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AB initio calculations of 2H and 14N quadrupolar coupling constants in hydrogen bonded dimers
Volume 89. number 6
CHEMICAL PHYS!CS LETTERS
9 July 1982
AB INlTlO CALCULATIONS OF *H AND 14N QUADRUPOLAR COUPLING CONSTANTS IN HYDROGEN BONDED DIMERS Brian A. PETTITT
and Russell J. BOYD and Kenneth E. EDCECOMBE Dcparmerrr
of Cherrlisr~. Lhdl~omc Ch rrsrr~. Uahfex, Nova Scotw, Canada
B3H 4J3
Rccclved 3 May 1982
SCF MO CIICUIXIO~S at the 6.31G** level of approumauon are reporred for ‘H and “N eleclrx licld gradients III HCN-HF, and CH3CN.m.HF dlmers, wth emphasis on the configurational dependence oi these quantitxs in (HCN),. In compxaon wth available experimentalnuclcm qu3drupolar coupling conslants, the calcularcd values for rhe monomers and drmers ckhlbit an accuracy of = 105, which is comparable lo that of other spectroscopic parameters. The unphcauons of hydrogen bondmg for quadrupolar spin-htticc rehution T;Ltes are bnefly discussed. HCN--HCN.
I, Introduction The nuclear electric quadrupolar interaction, the coupling between the quadrupole moment of a nuclear charge drstributlon and the gradient of the electric field at the nucleus produced by the remainin g charges in the system, is the origin of important features in gas-phase microwave spectra, liquid- and solid-state
NMR, and solid-state NQR. Even for those nuclei (?H and 14N) for which reasonably accurate quadrupole moments are known, the role of this interaction in liquid-state NhlR IS often difficult to interpret; and it is especially complicated for ions in solution and hydrogen-bonded species, where translational-rotational motion induces fluctuations in the magrutude of electric field gradients [ 1,2]. The configurational dependence of electric field gracbents is a problem akin to that of potential energy surfaces, and is open to investigation by the same methods of electronic structure calculation [3]. This paper contains the results of an ab initio SCF MO study of ‘H and ‘“N quadrupolar interactions in HCN-*-HCN,HCN--0HF, CH$N---HF dimers, with emphasis on configurational dependency in HCN*--HCN.Of course, it is too
and
478
simplistic ta expect that bimolecular effects give a satisfactory description of condensed phases such as liquid HCN, but calculations on even small clusters at the level of approximation used here (631G**) were quite unfeasible. Direct comparison of some of these calculations with experimental data is. however, made possible by the recent development of gas-phase supersonic nozzle expansion techniques in rotational microwave spectroscopy [4].
2. Theory
The electric field gradient at a point in a charge distnbution, p, is a second-rank tensor (symmetric and traceless in a Cartesian representation) with spherical components
given by [S]
e&z = / dr C?,,(44
,-3 PM ,
(1)
evaluated in a coordinate system with arbitrary orientation and origin at the point being considered. C~,??z= (477/5)1’2Y,,m. where-2<:
02.75 0 1982 North-Holland
Volume 89. number 6
tron’s charge (in esu). The diagonal form of this tensor is determined by q,t1=
9 July 1981
CHEMICAL PHYSICS LET7IRS
,,& G&w2)61 -_
(2)
in terms of Wigner transformation functions [6] of the Euler angles, R, of a rotation from the ;tyes of q;,, to the principal axes of qm, which are conventionally defmed such that qi,- = Zqo is the largest cartesian component - in which case qZ I= 0 and qt2 = (l/2&)& - q),.) [S]. For a nucleus with quadru-
pole moment eQ, it is conventional to interpret experimental and theoretical data in terms of a quadrupolar couphnng constant, x = e2qq,,Q/lr,and an asymmetry
parameter, rl = Mxr - ~YYl/q~~. Two major difficultiesarisein the theoretical investigation of quadrupolar interactions: (i) quadrupole moments of satisfactory accuracy are known only for ‘H (Q = (2.860 f 0.015) X 10mZ7 cm2 [7]) and t4N (Q = (1.93 +_0.08) X 10mZ6 cm’ [S]); and (ii) substantial maccuracies are incurred unless very good representations of the charge density are used. In the molecular structure model, where nuclei are regarded as fLved in equilibrium positions, p(r)=e~‘Z,6(r-r,)-eP(r),
(3)
where Z, is the atomic number of nucleus 01at position r, with respect to the nucleus being considered (the prime excludes this nucleus from the sum) and P(r) is the electron density. In this work,P(r) is determinedat the 6-31G** levelof ab initio molecularorbitaltheory [9] using the program GAUSSIAN 76 [lo], and the electnc field gradtents were evaluated by appending to this program a version of the properties package of GAUSSLAN 79 [ 1 I] adapted to run on the CDC 170-720 computer at Dalhousie Umverslty.
been reported to be 194.4 kHz (2H1’CLJN gas, microwave [ 13]), 199 kHz (‘H”C’“N in liquid-crystal solvent, NAIR [14]), and 207 ktlz (zH”Ct5N gas, microwave [IS]). A comp&on wi& c&&cd v&es: ?76 kHz
(INDO[ 16]),248 kHz(doublezeta [ 17]), 243
kHz (STO-3G [IS]), 226 kHz(6-31G**, this work), and 213 kHz (near Hartree-Fock [19]); mdicatesa general improvement with the flexlbhty of the b3i.s set. Tius expected in
behaviour
is not observed
for IJN,
which case x = 4.39 h!Hz (6-3 1G**, this work),
5.45 MHz (near Hartree-Fock
[ 19]), and 4.70 MHz
(experimental [ 131);and it is as well to bear in mind the case of ‘H in HzO, for which increasing the size of
the SCF basis set improres agreement with erperiment but configuration interaction makes it worse [XI]. The calculated
dipole moment
is 3.23 D, compared
with the experimcntrtlvalueof 2.99 D [2 I]. 3.2. HF At r,(exp) = 0.9169 A [??I, the 6-3 lG** value of x(‘H) IS 383 kHz, which can be compared will1 rite experimental value of 354 kHz [23] and Snyder’s double-zeta value of 426 kHz [ 171. The calculated and experimental values of the dipole moment are 1.97 and 1.83 D [22], respectively. 3.3. CHjCN With the spectroscopic values [24] rS(C-H) = 1.1023 A,r,(C-C) = 1.4584A,r,(C=N) = 1.1571 A, and LHCC= 109.S”,the 6-3X** value of x(?H)wlls
determinedto be 187kHz(with T]= 0.056).The doublc.zeta and experimental values are 208 kHz [ 171 and 167 kHz [25], respecuvely. For “N, x = 3.96 hlHz (6-3 1G**) and 4.22 hlHz (exp. [26]), _~(calc) = 4.09 D and =(exp) = 3.91 D [77].
3.4. HChc--HCh’ 3. Results
Buxton et al. [28] have analysed microwave spectra of (HCN)z dimers on the basis of an assumedlinear
3.1. HCN
pairmg of rigid monomers interacting via a radial Lennard-Jones potenti, giving a dissociation energy De = 4.40 kcal mol-’ and an intermolecular stretchmg frc-
Calculations were made using the experimental equilibrium bond lengths r&!-H) = 1.0655A and
re(CW)= 1.1532A [12]. The valueof x(‘H) has
quencyi&= 119cm-‘. The intermolecularN+I distancewasdeterminedto be ro(N..*C)= 3.287 A, and 479
Volume 89, number 100 ---__
6
CHEMICAL
PHYSICS LETTERS
--____
___-. .-88 K
9 July
1982
futed at fe(calc.) = 3.37 A,because ~5 0.01 and deviation of the principal axis of the electric field gradient from the appropriate monomer axis is
~I_c.I. Lower part: The 6-31C** stabdxzation energy, AE= E(dimer) - ZE(monomcr), for linear HCN-.HCN dtmers vcrsur(N - C). The t&t 1-0 wbntional levels, derrrmmed by littmg IO 3 Morse potcntul, are also shown. Upper part ‘H and “‘N electric field gradlcnls (q12), cxpresscd a nt~os io rhe irer monomer values (98-_), versus r(NX). The loner pau
Bevan et al. [30] have reported a microwave determination of ro(N-a-F) = 2.76 A and Soper et al. [3 I] have measured x = 3.73 MHz (H-bonded 14N). Rigid monomers at this experimental distance are stabilued by 8.06kcal mol-[ and havep = 7.19 D in the 6_31G*’ scheme. The corresponding electric field gmdients give x = 186 kHz (methyl ‘H; q = O-063), 349 kHz (H-bonded 7H of HF), and 3.43 MHz (H-bonded 1%).
of lu~csrefers 10H-bondednuclei Jnd rhc upperpG 10tcrminal nuclei.
4. the two “N nuclei were observed to have x = 4.10 hlHz (H-bonded t3N) and 4.44 MHz (terminal 14N). Fig. 1 displays the intermolecular potentA calculated as a function of r(N*aC) in the 6-31G’* approximation, aswming rigd monomer geometries: and the ratios of the ‘H and t4N electric field gradients along the molecular axis to their calculated monomer va.lues. The potential minimum occurs at r,(N=C) = 3.37 A, at which x = 4.08 hlHz (H-bonded “N), 4.34 MHz (terminal I%), 213 kHz (H-bonded ‘l-l), and 225 kHz (terminal %I). This potential, for which De = 4.70 kcal mol-‘, is sufficiently well described by a Morse potentid in the neiabourhood of the minimum to determine ii, = 107 cm-‘. The calculated dipole moment is 7.23 D. Fig. 2 illustrates the behaviour of the interaction energy and the electric field gradients for non-linear dimer geometries with a linear N---H-C configuration 480
Discussion
It is generally agreed that the structure and stability of R-CN--.H-X dimers are well described by the SCF hl0 method if a large enough basis set is used such that representations
of the electron densities are rea-
sonably close to the Hartree-Fock limit; and that monomer bond lengths are only marginally altered by hydrogen bonding (see ref. [32] and references therein). With res ect to the available experimental data, the *H and P4N quadrupolar coupling constants calculated here in the 6-31G** scheme are accurate to within ~10% - comparable to the dissociation energies, stretching
frequencies,
and dipole moments.
Better
apparent accuracy for x(14N) of HCN-..HCN is simply fortuitous, because the dimer calculations cannot be more accurate than those for the monomer and the experimental data are not equilibrium values but configurational averages of the zero-point motion [28].
Volume
89, number 6
CHEtIICAL
PHYSICS LETTERS
9 July 1982
essential point can be most easdy seen by assuming rhat 17= 0, m wllic!~ case the quadrupolar relaxation rate is proportiona! to t!le Fourier transform of (q_-;(O)P?(O) q--(1) PI(~)), a correlation function for both the magnitude and direction of the approxl-
mate!! axial electric field gradient. P?(r) = 4 [3 X cos-D(f) - I], where O(r) is the angle from a spacefuted reference axis to t!le instantaneous a?cisof t!le electric field gradient; and t!le angular brackets denote a time-ensemble average over t!12 approprlirte fluctuations. A credible simplification of t!ris function must
cope not only wit!1 molecular rotation [34] but wit!1 the contigumtlonal dependznce of q- as welt.
Acknowledgement
BAP is grateful to Dr. W.E. Jones for hospittity SIIOWII at the
Fg. 2. Loacr pan; && (xc rg. 1) for non-lmcar (HCN)2 dlmers arih a linear N --H-C geometry fLyed at r(N.0.C) = 3.37 A versus@, the angle betuecn the monomer ales. Upper part: ‘H and lJN electric
field gradlrnts
versus 0. Lmcs Idcn-
Chemistry Department, DaUlousie University, where t!ti work was done: and to Rod Wasy!ishen and A!exander Keith for stunulating discussIons. T~JS world. was supported in part by a grant to tUB from Th2 Natura! Sciences and Engineering Research
Councd of Canada.
tified as in I$. 1. References
However,figs.1 and 2 suggestthat ground-statevibrationalaveragjng would change x(ca!c.) by only 1 or 2%. esperimenta! data indicate a decrease in the “N field gradients of 13% (H-bonded 14N) and 6% (terminal 14N) on dimerization of HCN, the calculations signi!?cant!y underestimate these changes at 7% and 1%. For CH$N-#*HF. the experimental dimer geometry was used in the calculation and the 13% Whereas
the
decrease in x(t4N) on dimerization agrees with the 12% decrease observed [31]. The configurational dependence ofq- (figs. 1 and 2) has interestmg implications for the interpretation of spin-lattice relaxation rates of ‘H and “N nuclei in HCN and, by inference, other molecules that form hydrogen bonds. For molecules in which electric Field gradients
are enhrely
of intrarnoleculz
origin, these
rates are proportional to a single-molecule reorientationa! correlation time 1331; but if molecular motion is in part related to transient intermolecular forces that modulate the electric field gradients, then the interpretation is considerably more complicated. The
[l] S. Engstrom and 8. JBnsson. MoL Phys. -13 (1981) 1235. [2! 9. HaUcand H. Wcnncrsrrom, J. Chem. Phys. 75 (1981) 1928. [3J R. hloccr~ .md hl. Zandomencghr, m: Advances III nuclcx qudrupolc
rcsoruncc, Vol. 2. cd. J.A.s. Smrrh
(Heydcn. London, 1975). [4] T.J. IMJcand W H. Flygarc. Rev. So.
Instr. 52 (1981)
33. [S!
RL. Cook and F.C. de LUCKI. Am. J. Ph)s. 39 (1971)
1333. !6] h1.E. Rose, Elcmcnury
theory of Jngubr momcnrum
(Whey, New York, 1957). [7! D.M. Brshop snd L.M. Cheung. Phys. Rev. A10 (1979) 381. [S! H. Wmrer md H.J. Andra. Phys. Rev. A21 (1980) 581. 191 PC H3nhxx1 and J.A. Poplc. Thcoret Chm. Acla 28 (1973) 213. [LO] J-S. Bmkley.
RA
Whrtchead,
PC
H.nhxm.
R Sccgcr
and J.A. Poplc, QCPE 11 (1978) 368. [ll]
P. htarsh and D.E. Whims,
QCPE BuUctm 1 (1981)
38.
[12] C. Wrnnewuscr, A.G. blakl and D.R. Johnson, I. Mol. Specuy. 39 (1971) 119. 1131 EC. de Lucia and W. Gordy, Phys. Rev. 187 (1969)
58.
481
folumc 89. number 6
CHEMICAL PHYSICS LEITERS
131 F.S. Millet and B.P. Dady, J. Chem. Phys. 56 (1972)
3249. 151 G. Ca~zoli, C.D. EsposUand P.G. Farcro, J. Chem. Phys. 83 (1980) 1756.
161hl. BJrfirld. H.P.W. Golthcb and DA!. DoddreU, J. Chcm. Phys. 69 (1978) 4504. 171 L.C. Snyder. J. Chcm. Phys. 68 (1978) 391. ,181 A. Johansjon. P. Rollman and S. Rothcnberg, Theoret. Chnn_ .%cta 26 (1971) 97. 191 C.T. O’Konskl and T.-K. Ha. J. Chcm. Phys. 49 (1968) 5354. 201 BJ. Rosenberg and L Sbav~rt, J. Chcm. Phys. 63 (1975) 2162. :?I] A&. h!&, J. Chcm. Phys. Ref. Da13 3 (1974) Xl. ,22] F.C. de Lucn, p. Helmmgcr and W. Gordy, Phys. Rev. A3 (1971) 1849. ,231 J.S. Muenter and W. Klcmprrer, J. Chem. Phyr 52 (1970) 6033. :24] CC. Costan. J. Chem. Phys. 19 (1958) 864. 1251 S.G. Kukohch, J. Chem. Phys. 58 (1973) 3155.
182
9 July 1981
[ 261 S-G. Kukohch. G. Lind, hl. Barfield. L.. Fxhl nnd J.L_ MxsbaBU, J. Am. Chem Sot 100 (1978) 7155. [27] .%P- SIeinernnd W. Cordy. J. MoL .$pecm_ 21 (1966) 291. [ZSJ L.W. Buxton, EJ. Campbell and W.H. Flygare, Chem. Phys. 56 (1981) 399. 1291 A.C. Legon, D.J. hldlen and S.C. Rogers, Proc. Roy. Sot. A370 (1980) 213. 1301 J.W. Bevon. AC. Lcgon, D J. Mlllcn and S.C. Rogers, Proc. Roy. Sot. A370 (1980) 239. [ 311 P.D. Soper, AC. Legon, W&i Read and W.H. Fly&arc, J. Phys. Chcm. 85 (1981) 3410. 1321 A. Hkhliffe, Advk Mdl. Relax. Inl. Processes 19 (19811 227. [33] k. Ab&m, The prmc~ples of nucbr magnetism (OKford Univ. Press, London, 1961). 1341 hl. Evas. C. Evans and R. Lhvics. III’ Advances III chemlcal physics, Vol. 44, cds. I. Prigogme and S.A. R~ca OKdry-Interscience. New York. 1980).
CHEMICAL PHYS!CS LETTERS
9 July 1982
AB INlTlO CALCULATIONS OF *H AND 14N QUADRUPOLAR COUPLING CONSTANTS IN HYDROGEN BONDED DIMERS Brian A. PETTITT
and Russell J. BOYD and Kenneth E. EDCECOMBE Dcparmerrr
of Cherrlisr~. Lhdl~omc Ch rrsrr~. Uahfex, Nova Scotw, Canada
B3H 4J3
Rccclved 3 May 1982
SCF MO CIICUIXIO~S at the 6.31G** level of approumauon are reporred for ‘H and “N eleclrx licld gradients III HCN-HF, and CH3CN.m.HF dlmers, wth emphasis on the configurational dependence oi these quantitxs in (HCN),. In compxaon wth available experimentalnuclcm qu3drupolar coupling conslants, the calcularcd values for rhe monomers and drmers ckhlbit an accuracy of = 105, which is comparable lo that of other spectroscopic parameters. The unphcauons of hydrogen bondmg for quadrupolar spin-htticc rehution T;Ltes are bnefly discussed. HCN--HCN.
I, Introduction The nuclear electric quadrupolar interaction, the coupling between the quadrupole moment of a nuclear charge drstributlon and the gradient of the electric field at the nucleus produced by the remainin g charges in the system, is the origin of important features in gas-phase microwave spectra, liquid- and solid-state
NMR, and solid-state NQR. Even for those nuclei (?H and 14N) for which reasonably accurate quadrupole moments are known, the role of this interaction in liquid-state NhlR IS often difficult to interpret; and it is especially complicated for ions in solution and hydrogen-bonded species, where translational-rotational motion induces fluctuations in the magrutude of electric field gradients [ 1,2]. The configurational dependence of electric field gracbents is a problem akin to that of potential energy surfaces, and is open to investigation by the same methods of electronic structure calculation [3]. This paper contains the results of an ab initio SCF MO study of ‘H and ‘“N quadrupolar interactions in HCN-*-HCN,HCN--0HF, CH$N---HF dimers, with emphasis on configurational dependency in HCN*--HCN.Of course, it is too
and
478
simplistic ta expect that bimolecular effects give a satisfactory description of condensed phases such as liquid HCN, but calculations on even small clusters at the level of approximation used here (631G**) were quite unfeasible. Direct comparison of some of these calculations with experimental data is. however, made possible by the recent development of gas-phase supersonic nozzle expansion techniques in rotational microwave spectroscopy [4].
2. Theory
The electric field gradient at a point in a charge distnbution, p, is a second-rank tensor (symmetric and traceless in a Cartesian representation) with spherical components
given by [S]
e&z = / dr C?,,(44
,-3 PM ,
(1)
evaluated in a coordinate system with arbitrary orientation and origin at the point being considered. C~,??z= (477/5)1’2Y,,m. where-2<:
02.75 0 1982 North-Holland
Volume 89. number 6
tron’s charge (in esu). The diagonal form of this tensor is determined by q,t1=
9 July 1981
CHEMICAL PHYSICS LET7IRS
,,& G&w2)61 -_
(2)
in terms of Wigner transformation functions [6] of the Euler angles, R, of a rotation from the ;tyes of q;,, to the principal axes of qm, which are conventionally defmed such that qi,- = Zqo is the largest cartesian component - in which case qZ I= 0 and qt2 = (l/2&)& - q),.) [S]. For a nucleus with quadru-
pole moment eQ, it is conventional to interpret experimental and theoretical data in terms of a quadrupolar couphnng constant, x = e2qq,,Q/lr,and an asymmetry
parameter, rl = Mxr - ~YYl/q~~. Two major difficultiesarisein the theoretical investigation of quadrupolar interactions: (i) quadrupole moments of satisfactory accuracy are known only for ‘H (Q = (2.860 f 0.015) X 10mZ7 cm2 [7]) and t4N (Q = (1.93 +_0.08) X 10mZ6 cm’ [S]); and (ii) substantial maccuracies are incurred unless very good representations of the charge density are used. In the molecular structure model, where nuclei are regarded as fLved in equilibrium positions, p(r)=e~‘Z,6(r-r,)-eP(r),
(3)
where Z, is the atomic number of nucleus 01at position r, with respect to the nucleus being considered (the prime excludes this nucleus from the sum) and P(r) is the electron density. In this work,P(r) is determinedat the 6-31G** levelof ab initio molecularorbitaltheory [9] using the program GAUSSIAN 76 [lo], and the electnc field gradtents were evaluated by appending to this program a version of the properties package of GAUSSLAN 79 [ 1 I] adapted to run on the CDC 170-720 computer at Dalhousie Umverslty.
been reported to be 194.4 kHz (2H1’CLJN gas, microwave [ 13]), 199 kHz (‘H”C’“N in liquid-crystal solvent, NAIR [14]), and 207 ktlz (zH”Ct5N gas, microwave [IS]). A comp&on wi& c&&cd v&es: ?76 kHz
(INDO[ 16]),248 kHz(doublezeta [ 17]), 243
kHz (STO-3G [IS]), 226 kHz(6-31G**, this work), and 213 kHz (near Hartree-Fock [19]); mdicatesa general improvement with the flexlbhty of the b3i.s set. Tius expected in
behaviour
is not observed
for IJN,
which case x = 4.39 h!Hz (6-3 1G**, this work),
5.45 MHz (near Hartree-Fock
[ 19]), and 4.70 MHz
(experimental [ 131);and it is as well to bear in mind the case of ‘H in HzO, for which increasing the size of
the SCF basis set improres agreement with erperiment but configuration interaction makes it worse [XI]. The calculated
dipole moment
is 3.23 D, compared
with the experimcntrtlvalueof 2.99 D [2 I]. 3.2. HF At r,(exp) = 0.9169 A [??I, the 6-3 lG** value of x(‘H) IS 383 kHz, which can be compared will1 rite experimental value of 354 kHz [23] and Snyder’s double-zeta value of 426 kHz [ 171. The calculated and experimental values of the dipole moment are 1.97 and 1.83 D [22], respectively. 3.3. CHjCN With the spectroscopic values [24] rS(C-H) = 1.1023 A,r,(C-C) = 1.4584A,r,(C=N) = 1.1571 A, and LHCC= 109.S”,the 6-3X** value of x(?H)wlls
determinedto be 187kHz(with T]= 0.056).The doublc.zeta and experimental values are 208 kHz [ 171 and 167 kHz [25], respecuvely. For “N, x = 3.96 hlHz (6-3 1G**) and 4.22 hlHz (exp. [26]), _~(calc) = 4.09 D and =(exp) = 3.91 D [77].
3.4. HChc--HCh’ 3. Results
Buxton et al. [28] have analysed microwave spectra of (HCN)z dimers on the basis of an assumedlinear
3.1. HCN
pairmg of rigid monomers interacting via a radial Lennard-Jones potenti, giving a dissociation energy De = 4.40 kcal mol-’ and an intermolecular stretchmg frc-
Calculations were made using the experimental equilibrium bond lengths r&!-H) = 1.0655A and
re(CW)= 1.1532A [12]. The valueof x(‘H) has
quencyi&= 119cm-‘. The intermolecularN+I distancewasdeterminedto be ro(N..*C)= 3.287 A, and 479
Volume 89, number 100 ---__
6
CHEMICAL
PHYSICS LETTERS
--____
___-. .-88 K
9 July
1982
futed at fe(calc.) = 3.37 A,because ~5 0.01 and deviation of the principal axis of the electric field gradient from the appropriate monomer axis is
~I_c.I. Lower part: The 6-31C** stabdxzation energy, AE= E(dimer) - ZE(monomcr), for linear HCN-.HCN dtmers vcrsur(N - C). The t&t 1-0 wbntional levels, derrrmmed by littmg IO 3 Morse potcntul, are also shown. Upper part ‘H and “‘N electric field gradlcnls (q12), cxpresscd a nt~os io rhe irer monomer values (98-_), versus r(NX). The loner pau
Bevan et al. [30] have reported a microwave determination of ro(N-a-F) = 2.76 A and Soper et al. [3 I] have measured x = 3.73 MHz (H-bonded 14N). Rigid monomers at this experimental distance are stabilued by 8.06kcal mol-[ and havep = 7.19 D in the 6_31G*’ scheme. The corresponding electric field gmdients give x = 186 kHz (methyl ‘H; q = O-063), 349 kHz (H-bonded 7H of HF), and 3.43 MHz (H-bonded 1%).
of lu~csrefers 10H-bondednuclei Jnd rhc upperpG 10tcrminal nuclei.
4. the two “N nuclei were observed to have x = 4.10 hlHz (H-bonded t3N) and 4.44 MHz (terminal 14N). Fig. 1 displays the intermolecular potentA calculated as a function of r(N*aC) in the 6-31G’* approximation, aswming rigd monomer geometries: and the ratios of the ‘H and t4N electric field gradients along the molecular axis to their calculated monomer va.lues. The potential minimum occurs at r,(N=C) = 3.37 A, at which x = 4.08 hlHz (H-bonded “N), 4.34 MHz (terminal I%), 213 kHz (H-bonded ‘l-l), and 225 kHz (terminal %I). This potential, for which De = 4.70 kcal mol-‘, is sufficiently well described by a Morse potentid in the neiabourhood of the minimum to determine ii, = 107 cm-‘. The calculated dipole moment is 7.23 D. Fig. 2 illustrates the behaviour of the interaction energy and the electric field gradients for non-linear dimer geometries with a linear N---H-C configuration 480
Discussion
It is generally agreed that the structure and stability of R-CN--.H-X dimers are well described by the SCF hl0 method if a large enough basis set is used such that representations
of the electron densities are rea-
sonably close to the Hartree-Fock limit; and that monomer bond lengths are only marginally altered by hydrogen bonding (see ref. [32] and references therein). With res ect to the available experimental data, the *H and P4N quadrupolar coupling constants calculated here in the 6-31G** scheme are accurate to within ~10% - comparable to the dissociation energies, stretching
frequencies,
and dipole moments.
Better
apparent accuracy for x(14N) of HCN-..HCN is simply fortuitous, because the dimer calculations cannot be more accurate than those for the monomer and the experimental data are not equilibrium values but configurational averages of the zero-point motion [28].
Volume
89, number 6
CHEtIICAL
PHYSICS LETTERS
9 July 1982
essential point can be most easdy seen by assuming rhat 17= 0, m wllic!~ case the quadrupolar relaxation rate is proportiona! to t!le Fourier transform of (q_-;(O)P?(O) q--(1) PI(~)), a correlation function for both the magnitude and direction of the approxl-
mate!! axial electric field gradient. P?(r) = 4 [3 X cos-D(f) - I], where O(r) is the angle from a spacefuted reference axis to t!le instantaneous a?cisof t!le electric field gradient; and t!le angular brackets denote a time-ensemble average over t!12 approprlirte fluctuations. A credible simplification of t!ris function must
cope not only wit!1 molecular rotation [34] but wit!1 the contigumtlonal dependznce of q- as welt.
Acknowledgement
BAP is grateful to Dr. W.E. Jones for hospittity SIIOWII at the
Fg. 2. Loacr pan; && (xc rg. 1) for non-lmcar (HCN)2 dlmers arih a linear N --H-C geometry fLyed at r(N.0.C) = 3.37 A versus@, the angle betuecn the monomer ales. Upper part: ‘H and lJN electric
field gradlrnts
versus 0. Lmcs Idcn-
Chemistry Department, DaUlousie University, where t!ti work was done: and to Rod Wasy!ishen and A!exander Keith for stunulating discussIons. T~JS world. was supported in part by a grant to tUB from Th2 Natura! Sciences and Engineering Research
Councd of Canada.
tified as in I$. 1. References
However,figs.1 and 2 suggestthat ground-statevibrationalaveragjng would change x(ca!c.) by only 1 or 2%. esperimenta! data indicate a decrease in the “N field gradients of 13% (H-bonded 14N) and 6% (terminal 14N) on dimerization of HCN, the calculations signi!?cant!y underestimate these changes at 7% and 1%. For CH$N-#*HF. the experimental dimer geometry was used in the calculation and the 13% Whereas
the
decrease in x(t4N) on dimerization agrees with the 12% decrease observed [31]. The configurational dependence ofq- (figs. 1 and 2) has interestmg implications for the interpretation of spin-lattice relaxation rates of ‘H and “N nuclei in HCN and, by inference, other molecules that form hydrogen bonds. For molecules in which electric Field gradients
are enhrely
of intrarnoleculz
origin, these
rates are proportional to a single-molecule reorientationa! correlation time 1331; but if molecular motion is in part related to transient intermolecular forces that modulate the electric field gradients, then the interpretation is considerably more complicated. The
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