N). b Constrained S–N bond length optimizations, with all geometrical parameters but r(S–N) fixed at

their CCSD(T)/Ahlrichs-pVDZ optimized value. c The Ahlrichs VDZ basis set was used for the oxygen and hydrogen atoms.

1536 | Phys. Chem. Chem. Phys., 2008, 10, 1532–1539 This journal is �c the Owner Societies 2008

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SH radical by SO coupling lowers D0(S–N) by B0.5 kcal

mol�1, so that, overall, the relativistic (SR + SO) effects

reduce D0(S–N) by B0.8 kcal mol�1.

Our final trans-HSNO D0(S–N) calculated with CCSD(T)/

CBS, including an estimated correction for quadruple excita-

tions as well as ZPE, CV, SR, and SO corrections, is thus

29.2 kcal mol�1 (Table 4). The SO correction and the correc-

tion for quadruple excitations partially cancel each other.

Thus, the ZPE-corrected CCSD(T)/CBS D0(S–N) value (29.0

kcal mol�1) is close to the reference value of 29.2 kcal mol�1,

since the SR correction is relatively small.

The basis-set dependence of r(S–N) and D0(S–N) of HSNO

(Fig. 2, Tables 1 and 4) sheds light on inconsistencies observed

in the QCISD calculations by Baciu and Gauld,19 which yield

relatively good RSNO molecular geometries [r(S–N) = 1.82

A] but significantly underestimate D0(S–N) (20.4 kcal mol�1).

When used with double- or triple-zeta quality basis sets, the

CCSD method, which is similar to QCISD,49 predicts r(S–N)

close to the CCSD(T)/CBS limit, but underestimates D0(S–N)

by 8–9 kcal mol�1 (Fig. 2). Thus, QCISD/6-311++

G(3fd,3pd) predicts the correct HSNO geometry, presumably

because the errors arising from the use of an insufficiently large

basis set cancel those due to the absence of triple (and higher)

excitations in the QCISD correlation treatment.

DFT methods generally demonstrate much faster conver-

gence with basis-set size than ab initio methods.50,51 Baciu and

Gauld19 recommended using B3P86 with the 6-311+G(2d,2p)

basis set for RSNOs over the B3LYP functional with the same

basis set since the latter functional overestimates r(S–N) and

underestimates D0(S–N).19 The r(S–N) values calculated with

B3P86 and B3LYP (1.84 and 1.87 A, respectively) bracket our

reference r(S–N) for trans-HSNO (1.85 A, Table 2). B3LYP

underestimates the reference D0(S–N) (29.2 kcal mol�1,

Table 4) by 1.3 kcal mol�1 (27.9 kcal mol�1), whereas B3P86

(32.4 kcal mol�1) overestimates it by 3.2 kcal mol�1. Thus, the

use of both B3P86 and B3LYP functionals is recommended as

they yield HSNO r(S–N) and D0(S–N) values that bracket the

reference values.

Multireference character of HSNO

Fig. 2 clearly demonstrates the dramatic difference between

the CCSD and CCSD(T) description of the S–N bond in

HSNO. Coupled-cluster calculations that neglect triple (and

higher) excitations predict a significantly shorter but weaker

S–N bond. It is generally accepted that systems with high non-

dynamical electron correlation, for which the single-reference

approximation is no longer valid, are described much better

with CCSD(T) than with CCSD.28 Thus, the abrupt change in

the calculated properties of HSNO from the CCSD to the

CCSD(T) level, as well as the non-negligible effect of including

quadruple excitations into the coupled cluster expansion,

suggest that its wavefunction possesses multireference char-

acter. This was confirmed by examining the T1 and D1 coupled

cluster diagnostics,32,33 which are based on the analysis of

single amplitudes in the CCSD expansion. T1 (0.027) and D1

(0.076) calculated with CCSD/AVTZ for HSNO are above the

threshold values (T1 4 0.02 and D1 4 0.05) that render single-

reference-correlation treatments unreliable.32,33 In fact, the

coupled cluster diagnostics of HSNO are similar to those we

calculated with CCSD/AVTZ for ozone (T1 = 0.025 and D1

= 0.078), a molecule with notoriously strong multireference

character. Clearly, the electronic structure of HSNO can not

be adequately described by conventional single-reference

methods unless triple excitations (at the very least) are in-

cluded.

Following recognition of the multireference character of

the HSNO wavefunction, we questioned the quality of the

reference RHF wavefunction. Indeed, stability analysis52

revealed its RHF - UHF instability (the corresponding

stability eigenvalues calculated with the AVTZ basis set

being �0.022 and �0.013). Further optimization gave a

UHF solution with hS2i = 0.159 that is 0.6 kcal mol�1

lower in energy than the initial unstable RHF solution. How-

ever, the energy decrease and hS2i are too small to

assign genuine singlet biradical character to the HSNO elec-

tronic wavefunction. In comparison, the energy difference

between the RHF and UHF solutions for ozone, a molecule

with confirmed singlet biradical character, is 55.9 kcal mol�1,

hS2i is 0.941 for the UHF wavefunction, and the first stability

eigenvalue of the RHF wavefunction (�0.213, calculated

with the AVTZ basis set) is an order of magnitude larger than

that of HSNO. Nonetheless, the weak RHF - UHF

instability further supports the complex, multireference char-

acter of the HSNO wavefunction and casts additional doubt

on the reliability of single-reference-correlation calculations

such as MP2 and QCISD for RSNOs. We also note

that a similar multireference character was reported for

HONO, an analogue of HSNO where sulfur is substituted

by oxygen.53,54

The nature of the S–N bond in RSNOs, particularly its

bond order, is a subject of debate.1,6,19 Based on the high

interconversion barrier of B11 kcal mol�1 between cis- and

trans-RSNOs, Arulsamy et al.6 concluded that there is sig-

nificant electron delocalization in the SNO group, whereas

Bartberger et al.9 suggested that the S–N bond possesses

significant double-bond character. On the other hand, Baciu

and Gauld19 concluded, based on bond lengths, that the S–N

bond is an ‘‘elongated single bond’’ in RSNOs. We propose

that the hitherto unrecognized multireference character of the

HSNO wavefunction affects r(S–N) such that standard corre-

lations of bond order and bond length may not be applicable.

While a detailed investigation of the RSNO electronic

structure with multireference methods will be provided in a

future publication, we note that preliminary complete active

space self-consistent field25,55,56 (CASSCF) calculations of

HSNO with a (12,10) active space show a significant contribu-

tion of the excited s(S–N) - s*(S–N) configuration to the

HSNO CASSCF wavefunction. This may be a reflection of

some ionic (or biradical) character of the S–N bond, in

agreement with our recently proposed resonance description

of RSNOs.57

Finally, we note that in contrast to r(S–N), the energy

difference between trans-HSNO and cis-HSNO is insensitive

to the method or basis set used (Table 4). This suggests that

the conformation of RSNOs is determined by stereoelectronic

or similar effects that are not affected by dynamic or non-

dynamic electron correlation.

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Conclusions

In this work, we reported the first systematic coupled cluster

study of HSNO, the simplest RSNO, with particular emphasis

on the properties of the S–N bond. Accurate values obtained

with the CCSD(T) method extrapolated to the complete basis-

set limit (including corrections for quadruple excitations, core-

valence, relativistic effects and zero-point vibrational energy)

for the S–N bond length and the homolytic D0(S–N) of trans-

HSNO are 1.85 A and 29.2 kcal mol�1, respectively. If alkyl-

substituted RSNOs are more stable than HSNO,19 their

D0(S–N) estimated from kinetic data by Bartberger et al.

(28–31 kcal mol�1)16 should be more accurate than the calori-

metric results of Lu et al. (B25 kcal mol�1).17

The multireference character of the HSNO wavefunction,

which is mostly related to the complex nature of the S–N

bond, was revealed. Inconsistencies in the previously reported

computational results are attributed to variations in the degree

of electron correlation included in the calculations and to the

basis sets used. Single-reference post-Hartree–Fock methods

lacking triple excitations are not appropriate for RSNO

calculations. Further multireference ab initio calculations,

employing complete active space self-consistent field

(CASSCF) and multireference configuration interaction

(MRCI) methods, would further validate the high-level data

obtained in this work and shed more light on the multi-

reference nature of the SNO moiety and its possible connec-

tion to the recently proposed resonance description of RSNO

electronic structure.57 The physiological importance and unu-

sual electronic structure of RSNOs will undoubtedly drive

further theoretical analysis of these intriguing compounds.

Acknowledgements

This work was funded by grants from the Natural Sciences

and Engineering Research Council (NSERC) of Canada to

AME and GHP, and from the Canadian Institutes of Health

Research (CIHR) to AME. Calculations were performed in

the Centre for Research in Molecular Modeling, which was

established with the financial support of the Faculty of Arts

and Science, Concordia University, the Ministere de l’Educa-

tion du Quebec, and the Canada Foundation for Innovation

and using the resources of the Reseau quebecois de calcul de

haute performance (RQCHP). AME and GHP hold Concor-

dia University Research Chairs.

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