- Email: [email protected]
An ab initio calculation of the frequencies and IR intensities of the stretching vibrations of HN2+
Volume
107. number
CHEMICAL
6
AN AB INITIO CALCULATION
PHYSICS
OF THE FREQUENCIES
OF THE STRETCHING VIBRATIONS
15 June
LETTERS
1984
AND IR INTENSITIES
OF HN;
Peter BOTSCHWINA Fachbereich Received
Chemie
20 March
der Unirersikft 1984;
in tiial
Kaisersbutern. form
13 April
D-6750
Kakerslautern.
West Germmy
1984
The dependence of the potential energy and electric dipole moment of Hflz on the stretching coordinates has been calto tie at 2254 cm-‘. culated from highly correlated CEPA wavefunctions. The origin of the “3 band of H t4N; is predicted H&t is The vI band of H14N; is very strong., with S = 2682 atm-’ cm-* at 298 K. while vg has only a very small intensity. predicted to be an excellent IR emitter.
The present work is aimed mainly at an accurate prediction of the position and strength of the v3 (NN stretch) band on the bads ofbigbly correlated ab initio calculations employing the coupled electronpair approximation (CEPA) of Meyer [23,23]. Attempts to observe the v3 band in the laboratory are presently being undertaken at Ottawa [24] _In addition, we provide information on transitions to higher excited stretching vibrational states and effects of isotopic substitution. In order to obtain an idea of the accuracy of the R-dependent (NN stretch) part of the potential, we also report the results of analogous calculations on the nitrogen molecule_
1. Introduction Protonated nitrogen, HNZ, is an ion of great importance for ion-molecule reactions, particularly those occurring in the chemistry of interstellar clouds (see, For example, ref. [ 1 I)_ Although it has been investigated in the millimeter and sub-millimeter region, both in interstellar clouds [2-4] and in the laboratory [S--9], and more recently also by velocitymodulated infrared laser spectroscopy in the 3.1 /.un region [IO], its spectroscopic characterisation is still rather incomplete. In particular, nothing is known from experiment about both the NN stretching (v3) and angle-bending (~2) vibrations. I-Il$ has been the subject of several ab initio calculations [l l-211, which demonstrated that this ion has the expected linear equilibrium structure and were of help in assigning the radio-astronomical spectrum [ 131. The most extensive ab initio investigation of I-@ and several of its isotopomers has been carried out by Hennig et al. [16], who fitted a complete quartic force field to the computed points and calculated spectroscopic constants by means of conventional second-order Rayleigh-Schrikiinger perturbation theory. Since the anharmonic parts of the potentials of these authors show large numerical errors, several of the derived spectroscopic constants, especially the anharmonicity constants Xii, have rather unrealistic values.
0 009-2614/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
2. Methods and results The present SCF.and CEPA calculations of the potential energy and electric dipole-moment surfaces (only the dependence on the two stretching coordinates is investigated) employ a basis set of Gaussian-type orbitals (GTOs) which is briefly described as N I Is, 7p, 2d in contraction [8,5,2], and H 6s, 3-p contracted to [4,2] _The exponents of the s and p functions are taken from Huzinaga [X] : d exponents for nitrogen are 1.5 and 0.5 and the exponents of the p functions centered at the hydrogen nucleus are chosen to be 1.2 and 03. The basis sets thus comprise 66 and 76 contracted GTOs For N7 9-V.
53.5
and HN;, respectively. In the CEPA calculations, only the 25 valence electron pairs constructed from canonical molecular orbitals are correlated, version 1 of CEPA [24] (“CEPA-1”) being used throughout. The equilrbrium bond length R, of N2 is calculated to be 1.06643 a (SCF) and 1.09725 A (CEPA-I), wrth corresponding total energies of -10898984 and -109.34569 hartree, respectively. Compared with experiment [26], the present CEPA-I cakulations thus underestimate R, by only 5 X 10m4 A. In the range -0.4
v, = 0.761009
M2
- 0.979862
- 0.479354
AR5 + 0.27 1790 AR6
- 0.130383
AR7 + 0.036686
where the coefficients
15 June 1984
CHEhfICAL PHYSICS LETTERS
Volume 107, number 6
iIR3 + 0.759925
AR4
ARa,
(1)
of the powers in AR
(=R - R,) are given in atomic units. This potential
yields a harmonic frequency w, for 14N3 of 2396.8 cm-l, which is larger than the experimental
value [26] by 38.2 cm-l. The quartic equilibrium centrifugal distortion constant 0; is calculated to be 5.57 X lOA cm-l, which is smaller than Bendtsen’s experimental value [26] by 3%. The sextic equilibrium centrifugal distortion constant i$, for which no experimental value is known to the author, is found to be 5.12 X lo-” cm-l. The calculated vibrational term energies G(v) are (in cm-l) G(0) = 1195.0 (1175.5), G(1) = 3564.1 (35052), G(2) = 5905.3 (5806.4), G(3) = 8218.7 (8079.2), G(4) = 10504.1 (103232)and G(5)= 12761.5(12538.5),whereexperimental values, calculated from Bendtsen’s spectroscopic constants [26], are given in parentheses. The CEPA-1 calculations thus overestimate the vibrational term energies systematically by 1.7-l .8%. Agreement with experiment is improved by about two orders of magnitude by scaling all coefficients in eq. (1) by a uniform factor of 0.96745 (because of the small error in the calculated R, we apply no geometry correction). The errors in the six lowest vibrational term energies now amount to 0.05% (for G(5)) or less. The harmonic frequency is 2357.5 (2358.6) and the Dj value is 5.76 X lOA (5.74 X lOA) (in cm-l , experimental values being
Table 1 Equilibrium geometries and total energies of HN; from ab initio czlxlations Authors
Method and basis
‘e
FR 1111 VPB [ 12)
SCF, 25 CGTOs SCF, 27 CGTOs CI, 27 CGTOs
SMT [ 131 LCHLP [ 141 HK [lS] HRD (161
ST [17] Hw I181 hPD [ 191
P [211 this work
a)Assumed. 536
(A)
(+109 hartree)
R, (A)
16
1.024 1.026 1.027
1.077 1.094 a) 1.094 a)
0.033 -0.0748 -0.2443
SCF, DZ SCF. STO-3G SCF, 44 CGTOs CI, 44 CGTOs
1.041 1.077 1.023 1.031
1.099 1.140 1.065 1.097
1.27389 -0.163339 -0.414325
SCF, 52 CGTOs CI SD, 52 CGTOs b,
1.0668
Cl SDQ. 52 CGTOs b,
1.0224 1.0320 1.0356
SCF. 4-31G SCF. 27 CGTOs SCF. 37 CGTOs CISD, 54 CGTOs Cl SDQ. 54 CGTOs Cl SD. 69 CGTOs SCF, 6-3lG* SCF, 76 CGTOs CEPA- 1.76 CGTOs
1.0946
-0.169159 -0.474533
1.1043
-0.503348
1.017 1.032 1.0275 1.0297 1.0292 1.0294
1.077 1.095 1.0753 1.0930 1.0948 1.0838
0.04974 -0.1412
1.0255 1.0226 1.0337
1.0708 1.0597 1.0927
-0.13193 -0.181952 -0.542176
b, In these calculations, the inner-shell electrons are correlated.
Volume 107, number 6 given in parentheses).
ugal distortion
contsant
CHEMICAL
The sextic equilibrium centrifis slightly changed to
PHYSICS LE-ITERS
15June 198-I
the polynomial
5.47X 10-l* cm-l. Since the electronic structure is usually only slightly changed upon protonation, we will apply the same correction factor to the R (NN stretch) potential of HNZ. ~Equilibrium geometries and total energies for HN; obtained from various ab initio calculations are given in table 1. Among them, the present calculations made use of the largest basis set and yielded the lowest total energy. The CEPA-1 equilibrium bond lengths (re = 1.0337 A and R, = 1.0927ii)are believed to be accurate to about 10s3 A. The equilibrium bond length of the nitrogen molecule is thus shortened by only 0.0047 A upon protonation, which is only about one fifth of the bond-length change calculated for protonation of isoelectronic carbon monoxide at the carbon site [27]. From microwave data, only a substitution structure could be calculated for protonated nitrogen [7] : rs = 1.0320( 1) A and R, = 1.0947(4) A. The differences with respect to the CEPA-1 equilibrium bond lengths of -0.0018 A (I-) and +0.0021 A (R)are very similar to the differences between the experimental substitution and equilibrium structure of HCN (-0.0023 A (r) and +0.0019 W CR) according to ref. [28]), a mol-
ecule which behaves spectroscopically rather similarly to HNZ. From the CEPA-1 equilibrium geometry, the equi!ibrium rotational constants B, of H13Nt and D14!$ are predicted to be 46844 and 38724 MHz. respectively. If one assumes the same error in R,(HNN+) asfor the nitrogen molecule (-0.0005) and leaves r-e at the calculated value, the Be values would have to be reduced by 36 MHz for Ht4Ns and 27 MHz for D14N;. From experiment, only B, values are known [7,8], which are 46587 MHz (H14N> and 38555 MHz (D14N3. The differences of 257 or 221 MHz and 169 or 142 MHz between calculated or estimated Be and experimental B. values of H14N: and D14cz compare reasonably wel! with the corresponding experimental values of 196 and 122 MHz for H’kr4N and D1*C14N [28]. The dependence of the potential energy on the stretching coordinates
Ar = r - re and AA = R - R,
has
been calculated for H!$ at 22 different nuclear configurations in the range -0.5 d Ar d 1.2 u. and -0.4 < AR < 0.4 ao. The calculated energy points
are we!! fitted (to better than 2 X low6 hartree) by
(2) Cubic and lugher potential coupling terms are neglected since their influence on the stretching vibrational states lying less than 10000 cm-* above the
vibrational ground state turned out to be very small (less than 0.1%) for comparable molecules like HCO+ [27] or HCN [29] _The po!Fomia! coefficients (“force constants”)tik)./R’ and frR calculated for protonated nitrogen are Listed in table 2 and are compared with the SCF, Cl SD and Cl SDQ values of Hennig et a!. [ 161. The quadratic terms obtained by CEPA-I and Cl SDQ are rather similar. The diagona! quadratic termsfrzZ) and &?) are also seen to agree we!! between the two SCF calculations, but the SCF value quoted for frR by Her-kg et a!. is too large by about a factor of two. The CEPA-1 diagonal cubic term flz) should have about the same error as for N2 (3%) and the error in d’) is probably even ;ma!!er. Wh!!e the diagonal cubic temrs agree within 7% be-
tween CEPA-1 and both Cl SD and CI SDQ of Hennig, Kraemer and Diercksen (HKD). the quartic term ti4) is overestimated by more than 30% by HKD. The present CEPA-I calculations yield a substantial decrease of 19% in #) with respect IO SCF, which is the usual situation when electron correlation lengthens a bond. The correlation effect on this force constant obtained by HKD is unphysically sma!! and even positive_ The numerical errors in the fits of H!W are even much mom pronounced for the anhamronic coupling temts which are not given in tab!e 2.
Stretching vibrational frequencies of several isotopomers of HN; !rave been calculated variationally by diagonalizing an approtimate vibrational Hamiltonian which neglects the anharmonic intrraction between stretching and bending motions, in a sufficiently large basis set of harmonic-osci!!ator product functions [29]. The results of these calculations are given in tabie 3. The CEPA-1 value for u~(H’~!Q of 3254.3 cm-’ is larger than the experi-
mental value [IO] by 20.3 cm-l or 0.6%. This error is very similar to those obtained from comparable 537
Volume
107, number
Table 2 Ab initio potential
CHEMlCAL
6
energy functions
PEF terms =)
(stretching
coordinates
only)
LETTERS
6.6741
2424.124
-0.233
frR
-0.208
Pr 4) 3)
-214.1 249.7
$rS) 4)
-1527 1269
6.761
6.332
6.170
31.816
25.863
23.712
-0.507
-0.284
-0.218
-49.79
-40.49
-37.41
-177.1 234.3
-216.5 332.6
-183.8 331.6
-172.8 331.4
1107
1116
1118
-1426 1029
-7924 9983
-6610 9335
-59582 39849
-57203 39849
;(B) r
214069
214069
where n denotes
the number of stretching
$;
CI SDQ
-40.21
-43.49
d3)
CI SD
SCF
6.1315
31.843
rk’)
1984
HKD [16] CEPA-I
A*)
ISJune
for HN;
This work SCF
5r6)
PHYSICS
)
a) ln aJ A-“, energy.
coordinates
involved
in the partial differential
quotient
of the potential
Table 3 Stretching
vibrational
and anharmonicity
SCF 3579.0 2642.8 26153 3440.0 5213.7 6015.2 6766.4
Wl
a3 y3
“1 b3 “I+“3 bl
7795.1 2~3
2vr + "3
4"s 3"l X11 x13 x33
8572.1
9290.7 10359.6 9993.4 -56.8 (-62.9) 40.1 (-30.4)
-8.5 (-8.4)
constants
(in cm-‘)
D’ON;
H14N;
Band
3v3 VI +
frequencies
for different
isotopomers
of protonated
nitrogen
a)
T14N;
H’SN14N+
H 14Nr4N+ b)
HISN;
CEPA-1
CEPA-1
CEPA-1
CEPA-1
16.6 29.1 27.6 16.5 55.0 41.0 34.7 82.0 65.3 55.5 108.8 55.2 -64.4 (-69.1) -22.3 (-18.3) -11.5 (-11.4)
2.2 38.8 37.5 2.6 74.4 38.3 6.5 110.6 73.5 39.9 146.0 12.2 -64.2 (-69.0) -23.6 (-19.5) -11.3 (-11.2)
18.5 69.0 66.1 18.7 131.3 80.2 40.3 195.5 140.9 96.0 258.7 66.0 -65.0 (-69.5) -20.8 (-17.2) -11.2 (-11.1)
CEPA-1
est.
CEPA-1
est.
3399.4 2326.5 2292.4 32543 4561.6 5521.3 6381.5 6807.2 7765.9 8616.5 9029.0 9029.0 43.6 (-68.5) -25.4 (-20.8) -11.6 (-11.6)
3396 2291 2254 3234 4485 5464 6338 6692 7672 8538 8874 9322 -65.0 (-69.0) -23.8 (-19.4) -11.8 (-11.6)
2734.9 2080.8 2035.5 2670.4 4048.7 4656.9 5303.3 6038.3 6620.1 7242.7 8003.0 7900.3 -18.8 (-20.7) 49.0 (-48.7) -11.2 (-10.1)
2714 2062 2022 2636 4022 4608 5232 6000 6559 7158 7955 7792 -19.4 (-21.7) 48.8
26 10.0 1811.2 1770.2 2564.0 3515.8 4300.8 5099.5 5236.0 6013.7 6803.1 6930.1 7606.2 -14.3 (-14.4) -33.4
(-47.8) -10.6 (-9.6)
(I;;;) (-11:7)
b)
a) The anharmonicity constants Xv have been obtained both from the variationally calculated vibrational frequencies via the formulas 2Xii c (2ui) - tii and Xv SJ (vi + vj) - vf - uj and by conventional 2nd order Raylei@r-S&rower perturbation theory, the latter values being given in parentheses. b, Frequency differenceswith respect to Hr4N; are quoted.
538
L’
CHEhiICAI..
Volume 107, number 6
c~culatia~~ for HCO+ [27] and HCNHi 1301. In order to further improve the ab initio v&es, two types of corrections are employed: first, the diagonal R-dependent part of the CEPA-1 potential is scaled by a factor of 096745, as was found to be appropriate for N,. Secondly, the stretch-bend (s-b) interaction is ~mp~cidy taken into account by adding the term A,_&+
u3) = ~&‘1
-f- 112) •t- X23(UJ
+ 112)
W
to the diagonal matrix elements (u,, u~IH,,,,ILQ, us>. The parameter XI2 of H14N3 is fitted to the experi-
mental vI1 resulting inX12 g-14.7 cm-l, and for X@1‘&$) the spectroscopic value for H12CX”N [I3f f is adopted _The ~rrespond~ng values for D14Ni are chosen to be -12.4 and +3.0 cmMi, estimated on the basis of spectroscopic data for D12C14N. From these cahzulations, the origin of the p3 band of Ht4N$ is estimated to be 22.54 cm-l, 76 cm-l lower than in the nitrogen molecule. This is qualitatively different from CO, where protonation increases the CO stretching frequency by 43 cm-” [2732]. The CO bond is, however, strengthened relatively more upon protonation than the NN bond (the diagonal quadratic force constant/J) is increased by 16% for carbon monoxide and by only 2% for the nitrogen rno~ec~e~ so that the decrease in the frequency due to kinematic coupling is overcompensated in HCO+. The stretching fundamentals of Dj4N$ are predicted to occur at 2636 and 2022 cm-l. The stretching vibrational frequencies predicted for H14N; and D14Nz are thus rather similar to those known for H12C14N and D1q14N, the largest difference being 157 cm-l. According to the ab initio calculations of HKD 1161, there is also no great difference in the bending vibrational frequencies. Calculated and estimated vibrational frequencies for transitions to higher excited stretching vibrational states and for other isotopomers of protonated nitrogen are also listed in table 3.
The quartic equilibrium centrifugal distortion constant Dj of H141$ is calculated to be 8397 kHz from the CEPA-I
potential
and 86.47 kHr from the
corrected potential. The co~espond~g
values for
D14N$ are 58.04 and 59.43 kHz, respectively. The experimental & -.alues ES] are larger by a few percent, whit”. is quite a common situation for linear molecules [ZP] . The sextic equilibrium centrifugal
PHYSICS
LETTERS
15June
1984
distortion constantsI$ of H’“N$ and Di3N$ are predicted to be (in mHz) 48 (50) and 31 f35), respe&vely, where the values in parentheses refer to the corrected CEPA-1 potential. Similar values hate been previously calculated for HgkfGN and D17C14N f29]. The dependence of the z-component of the electric dipole moment, which gives the only non-vanishing contribution to the dipole moment of linear molecules if one restricts oneself to the consideration of stretching vibrations, has been calculated by SCF. CEPA-I(W) and CEPA-I(ED), where the abbreviations EV and ED stand for expectation value and energy derivative, respectively. As usu& most credit should be given to ~EPA-~~~~~ (see, for esample, ref. 1331). The pointwise catculared dipole moments are well fitted by the expression
+
c,,bm,
(41
the polynomial coefficients being given in table 4. The equilibrium dipoie momenr pe of H14N$ is predicted to br: -3 374 D ~~EPA-~~~D~~, which should be accurate to about 0.02 D. The corre~~jon effect on pLeis calculated zo be very small, less than 15. Previous ab initio calculations [13,l5.lS.19]_ carried out at somewhat different geometries. yieided similar dipole momenrs ranging from -32 to -3.5 D. in contrast to isoelectronic HCO+ 1271, where SCF yields a poor description of the variation of the dipole moment with the stretching coordinate JU?, SCF overestimates the first derivative C$’ z (&K/M), of H1”Nz by oniy 22%. From the analytical dipole-moment functions of tabfe 4 and the ~ha~o~c ~br~rjon~ 3v~~~~u~cFjo~~ calculated from the corrected CEPA-1 porential under inclusion of stretch-bend interaction, integrared molar IR intensities of absorption have been ca.lcuhted for transitions from the vibrational ground state to excited stretching vibrational states. The results for H14Ni and DllNi are given in table 5. A large value of 20257 cmz m~&-l, corresponding to a band strength of 2682 atm-l cm-2 at 298 K, is predicted for H14N$. Similar to H1’G14N (see ref. [33] and references therein), the intensity of the ~3 vibration 539
Table 4 Electric dipolemoment EDMF term
St, & 43) (94)
?t) 1 > 1c 4, GR
ISJune 1984
CHEMICAL PHYSiCS LETTERS
Votume 107, number 6
functions of Hr4Nt a)
SCF
CEPA-I(EV)
CEPA-I(ED)
-1.32179 -0.84755 -0.22356 -0.00779 0.01578 0.38476 0.12781 -0.13959 0.01025 -0.148
-J.35757 -0.75557 -0.15100 0.02050 0.00158 0.22556 0.00140 -0.108t7 0.06124 -0.040
-1.32744 -0.76448 -0.15378 0.02041 -0.00249 0.31466 0.07973 -0.14337 -0.01539 -0.068
The matrix elements L13 and L3, (the L matrix connects the internal coordinates with the normal coordinates) are of equal sign, but ($.@W), and (+&V2)e are of opposite sign and both terms cancel each other largely in the case of HX4N$. The situation is much more favorable for D14@2, where the first term in eq. (5) dominates over the second, y3 of D14N$ thus getting most of its intensity of 3363 cm2 mol-1 from the r-dependent
part of the dipole moment
function. The “double ha~oni~ appro~mation” works weil for the intensities of the v1 bands, but, expressed as a percentage, is rather poor for the ua bands. Due to large transition dipole moments and rather high vibrational frequencies, H14N$ is an excellent IR emitter. The Einstein coefficients of spont~eous emission for Au1 = u; - u;’ = 1 transitions are (in s-l) 857,1592 and 2213 for u;‘= 0.1 and 2. Spectroscopic properties of highly excited stretching vibrational states extending close to the dissociation limit of the NH bond will be dealt with in a forthcoming publication_ Using CEPA-I , the equilibrium proton affiity of N,, denoted by PA,, is calculated to be 5 15 9 kl molW1. The zero-point vibrational energy of H14e2 is found to be 42.: kJ mol-I by adding a contribu-
ai The EDhiFs are expanded around the CEPA-1 equiliirium geometry (see table If and refer to the center of mttss of the molecule. EDMF terms are given in atomic units. The EDMF of Dt4N; is obtained by adding the fotlowving contributions to the values for H14Nl: &I, = 0.0966 I, AC;‘) = 0.03236 and a$) = 0.01618. of Hl4@ is very low. which will render the experimental observation of this band difficult. The low intensity may be easily explained within the familiar
“double harmonic approximation”, where the derivative of the dipole moment with respect to normal coordinate Q3 is given by
Table 5 Integrated mohu IR intensities of absorption ‘in cm2 mof-r) for transitions from the vibrational ground state to the ten lowest stretching vibrational states of H14Nz and D*“N: a) Band
wr(DH) w(DH) “3
y1 L3 w*y3
2vt 3v3
u1 + 25 &+v3
4v3 3u1
Ht4N$
D14Nf
SCF
CEPA-l(EVj
CEPA-RED)
SCF
CEPA-1fEVf
CEPA-RED)
23859 33.6
18215 187
19201 57.4
13645 3177
9482 3138
10671 2721
122 25637 5.1
323
142
4038
3796
3363
19171
20257
13iO8
9349
10582
48.2 87.5 I-of-2) 1.1(-l) &-5, 1.4
3.0
58.5 84.5 l-7(-2)
3.1
55.7 91.2 7-q-3)
13.9
17-2
17.4
66.6 3.6 2.3( -1)
635 1.9 2.9(-1)
66.4 3.1 3.1(-l)
2.4(-l)
1.9(-I)
6.9(-l!
7.5(-l)
7.5(--1)
1.3 2.q-61 1.3
1.3 6 .O(-5) 1.S
2.2(-1) 7.1(-3) 4.2( -2)
1-U-l) 7.9(-3) 3.4(-2)
1.9(--l) 8.0(-3) 3.3(-2)
a) Vibrational wavefunctions obtained from the corrected CEPA-1 potentia.l and inclusion of stretch-bend interaction are empfoyed. The abbreviation ‘DH” stands for “double-h~o~c approximation”.
540
Volume 107, number 6
CHEMKAL
tion of 8.6 w mol- J. for the bending vibrations, as
estimated on the basis of the ab initio calculations of HKD [16], to the present co~t~butjo~ of 33.5 kJ moi-’ from the stret~~g vibrations. %he previous SCF value of Del Bene et al. f2Oj, cahzufated within the harmonic appro~mat~on, is larger by 1355, which is quite a typical error for such calculations. With the zero-point energy of 14.3 kJ mol-’ for t4Nz1 we arrive at a calculated proton affinity at zero temperature of PA, = 488.1 k3 mol- t . The corresponding value of Del Bene et al. fZOj, obtained by 4rh order M#ler-Plesset ~rturba~~on theory and the zeropoint vibrational contribution from SCF, is 492.9 kf molwi. At T = 298 K, we cafculate a proton affinity of 491.3 kJ mol -1, which is in excellent agreement with the experimental value of 49 1.2 + 2.9 kJ moY1 r341.
Thanks are due to Professor Reins&r and Dr. Werner
for the use
of their
SCEP programme.
Support of this work by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 9 I is gratefully acknowledged _
RJ. SaykalJy attd R.C. Woods, Arm. Rev. Phys. Chem. 32 f19811403. B.E. Turner, Astrophys. 3.193 (19741 L83. P. Thaddeus and B.E. Turner, Astrophys. Y. 201119351 L2S. LE. Snyder, J.M. HolJk+, D. BUN and W.D. Watsan, Astrophys. J. 218 (1977) L61. RJ. Sayka.By,TSt. Di..on, T.G. Anderson, P.G. Stanto and R.C. Woods,As~ophys. 5.205 (1976) L101. T.G. Anderson,T.A. Di..on, N.D. PiJtch. R.J. SaykaUy, PG. Szanto and RX. Woods, Astrophyn 3.216 (1977) L85. P.G. Sz~ro,T.G.And~Kon, R.J. Sa~k~i~, N.D. PiJteh, TsZ. Dixon and R.C. Woods, J. Chem. pnys. 7.5 (1981) 4261.
PHYSICS LETTERS
15 June 1984
]8] K.V.L.N. Sastry, P. Hemringer, E. Herbsr and F.C. De Lucia, &hem. Phys. Letters 84 (1981) 286. ]9] F.C. van den Heuvel and A. Dymnnus, Chem. Phys. Letters 92 (1982) 219. ] IQ] CS. Gudeman, MM, Begemann, J_ Pfaff and Rf. SaykaLly. J. Chem. Phys. 78 (1983) 5837. ]I 1 ] C. Forsin and B. Roos. Chem. Phys. Letters 6 (1970) 126. I121 FL Vasudevan, G.D. Peyerimhoff and R J. Buenker, Chem. Phys. S (9171) 149_ { 131 S. Green, J.A. ~lontsorne~ and P. Thaddeus. Astro” phys. J. I93 t 1974) L89. f 141 \%‘.A. Lathan, LA. Cur&s. W.J. Hebre, J.3. Lisk and J.A. Pople, Pro& Phys. Org, Chem. I I ( 1973) 17.5. [ 151 I.H. HiBier and J. Rendrick, J. Chem. Sot. Chem. Commun. { 1975) 526. [ 161 P. Hem@. W.P. Kraemer and G-HI. Diercksen, IfPI/ PAE Astro report No. 135, ~¶as-Plonk-~nst~tut fur PhysL und Astrophysik, Munich (1977). 1171 N.L. Summers and J. Tyrrelf, 1. Am. Chem. Sot. 99 fl97-t) 336~;Tbeoret.Cb~. Acta 47 (f978) 22.J. ] 181 N-N. Waese and R.C. tvoods, Chem. Phys. Letters 61 f 197% 396. ] i91 J.A. Xton%omeryand C.E. Dykstra, 1. Chem. Phys. 71 (1979) 1380. ]30f J.E. Del Bene, J.J. Frisch. Ii. Raghavarhari and JA. Pople, J. Phys. Chem. 56 (1982) 1529. [II ] J_A. Fopfe, in: ifohcufar ions. geomrtric and elzcuonic structures, eds. J. Berkowitz and K-0. Groenevefd (Plenum Press, New Yorl;, 1983). [22] W. Meyer, J. Chem. Phys. 58 (1973) 1017. ]23] W. Xeyer, J. Chem. Phys. 64 (1976) 2901. (241 A.R.W. McKeBar. private commu~cation. ]25] S. Huzinaga. Approximate Atomic Functions it, Technical Report, Division ofTheoretical Chemistry, The University of Alberta (197f); J. Chem. Phys. 42 (1965) 1293. [26] 3. Bendtsen, J. Ramsn Specuy. 2 (1973) 133. [27] P. Bouchwina, Chem. Phys., to be published. ]28] G.~~‘~e~,~r, A.G. flakiand DR. Johnson,J. Mol. spew-y. 39 (1971) 149_ 1291 P. Botschwina. Chem. Phys. 6X f1983) -tl; unpublished work: [30) P. Botschwina, to be published. ]3 I ] J. Bmdrsen and H.G_M. Edwards, J. Raman Spz~r~. 2 (1974) 407. f32f SC. Foster, A.R.W. McReBar and T.J. Sears, J. Chem. Phys,. submitted for pubBcation. (33 f P. 3otschwina, Chem. Phys. 81 (1983) 73. f34J DX. Bobme. G.f. Mackay and H.I. S&J%. J. Chem. Phys. 73 { 1980) 4976.
541
107. number
CHEMICAL
6
AN AB INITIO CALCULATION
PHYSICS
OF THE FREQUENCIES
OF THE STRETCHING VIBRATIONS
15 June
LETTERS
1984
AND IR INTENSITIES
OF HN;
Peter BOTSCHWINA Fachbereich Received
Chemie
20 March
der Unirersikft 1984;
in tiial
Kaisersbutern. form
13 April
D-6750
Kakerslautern.
West Germmy
1984
The dependence of the potential energy and electric dipole moment of Hflz on the stretching coordinates has been calto tie at 2254 cm-‘. culated from highly correlated CEPA wavefunctions. The origin of the “3 band of H t4N; is predicted H&t is The vI band of H14N; is very strong., with S = 2682 atm-’ cm-* at 298 K. while vg has only a very small intensity. predicted to be an excellent IR emitter.
The present work is aimed mainly at an accurate prediction of the position and strength of the v3 (NN stretch) band on the bads ofbigbly correlated ab initio calculations employing the coupled electronpair approximation (CEPA) of Meyer [23,23]. Attempts to observe the v3 band in the laboratory are presently being undertaken at Ottawa [24] _In addition, we provide information on transitions to higher excited stretching vibrational states and effects of isotopic substitution. In order to obtain an idea of the accuracy of the R-dependent (NN stretch) part of the potential, we also report the results of analogous calculations on the nitrogen molecule_
1. Introduction Protonated nitrogen, HNZ, is an ion of great importance for ion-molecule reactions, particularly those occurring in the chemistry of interstellar clouds (see, For example, ref. [ 1 I)_ Although it has been investigated in the millimeter and sub-millimeter region, both in interstellar clouds [2-4] and in the laboratory [S--9], and more recently also by velocitymodulated infrared laser spectroscopy in the 3.1 /.un region [IO], its spectroscopic characterisation is still rather incomplete. In particular, nothing is known from experiment about both the NN stretching (v3) and angle-bending (~2) vibrations. I-Il$ has been the subject of several ab initio calculations [l l-211, which demonstrated that this ion has the expected linear equilibrium structure and were of help in assigning the radio-astronomical spectrum [ 131. The most extensive ab initio investigation of I-@ and several of its isotopomers has been carried out by Hennig et al. [16], who fitted a complete quartic force field to the computed points and calculated spectroscopic constants by means of conventional second-order Rayleigh-Schrikiinger perturbation theory. Since the anharmonic parts of the potentials of these authors show large numerical errors, several of the derived spectroscopic constants, especially the anharmonicity constants Xii, have rather unrealistic values.
0 009-2614/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
2. Methods and results The present SCF.and CEPA calculations of the potential energy and electric dipole-moment surfaces (only the dependence on the two stretching coordinates is investigated) employ a basis set of Gaussian-type orbitals (GTOs) which is briefly described as N I Is, 7p, 2d in contraction [8,5,2], and H 6s, 3-p contracted to [4,2] _The exponents of the s and p functions are taken from Huzinaga [X] : d exponents for nitrogen are 1.5 and 0.5 and the exponents of the p functions centered at the hydrogen nucleus are chosen to be 1.2 and 03. The basis sets thus comprise 66 and 76 contracted GTOs For N7 9-V.
53.5
and HN;, respectively. In the CEPA calculations, only the 25 valence electron pairs constructed from canonical molecular orbitals are correlated, version 1 of CEPA [24] (“CEPA-1”) being used throughout. The equilrbrium bond length R, of N2 is calculated to be 1.06643 a (SCF) and 1.09725 A (CEPA-I), wrth corresponding total energies of -10898984 and -109.34569 hartree, respectively. Compared with experiment [26], the present CEPA-I cakulations thus underestimate R, by only 5 X 10m4 A. In the range -0.4
v, = 0.761009
M2
- 0.979862
- 0.479354
AR5 + 0.27 1790 AR6
- 0.130383
AR7 + 0.036686
where the coefficients
15 June 1984
CHEhfICAL PHYSICS LETTERS
Volume 107, number 6
iIR3 + 0.759925
AR4
ARa,
(1)
of the powers in AR
(=R - R,) are given in atomic units. This potential
yields a harmonic frequency w, for 14N3 of 2396.8 cm-l, which is larger than the experimental
value [26] by 38.2 cm-l. The quartic equilibrium centrifugal distortion constant 0; is calculated to be 5.57 X lOA cm-l, which is smaller than Bendtsen’s experimental value [26] by 3%. The sextic equilibrium centrifugal distortion constant i$, for which no experimental value is known to the author, is found to be 5.12 X lo-” cm-l. The calculated vibrational term energies G(v) are (in cm-l) G(0) = 1195.0 (1175.5), G(1) = 3564.1 (35052), G(2) = 5905.3 (5806.4), G(3) = 8218.7 (8079.2), G(4) = 10504.1 (103232)and G(5)= 12761.5(12538.5),whereexperimental values, calculated from Bendtsen’s spectroscopic constants [26], are given in parentheses. The CEPA-1 calculations thus overestimate the vibrational term energies systematically by 1.7-l .8%. Agreement with experiment is improved by about two orders of magnitude by scaling all coefficients in eq. (1) by a uniform factor of 0.96745 (because of the small error in the calculated R, we apply no geometry correction). The errors in the six lowest vibrational term energies now amount to 0.05% (for G(5)) or less. The harmonic frequency is 2357.5 (2358.6) and the Dj value is 5.76 X lOA (5.74 X lOA) (in cm-l , experimental values being
Table 1 Equilibrium geometries and total energies of HN; from ab initio czlxlations Authors
Method and basis
‘e
FR 1111 VPB [ 12)
SCF, 25 CGTOs SCF, 27 CGTOs CI, 27 CGTOs
SMT [ 131 LCHLP [ 141 HK [lS] HRD (161
ST [17] Hw I181 hPD [ 191
P [211 this work
a)Assumed. 536
(A)
(+109 hartree)
R, (A)
16
1.024 1.026 1.027
1.077 1.094 a) 1.094 a)
0.033 -0.0748 -0.2443
SCF, DZ SCF. STO-3G SCF, 44 CGTOs CI, 44 CGTOs
1.041 1.077 1.023 1.031
1.099 1.140 1.065 1.097
1.27389 -0.163339 -0.414325
SCF, 52 CGTOs CI SD, 52 CGTOs b,
1.0668
Cl SDQ. 52 CGTOs b,
1.0224 1.0320 1.0356
SCF. 4-31G SCF. 27 CGTOs SCF. 37 CGTOs CISD, 54 CGTOs Cl SDQ. 54 CGTOs Cl SD. 69 CGTOs SCF, 6-3lG* SCF, 76 CGTOs CEPA- 1.76 CGTOs
1.0946
-0.169159 -0.474533
1.1043
-0.503348
1.017 1.032 1.0275 1.0297 1.0292 1.0294
1.077 1.095 1.0753 1.0930 1.0948 1.0838
0.04974 -0.1412
1.0255 1.0226 1.0337
1.0708 1.0597 1.0927
-0.13193 -0.181952 -0.542176
b, In these calculations, the inner-shell electrons are correlated.
Volume 107, number 6 given in parentheses).
ugal distortion
contsant
CHEMICAL
The sextic equilibrium centrifis slightly changed to
PHYSICS LE-ITERS
15June 198-I
the polynomial
5.47X 10-l* cm-l. Since the electronic structure is usually only slightly changed upon protonation, we will apply the same correction factor to the R (NN stretch) potential of HNZ. ~Equilibrium geometries and total energies for HN; obtained from various ab initio calculations are given in table 1. Among them, the present calculations made use of the largest basis set and yielded the lowest total energy. The CEPA-1 equilibrium bond lengths (re = 1.0337 A and R, = 1.0927ii)are believed to be accurate to about 10s3 A. The equilibrium bond length of the nitrogen molecule is thus shortened by only 0.0047 A upon protonation, which is only about one fifth of the bond-length change calculated for protonation of isoelectronic carbon monoxide at the carbon site [27]. From microwave data, only a substitution structure could be calculated for protonated nitrogen [7] : rs = 1.0320( 1) A and R, = 1.0947(4) A. The differences with respect to the CEPA-1 equilibrium bond lengths of -0.0018 A (I-) and +0.0021 A (R)are very similar to the differences between the experimental substitution and equilibrium structure of HCN (-0.0023 A (r) and +0.0019 W CR) according to ref. [28]), a mol-
ecule which behaves spectroscopically rather similarly to HNZ. From the CEPA-1 equilibrium geometry, the equi!ibrium rotational constants B, of H13Nt and D14!$ are predicted to be 46844 and 38724 MHz. respectively. If one assumes the same error in R,(HNN+) asfor the nitrogen molecule (-0.0005) and leaves r-e at the calculated value, the Be values would have to be reduced by 36 MHz for Ht4Ns and 27 MHz for D14N;. From experiment, only B, values are known [7,8], which are 46587 MHz (H14N> and 38555 MHz (D14N3. The differences of 257 or 221 MHz and 169 or 142 MHz between calculated or estimated Be and experimental B. values of H14N: and D14cz compare reasonably wel! with the corresponding experimental values of 196 and 122 MHz for H’kr4N and D1*C14N [28]. The dependence of the potential energy on the stretching coordinates
Ar = r - re and AA = R - R,
has
been calculated for H!$ at 22 different nuclear configurations in the range -0.5 d Ar d 1.2 u. and -0.4 < AR < 0.4 ao. The calculated energy points
are we!! fitted (to better than 2 X low6 hartree) by
(2) Cubic and lugher potential coupling terms are neglected since their influence on the stretching vibrational states lying less than 10000 cm-* above the
vibrational ground state turned out to be very small (less than 0.1%) for comparable molecules like HCO+ [27] or HCN [29] _The po!Fomia! coefficients (“force constants”)tik)./R’ and frR calculated for protonated nitrogen are Listed in table 2 and are compared with the SCF, Cl SD and Cl SDQ values of Hennig et a!. [ 161. The quadratic terms obtained by CEPA-I and Cl SDQ are rather similar. The diagona! quadratic termsfrzZ) and &?) are also seen to agree we!! between the two SCF calculations, but the SCF value quoted for frR by Her-kg et a!. is too large by about a factor of two. The CEPA-1 diagonal cubic term flz) should have about the same error as for N2 (3%) and the error in d’) is probably even ;ma!!er. Wh!!e the diagonal cubic temrs agree within 7% be-
tween CEPA-1 and both Cl SD and CI SDQ of Hennig, Kraemer and Diercksen (HKD). the quartic term ti4) is overestimated by more than 30% by HKD. The present CEPA-I calculations yield a substantial decrease of 19% in #) with respect IO SCF, which is the usual situation when electron correlation lengthens a bond. The correlation effect on this force constant obtained by HKD is unphysically sma!! and even positive_ The numerical errors in the fits of H!W are even much mom pronounced for the anhamronic coupling temts which are not given in tab!e 2.
Stretching vibrational frequencies of several isotopomers of HN; !rave been calculated variationally by diagonalizing an approtimate vibrational Hamiltonian which neglects the anharmonic intrraction between stretching and bending motions, in a sufficiently large basis set of harmonic-osci!!ator product functions [29]. The results of these calculations are given in tabie 3. The CEPA-1 value for u~(H’~!Q of 3254.3 cm-’ is larger than the experi-
mental value [IO] by 20.3 cm-l or 0.6%. This error is very similar to those obtained from comparable 537
Volume
107, number
Table 2 Ab initio potential
CHEMlCAL
6
energy functions
PEF terms =)
(stretching
coordinates
only)
LETTERS
6.6741
2424.124
-0.233
frR
-0.208
Pr 4) 3)
-214.1 249.7
$rS) 4)
-1527 1269
6.761
6.332
6.170
31.816
25.863
23.712
-0.507
-0.284
-0.218
-49.79
-40.49
-37.41
-177.1 234.3
-216.5 332.6
-183.8 331.6
-172.8 331.4
1107
1116
1118
-1426 1029
-7924 9983
-6610 9335
-59582 39849
-57203 39849
;(B) r
214069
214069
where n denotes
the number of stretching
$;
CI SDQ
-40.21
-43.49
d3)
CI SD
SCF
6.1315
31.843
rk’)
1984
HKD [16] CEPA-I
A*)
ISJune
for HN;
This work SCF
5r6)
PHYSICS
)
a) ln aJ A-“, energy.
coordinates
involved
in the partial differential
quotient
of the potential
Table 3 Stretching
vibrational
and anharmonicity
SCF 3579.0 2642.8 26153 3440.0 5213.7 6015.2 6766.4
Wl
a3 y3
“1 b3 “I+“3 bl
7795.1 2~3
2vr + "3
4"s 3"l X11 x13 x33
8572.1
9290.7 10359.6 9993.4 -56.8 (-62.9) 40.1 (-30.4)
-8.5 (-8.4)
constants
(in cm-‘)
D’ON;
H14N;
Band
3v3 VI +
frequencies
for different
isotopomers
of protonated
nitrogen
a)
T14N;
H’SN14N+
H 14Nr4N+ b)
HISN;
CEPA-1
CEPA-1
CEPA-1
CEPA-1
16.6 29.1 27.6 16.5 55.0 41.0 34.7 82.0 65.3 55.5 108.8 55.2 -64.4 (-69.1) -22.3 (-18.3) -11.5 (-11.4)
2.2 38.8 37.5 2.6 74.4 38.3 6.5 110.6 73.5 39.9 146.0 12.2 -64.2 (-69.0) -23.6 (-19.5) -11.3 (-11.2)
18.5 69.0 66.1 18.7 131.3 80.2 40.3 195.5 140.9 96.0 258.7 66.0 -65.0 (-69.5) -20.8 (-17.2) -11.2 (-11.1)
CEPA-1
est.
CEPA-1
est.
3399.4 2326.5 2292.4 32543 4561.6 5521.3 6381.5 6807.2 7765.9 8616.5 9029.0 9029.0 43.6 (-68.5) -25.4 (-20.8) -11.6 (-11.6)
3396 2291 2254 3234 4485 5464 6338 6692 7672 8538 8874 9322 -65.0 (-69.0) -23.8 (-19.4) -11.8 (-11.6)
2734.9 2080.8 2035.5 2670.4 4048.7 4656.9 5303.3 6038.3 6620.1 7242.7 8003.0 7900.3 -18.8 (-20.7) 49.0 (-48.7) -11.2 (-10.1)
2714 2062 2022 2636 4022 4608 5232 6000 6559 7158 7955 7792 -19.4 (-21.7) 48.8
26 10.0 1811.2 1770.2 2564.0 3515.8 4300.8 5099.5 5236.0 6013.7 6803.1 6930.1 7606.2 -14.3 (-14.4) -33.4
(-47.8) -10.6 (-9.6)
(I;;;) (-11:7)
b)
a) The anharmonicity constants Xv have been obtained both from the variationally calculated vibrational frequencies via the formulas 2Xii c (2ui) - tii and Xv SJ (vi + vj) - vf - uj and by conventional 2nd order Raylei@r-S&rower perturbation theory, the latter values being given in parentheses. b, Frequency differenceswith respect to Hr4N; are quoted.
538
L’
CHEhiICAI..
Volume 107, number 6
c~culatia~~ for HCO+ [27] and HCNHi 1301. In order to further improve the ab initio v&es, two types of corrections are employed: first, the diagonal R-dependent part of the CEPA-1 potential is scaled by a factor of 096745, as was found to be appropriate for N,. Secondly, the stretch-bend (s-b) interaction is ~mp~cidy taken into account by adding the term A,_&+
u3) = ~&‘1
-f- 112) •t- X23(UJ
+ 112)
W
to the diagonal matrix elements (u,, u~IH,,,,ILQ, us>. The parameter XI2 of H14N3 is fitted to the experi-
mental vI1 resulting inX12 g-14.7 cm-l, and for X@1‘&$) the spectroscopic value for H12CX”N [I3f f is adopted _The ~rrespond~ng values for D14Ni are chosen to be -12.4 and +3.0 cmMi, estimated on the basis of spectroscopic data for D12C14N. From these cahzulations, the origin of the p3 band of Ht4N$ is estimated to be 22.54 cm-l, 76 cm-l lower than in the nitrogen molecule. This is qualitatively different from CO, where protonation increases the CO stretching frequency by 43 cm-” [2732]. The CO bond is, however, strengthened relatively more upon protonation than the NN bond (the diagonal quadratic force constant/J) is increased by 16% for carbon monoxide and by only 2% for the nitrogen rno~ec~e~ so that the decrease in the frequency due to kinematic coupling is overcompensated in HCO+. The stretching fundamentals of Dj4N$ are predicted to occur at 2636 and 2022 cm-l. The stretching vibrational frequencies predicted for H14N; and D14Nz are thus rather similar to those known for H12C14N and D1q14N, the largest difference being 157 cm-l. According to the ab initio calculations of HKD 1161, there is also no great difference in the bending vibrational frequencies. Calculated and estimated vibrational frequencies for transitions to higher excited stretching vibrational states and for other isotopomers of protonated nitrogen are also listed in table 3.
The quartic equilibrium centrifugal distortion constant Dj of H141$ is calculated to be 8397 kHz from the CEPA-I
potential
and 86.47 kHr from the
corrected potential. The co~espond~g
values for
D14N$ are 58.04 and 59.43 kHz, respectively. The experimental & -.alues ES] are larger by a few percent, whit”. is quite a common situation for linear molecules [ZP] . The sextic equilibrium centrifugal
PHYSICS
LETTERS
15June
1984
distortion constantsI$ of H’“N$ and Di3N$ are predicted to be (in mHz) 48 (50) and 31 f35), respe&vely, where the values in parentheses refer to the corrected CEPA-1 potential. Similar values hate been previously calculated for HgkfGN and D17C14N f29]. The dependence of the z-component of the electric dipole moment, which gives the only non-vanishing contribution to the dipole moment of linear molecules if one restricts oneself to the consideration of stretching vibrations, has been calculated by SCF. CEPA-I(W) and CEPA-I(ED), where the abbreviations EV and ED stand for expectation value and energy derivative, respectively. As usu& most credit should be given to ~EPA-~~~~~ (see, for esample, ref. 1331). The pointwise catculared dipole moments are well fitted by the expression
+
c,,bm,
(41
the polynomial coefficients being given in table 4. The equilibrium dipoie momenr pe of H14N$ is predicted to br: -3 374 D ~~EPA-~~~D~~, which should be accurate to about 0.02 D. The corre~~jon effect on pLeis calculated zo be very small, less than 15. Previous ab initio calculations [13,l5.lS.19]_ carried out at somewhat different geometries. yieided similar dipole momenrs ranging from -32 to -3.5 D. in contrast to isoelectronic HCO+ 1271, where SCF yields a poor description of the variation of the dipole moment with the stretching coordinate JU?, SCF overestimates the first derivative C$’ z (&K/M), of H1”Nz by oniy 22%. From the analytical dipole-moment functions of tabfe 4 and the ~ha~o~c ~br~rjon~ 3v~~~~u~cFjo~~ calculated from the corrected CEPA-1 porential under inclusion of stretch-bend interaction, integrared molar IR intensities of absorption have been ca.lcuhted for transitions from the vibrational ground state to excited stretching vibrational states. The results for H14Ni and DllNi are given in table 5. A large value of 20257 cmz m~&-l, corresponding to a band strength of 2682 atm-l cm-2 at 298 K, is predicted for H14N$. Similar to H1’G14N (see ref. [33] and references therein), the intensity of the ~3 vibration 539
Table 4 Electric dipolemoment EDMF term
St, & 43) (94)
?t) 1 > 1c 4, GR
ISJune 1984
CHEMICAL PHYSiCS LETTERS
Votume 107, number 6
functions of Hr4Nt a)
SCF
CEPA-I(EV)
CEPA-I(ED)
-1.32179 -0.84755 -0.22356 -0.00779 0.01578 0.38476 0.12781 -0.13959 0.01025 -0.148
-J.35757 -0.75557 -0.15100 0.02050 0.00158 0.22556 0.00140 -0.108t7 0.06124 -0.040
-1.32744 -0.76448 -0.15378 0.02041 -0.00249 0.31466 0.07973 -0.14337 -0.01539 -0.068
The matrix elements L13 and L3, (the L matrix connects the internal coordinates with the normal coordinates) are of equal sign, but ($.@W), and (+&V2)e are of opposite sign and both terms cancel each other largely in the case of HX4N$. The situation is much more favorable for D14@2, where the first term in eq. (5) dominates over the second, y3 of D14N$ thus getting most of its intensity of 3363 cm2 mol-1 from the r-dependent
part of the dipole moment
function. The “double ha~oni~ appro~mation” works weil for the intensities of the v1 bands, but, expressed as a percentage, is rather poor for the ua bands. Due to large transition dipole moments and rather high vibrational frequencies, H14N$ is an excellent IR emitter. The Einstein coefficients of spont~eous emission for Au1 = u; - u;’ = 1 transitions are (in s-l) 857,1592 and 2213 for u;‘= 0.1 and 2. Spectroscopic properties of highly excited stretching vibrational states extending close to the dissociation limit of the NH bond will be dealt with in a forthcoming publication_ Using CEPA-I , the equilibrium proton affiity of N,, denoted by PA,, is calculated to be 5 15 9 kl molW1. The zero-point vibrational energy of H14e2 is found to be 42.: kJ mol-I by adding a contribu-
ai The EDhiFs are expanded around the CEPA-1 equiliirium geometry (see table If and refer to the center of mttss of the molecule. EDMF terms are given in atomic units. The EDMF of Dt4N; is obtained by adding the fotlowving contributions to the values for H14Nl: &I, = 0.0966 I, AC;‘) = 0.03236 and a$) = 0.01618. of Hl4@ is very low. which will render the experimental observation of this band difficult. The low intensity may be easily explained within the familiar
“double harmonic approximation”, where the derivative of the dipole moment with respect to normal coordinate Q3 is given by
Table 5 Integrated mohu IR intensities of absorption ‘in cm2 mof-r) for transitions from the vibrational ground state to the ten lowest stretching vibrational states of H14Nz and D*“N: a) Band
wr(DH) w(DH) “3
y1 L3 w*y3
2vt 3v3
u1 + 25 &+v3
4v3 3u1
Ht4N$
D14Nf
SCF
CEPA-l(EVj
CEPA-RED)
SCF
CEPA-1fEVf
CEPA-RED)
23859 33.6
18215 187
19201 57.4
13645 3177
9482 3138
10671 2721
122 25637 5.1
323
142
4038
3796
3363
19171
20257
13iO8
9349
10582
48.2 87.5 I-of-2) 1.1(-l) &-5, 1.4
3.0
58.5 84.5 l-7(-2)
3.1
55.7 91.2 7-q-3)
13.9
17-2
17.4
66.6 3.6 2.3( -1)
635 1.9 2.9(-1)
66.4 3.1 3.1(-l)
2.4(-l)
1.9(-I)
6.9(-l!
7.5(-l)
7.5(--1)
1.3 2.q-61 1.3
1.3 6 .O(-5) 1.S
2.2(-1) 7.1(-3) 4.2( -2)
1-U-l) 7.9(-3) 3.4(-2)
1.9(--l) 8.0(-3) 3.3(-2)
a) Vibrational wavefunctions obtained from the corrected CEPA-1 potentia.l and inclusion of stretch-bend interaction are empfoyed. The abbreviation ‘DH” stands for “double-h~o~c approximation”.
540
Volume 107, number 6
CHEMKAL
tion of 8.6 w mol- J. for the bending vibrations, as
estimated on the basis of the ab initio calculations of HKD [16], to the present co~t~butjo~ of 33.5 kJ moi-’ from the stret~~g vibrations. %he previous SCF value of Del Bene et al. f2Oj, cahzufated within the harmonic appro~mat~on, is larger by 1355, which is quite a typical error for such calculations. With the zero-point energy of 14.3 kJ mol-’ for t4Nz1 we arrive at a calculated proton affinity at zero temperature of PA, = 488.1 k3 mol- t . The corresponding value of Del Bene et al. fZOj, obtained by 4rh order M#ler-Plesset ~rturba~~on theory and the zeropoint vibrational contribution from SCF, is 492.9 kf molwi. At T = 298 K, we cafculate a proton affinity of 491.3 kJ mol -1, which is in excellent agreement with the experimental value of 49 1.2 + 2.9 kJ moY1 r341.
Thanks are due to Professor Reins&r and Dr. Werner
for the use
of their
SCEP programme.
Support of this work by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 9 I is gratefully acknowledged _
RJ. SaykalJy attd R.C. Woods, Arm. Rev. Phys. Chem. 32 f19811403. B.E. Turner, Astrophys. 3.193 (19741 L83. P. Thaddeus and B.E. Turner, Astrophys. Y. 201119351 L2S. LE. Snyder, J.M. HolJk+, D. BUN and W.D. Watsan, Astrophys. J. 218 (1977) L61. RJ. Sayka.By,TSt. Di..on, T.G. Anderson, P.G. Stanto and R.C. Woods,As~ophys. 5.205 (1976) L101. T.G. Anderson,T.A. Di..on, N.D. PiJtch. R.J. SaykaUy, PG. Szanto and RX. Woods, Astrophyn 3.216 (1977) L85. P.G. Sz~ro,T.G.And~Kon, R.J. Sa~k~i~, N.D. PiJteh, TsZ. Dixon and R.C. Woods, J. Chem. pnys. 7.5 (1981) 4261.
PHYSICS LETTERS
15 June 1984
]8] K.V.L.N. Sastry, P. Hemringer, E. Herbsr and F.C. De Lucia, &hem. Phys. Letters 84 (1981) 286. ]9] F.C. van den Heuvel and A. Dymnnus, Chem. Phys. Letters 92 (1982) 219. ] IQ] CS. Gudeman, MM, Begemann, J_ Pfaff and Rf. SaykaLly. J. Chem. Phys. 78 (1983) 5837. ]I 1 ] C. Forsin and B. Roos. Chem. Phys. Letters 6 (1970) 126. I121 FL Vasudevan, G.D. Peyerimhoff and R J. Buenker, Chem. Phys. S (9171) 149_ { 131 S. Green, J.A. ~lontsorne~ and P. Thaddeus. Astro” phys. J. I93 t 1974) L89. f 141 \%‘.A. Lathan, LA. Cur&s. W.J. Hebre, J.3. Lisk and J.A. Pople, Pro& Phys. Org, Chem. I I ( 1973) 17.5. [ 151 I.H. HiBier and J. Rendrick, J. Chem. Sot. Chem. Commun. { 1975) 526. [ 161 P. Hem@. W.P. Kraemer and G-HI. Diercksen, IfPI/ PAE Astro report No. 135, ~¶as-Plonk-~nst~tut fur PhysL und Astrophysik, Munich (1977). 1171 N.L. Summers and J. Tyrrelf, 1. Am. Chem. Sot. 99 fl97-t) 336~;Tbeoret.Cb~. Acta 47 (f978) 22.J. ] 181 N-N. Waese and R.C. tvoods, Chem. Phys. Letters 61 f 197% 396. ] i91 J.A. Xton%omeryand C.E. Dykstra, 1. Chem. Phys. 71 (1979) 1380. ]30f J.E. Del Bene, J.J. Frisch. Ii. Raghavarhari and JA. Pople, J. Phys. Chem. 56 (1982) 1529. [II ] J_A. Fopfe, in: ifohcufar ions. geomrtric and elzcuonic structures, eds. J. Berkowitz and K-0. Groenevefd (Plenum Press, New Yorl;, 1983). [22] W. Meyer, J. Chem. Phys. 58 (1973) 1017. ]23] W. Xeyer, J. Chem. Phys. 64 (1976) 2901. (241 A.R.W. McKeBar. private commu~cation. ]25] S. Huzinaga. Approximate Atomic Functions it, Technical Report, Division ofTheoretical Chemistry, The University of Alberta (197f); J. Chem. Phys. 42 (1965) 1293. [26] 3. Bendtsen, J. Ramsn Specuy. 2 (1973) 133. [27] P. Bouchwina, Chem. Phys., to be published. ]28] G.~~‘~e~,~r, A.G. flakiand DR. Johnson,J. Mol. spew-y. 39 (1971) 149_ 1291 P. Botschwina. Chem. Phys. 6X f1983) -tl; unpublished work: [30) P. Botschwina, to be published. ]3 I ] J. Bmdrsen and H.G_M. Edwards, J. Raman Spz~r~. 2 (1974) 407. f32f SC. Foster, A.R.W. McReBar and T.J. Sears, J. Chem. Phys,. submitted for pubBcation. (33 f P. 3otschwina, Chem. Phys. 81 (1983) 73. f34J DX. Bobme. G.f. Mackay and H.I. S&J%. J. Chem. Phys. 73 { 1980) 4976.
541