J. Phys. Chem. 1987, 91, 828-834
828
Nuclear Quadrupole Coupling Tensors for Hydrazine, Methylhydrazine, and 1,2-DimethyIhydrazine As Determined by Microwave Spectroscopy and ab Initio Calculation Kaoru Yamanouchi,+Shigeki Kato,* Department of Pure and Applied Sciences and Department of Chemistry, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
Keiji Morokuma, Institute for Molecular Science, Myodaiji. Okazaki 444, Japan
Masaaki Sugie, Harutoshi Takeo, Chi Matsumura, National Chemical Laboratory for Industry, Yatabe, Tsukuba-gun, Zbaraki 305, Japan
and Kozo Kuchitsu* Department of Chemistry, Faculty of Science, The University of Tokyo, Hongo, Bunkyo- ku, Tokyo 1 1 3, Japan (Received: July 14, 1986)
The nuclear quadrupole coupling constants for the I4N nuclei in hydrazine (HY) and the two conformers of 1,24imethylhydrazine (DMH) were determined by a least-squares analysis of the observed hyperfine structures as follows (in MHz): xao = 4.14 (8) and xb6 = -2.15 (15) for HY; xwrl= 2.92 (30), xbbl = 1.35 (32), xuu2= 2.38 (33), and xbb2= -4.69 (35) for the inner-outer conformer of DMH; xu. = 2.84 (30) and Xbb = 0.32 (43) for the outer-outer conformer of DMH. The coupling constants for HY, DMH, and the inner and outer conformers of methylhydrazine were evaluated by ab initio calculations. Configuration interaction calculations were also performed for HY. The calculated coupling constants were compared with the observed ones and used to derive the principal values of the coupling constants by a procedure developed in the present study. The characteristic dependence of the x tensors on the conformational structure demonstrates practical utility of an ab initio calculation of hyperfine structures for a spectral analysis.
Introduction The geometrical parameters, dipole moments, and vibrational frequencies of medium-sized molecules can be estimated by an ab initio MO calculation with reasonable accuracy.’** The nuclear quadrupole coupling constants based on S C F calculations have also been r e p ~ r t e d . ~ ”However, there seems to be no systematic comparison of calculated values with experimental values obtained by microwave spectroscopy. As for the nuclear quadrupole coupling constants for the 14Nnucleus, calculated values are almost restricted to those for the CEN bond or those related to planar aromatic molecules. Winter and Andra’ reported a reliable quadrupole moment of the 14N nucleus; it enables a comparison of the calculated field gradients at the nuclei with experimental nuclear quadrupole coupling constants. Our attention has been focused on the nuclear quadrupole coupling constants in hydrazine derivatives, because they are suitable for studying the influence of internal rotation on the quadrupole coupling constants of the nitrogen nuclei on both sides of the N-N rotation axis. Our recent a b initio calculation^^^^ on the nuclear quadrupole coupling constants for various molecules showed that an S C F calculation with a basis set of the double-{ type gave good estimates of the coupling constants in many cases. Therefore, prediction of the coupling constants by an a b initio calculation is expected to be useful for an analysis of the hyperfine structures of rotational transitions. In the present report, the nuclear quadrupole coupling tensors, x,for the two conformers of 1,2-dimethylhydrazine (DMH), the two conformers of methylhydrazine (MH), and hydrazine (HY) ‘Department of Pure and Applied Science. *Department of Chemistry.
0022-3654/87/2091-0828$01 .50/0
(see Figure 1) are investigated. These molecules have two I4N nuclei, and their rotational transitions are split into complicated hyperfine structures; therefore, it is not easy to determine two sets of the x tensors only from observed hyperfine structures. The x tensors for the hydrazine derivatives are thus evaluated by an a b initio calculation, and the hyperfine splittings are simulated. By taking advantage of the good agreement of the calculated and observed spectra, we can utilize the calculated coupling constants in the analysis of the observed hyperfine structures and determine the coupling constants for HY and DMH. The coupling constants determined from the experiments are diagonal elements of the x tensor projected onto the molecular principal axis system, and therefore, these constants should be converted to the principal values of the x tensor for a systematic comparison of the local electronic environment around the I4N nucleus. Isotopic substitutionlo may be useful for this purpose, but this method is not always practicable. In order to extract the influence of rotational isomerism on the electronic structure at the I4N nuclei for the hydrazine derivatives, a method for esti(1) Hamada, Y.; Tanaka, N.; Sugawara, Y.; Hi-akawa, A. Y.; Tsuboi, M.; Kato, S.;Morokuma, K. J. Mol. Spectrosc. 1982, 06, 313. (2) Tanaka, N.; Hamada, Y.; Sugawara, Y.; Tsutsi, M.; Kato, S.; Morokuma, K. J. Mol. Spectrosc. 1983, 99, 245. (3) Ha, T.-K. Chem. Phys. Lett. 1976, 37, 315. (4) Kochanski, E.; Lehn, J. M.; Levy, B. Theor. Chim. Acto 1571,22, 1 1 1. (5) O’Konski, C. T.; Ha, T.-K. J . Chem. Phys. 1968, 49, 5354. (6) Ha, T.-K. Chem. Phys. Lett. 1984, 107, 117. (7) Winter, H.; Andra, H. J. Phys. Reo. A 1980, A21, 144. (8) Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Kuchitsu, K. J . Mol. Spectrosc. 1985, 126, 320. (9) Yamanouchi, K.; Sugie, M.; Kuchitsu, K., unpublished results. (10) Blackman, G. L.; Brown, R. D.; Burden, F. R.; Garland, W. J . Mol. Spectrosc. 1977, 65, 3 13.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 829
Nuclear Quadrupole Coupling Tensors for Hydrazines HY
inner
TABLE I: Bond Lengths (A), Bond Angles (deg), and Dihedral Angles (deg) around the N-N Axis for Hydrazine, Methylhydrazine, and 1,2-Dimethylhydrazine and Dihedral Angles (deg) around the C-N Axis for Methylhydrazine and 1,2-Dimethylhydrazine Calculated with the 4-31G(N1) Basis Set”
DMH
MH
outer
inner-outer outer-outer
Figure 1. Newman projections of hydrazine derivatives. The terms “inner” and “outer” indicate the locations of the methyl group. The two nitrogen atoms for H Y and the outer-outer conformer of DMH are equivalent, whereas those for the inner and outer conformers of MH and the inner-outer conformer of DMH are inequivalent.
Y
(a)
( b)
Figure 2. Definitions of the inner and outer positions and dihedral angles
of hydrazine derivatives. (a) Newman projection with respect to the
a. Bond Lengths HY r(N-N) 1.4127 r(C,-N)b r(C1-N) r(N-Ho)c 0.9990 r(N-HI) 1.0027 r(Nm-Ho) riNm-HJ r(Cb-Ha) r(ci-Hb) r(C,-HJ r(Co-Ha) r(coCHb) r(Co-Hc)
MH(I)
MH(0)
DMH(I0)
DMH(O0)
1.4071
1.4087 1.4525
1.4052 1.4536 1.4542
1.4058 1.4495
1.4532 1.0008 1.0054 0.9993
1.0030 1.0822 1.0821 1.0901 1.0895 10829 1.0792
N-N bond. W and X are the outer positions and Y and Z are the inner
positions. Each position is occupied by a hydrogen atom or a methyl group. In case it is occupied by a methyl group, the corresponding letter is listed in the last row of Table IC. (b) Newman projection with respect to the C-N bond. mation of the principal values of the x tensors is developed on the basis of the observed and calculated nuclear quadrupole coupling constants. The optimized geometry for HY, the two conformers of M H , and the two conformers of D M H are also obtained by a gradient method with the 4-31G(N*) basis set. The calculated geometrical parameters are compared systematically and utilized for an a b initio constrained analysis of the electron diffraction (ED) intensity with the rotational constants determined by microwave spectroscopy (MW).”-’*
Ab Initio Calculation The nuclear quadrupole coupling constant, xl,,.where i and J represent the Cartesian axes x, y , and z , is defined in terms of the electronic field gradient, qlJ,a t the nuclear position as xij
= eq&
(1)
where Q represents the nuclear quadrupole moment. The quadrupole moment for the I4N nucleus has been reported by cm2. The field gradient Winter and Andra’ to be 1.93 (8) X qv is expressed as
0.9989 1.0039 0.9999 1.0057 1.0810 1.0816 1.0906 1.0882 1.0825 1.0794
1.0063
1.0909 1.0822 1.079 1
b. Bond Angles LH-N-H LN-N-H, LN-N-H, LN-N,-H, LN-N,-H, LN-N-C, LN-N-C, LC-N-H, LC-N-H, LN-C,-H, LN-C,-Hb LN-C,-H, AN-C,-Ha LN-C,-Hb LN-C,-H, LH,-C,-Hb LHb-C,-H, LH,-C,-Ha LH,-C,-Hb LHb-C,-H, AH,-C,-Ha
HY
MH(1)
MH(0)
108.17 112.20 107.94
107.95 111.31 108.23
108.17 112.14 108.20 111.21
106.74 114.40 110.53 109.92 110.27 109.30 109.40 113.41 108.49 108.89 113.79 108.04 108.38 108.18 108.76 108.68 108.89
D M H ( I 0 ) DMH(O0)
110.40 107.18 113.90 110.81 109.98 110.55 109.23 109.45 113.43 108.47 108.96 113.99 107.84 108.61 108.12 108.87 108.34 108.10
110.53 109.78
110.01
108.15 108.55 113.28
108.17 108.53 109.08
c. Dihedral Angles around the N-N Axisd HY MH(I) MH(0) DMH(I0) D M H ( 0 0 1 90.00 29.09 90.00
LX-N-N-Y LY-N-N-Z LZ-N-N-W
90.46 31.79 86.67
89.00 33.38 85.84
Z
X
methyl position‘
87.50 34.58 88.02
70.01 51.52 70.01
x, y
x, w
d. Dihedral Angles around the C-N Axisd where Rlkand rll are the i coordinates of nucleus k and electron I , respectively, Zk is the charge of nucleus k, and $ represents the electronic wavefunction. The second term of eq 2 was evaluated by using Rys polynomials.’) The 4-3 l G ( N * ) basis set and Dunning-Huzinaga’s double-( basis set with polarization functions (DZ+P)14 were used. The contraction for the DZ+P basis set was [9sSp/4s2p], and the exponent for the polarization functions on the nitrogen nucleus was 0.75. In the calculation of configuration interaction (CI) the single and double excitations from the Hartree-Fock reference configuration (SDCI) were considered. The optimized geometrical parameters for HY, MH, and D M H were obtained by the S C F gradient method with the 4-31G(N*) basis set, and the qiJconstants were evaluated a t these optimized geometries. For H Y and D M H the qV constants were also evaluated at the following experimental geometries: for H Y the
DMH(O0)
MH(0)
outer
inner
outer
outer
62.54 58.24 62.06 59.05
61.84 58.56 64.57 56.81
61.28 59.39 61.35 60.12
62.71 57.77 64.56 56.57
56.85 63.04 58.80 62.52
inner
LH,-C-N-N LH,-C-N-N LH,-C-N-H LHb-C-N-H
DMH(lo)
MH(1)
“MH(1) and M H ( 0 ) represent the inner and outer conformers of methylhydrazine, respectively, and D M H ( I 0 ) and D M H ( O 0 ) represent the inner-outer and outer-outer conformers of 1,2-dimethylhydrazine, respectively. bSuffices i and o represent the inner and outer positions, respectively. The nitrogen atom with a methyl group is represented as N, in case discrimination from the nitrogen atom without a methyl group is needed. ‘Definitions for hydrogen atoms, Ha,Hb, and H,, in the methyl group are shown in Figure 2. dSee Figure 2. ‘Position of the methyl group, shown in Figure 2. rastructure determined by Kohata et al.I5 by a joint analysis of
Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Nakata, M.; Nakata, T.; Kuchitsu, K. J . Phys. Chem., preceding article in this issue. (12) Nakata, M.;Takeo, H.; Matsumura, C.; Yamanouchi, K.; Kuchitsu, K.; Fukuyama, T. Chem. Phys. Lett. 1981, 83, 246. (13) King, H. F.; Dupuis, M. J . Compur. Phys. 1976, 21, 144. (14) Dunning, T. H., Jr. J . Chem. Phys. 1970, 53, 2823. (1 1)
ED and MW data and for the two conformers of D M H the rz structure determined by Yamanouchi et al.” by a similar technique (15) Kohata, K.; Fukuyama, T.; Kuchitsu, K. J . Phys. Chem. 1982, 86, 602.
830 The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 TABLE 11: Calculated and Observed Dipole Moments (D) for Hydrazine, Methylhydrazine, and 1,2-Dimethylhydrazine'
Hvdrazineb ra
TC
4-31G(N*1 2.22 ,
PlOI
I
4-31G(N*I 2.30 I
,
DZ+P DZ+P(SDCI1 MW' 2.28 2.26 1.75 (8)
Methylhydrazined inner Po
Pb Pc Plot
4-31G(N*) 1.22 1.51 0.59 2.02
MW' 1.04 (2) 1.21 (4) 0.46 (9) 1.66 (3)
Pa
0.9 1
Wb
Ptor
0.87 1.29 1.80
Plot
1.94
PUC
MH(O1) 3.51 (28)"
obsd
MWf 0.63 (5) 0.61 (5) 1.41 (5) 1.66 (5) 1.74 (5)
' 1 D 3.3356 X C m. breand ra are the geometries used for the calculation, where re represents the equilibrium geometry based on the 4-31G(N*) basis set and ro is the experimental geometry reported in ref 15. Reference 22. dDerived from an SCF calculation using an optimized geometry, re, by the 4-31G(N*) basis set. 'Reference 24. f r z and re represent the geometries used for the SCF calculation. The r z structure is that derived in ref 11. fReference 1 I . with additional structural constraints based on the a b initio optimized geometry derived in the present study. Calculations were mainly performed at the Computer Center of the Institute for Molecular Science.
Calculated Results with the 4-31G(N*) Basis Set Optimized Geometry. The optimized geometry for the hydrazine derivatives were obtained as listed in Table I. The definitions of the nuclei are given in Figure 2. The equilibrium bond lengths obtained from an S C F calculation are in general known to be slightly too short.I6 For both hydrazine and the two conformers of DMH the calculated bond lengths, re(N-N), are found to be about 0.036 A shorter than the experimental rBdistances,"~'~whereas the lengths of other bonds are underestimated by about 0.01 A. Such an excessive underestimation for re(N-N) has been found to be characteristic of the 4-31G" and 4-31G(N*) basis sets. The tilt of the methyl groups in the direction of the lone pair of the nitrogen atom is also observed in Table Ib. A similar tilt has been reported experimentally for the methyl groups in dimethylamine.'s.'9 Dipole Moments and Stabilities of Conformers. The dipole moments evaluated a t the optimized geometry and the experimental geometry are summarized in Table I1 and are compared with the available experimental dipole moments. The calculated total dipole moments are 1.1-1.3 times as large as those determined by experiment. The calculated results for H Y show that the single and double excitations in the C I calculation are not sufficient for reproducing the experimental dipole moments. This table also shows that the dipole moment is not too sensitive to the basis set used in the present calculations. The calculated values of the relative energy difference between the two conformers of M H and D M H are also compared with the corresponding experimental values in Table 111. The inner ( 1 6 ) Pople, J. A.; In Applications of Electronic Structure Theory; Schaefer, H. F., 111 Ed., Plenum: New York, 1977; Chapter 1. (17) Chiu, N. S.; Sellers, H. L.; Schafer, L.; Kohata, K. J . Am. Chem. Soc. 1979, 101, 5883. (18) Wollrab, J . E.; Laurie, V. W. J . Chem. Phys. 1968, 48, 5058. (19) McKean, D. C. J . Chem. Phys. 1984, 79, 2095.
DMH(O0-IO) 0.21 (84)b
re
4-3 lG(N*) 4-31G'
2.04
0.1 I
-0.42
DZ+P
0.16
Reference 24. Reference 1 1 . Reference 17. Reference 1 1 .
A
0.44 n
r,
DZ+P 4-31G(N*) Inner-Outer 0.93 0.9 1 0.80 0.86 1.29 1.28 1.78 1.79 Outer-Outer 1.99 1.96
TABLE 111: Calculated Energy Difference and Experimental Enthalpy Difference (kJ/mol) for the Conformers of Methylhydrazine and 1,2-Dimethylhydrazine
r,d
outer 4-31G(N*) MW' 0.26 (3) 0.38 0.65 0.60 (20) 1.86 1.70 (3) 2.01 1.82 (5)
1,2-Dimethylhydrazind 4-31G(N*)
Yamanouchi et al.
1;;
@ I 0.32 ./
-6.4
1 I
4
I
I
I
, ,
-6.0
-5.6
Figure 3. Principal values of the x tensors. The letters indicate the conformers and the locations of the methyl group attached to the nitrogen as follows: (A) HY, (B) MH(I,i), ( C ) MH(I), (D) MH(O,o), (E) MH(IO,o), (F) DMH(IO,i), (G) DMH(IO,o), and (H) DMH(O0,o). For example, (I0,i) denotes the nitrogen nucleus to which the inner methyl group is attached in the inner-outer conformer of DMH.
conformer of M H is found to be more stable than the outer conformer byzoabout 300 cm-' and the two conformers of DMH have nearly equal stabilities;" the present theoretical predictions are thus consistent with the observations. As far as the energy difference between the conformers is concerned, an S C F calculation with a reasonable basis set seems to provide a good estimate. Calculated x Tensors. The calculated principal values of the x tensors, xrr, and v, defined as 7=
KXXX
-
xyJ/xzzl
(3)
for the three molecules are summarized in Figure 3. The results of the calculation are summarized in Table IV. As shown in Figure 3 for hydrazine derivatives, the xrrand 7 for the I4N nucleus to which the methyl group is attached are -6.3 M H z and 0.35, respectively, while those for the 14N nucleus with no methyl group are about -5.8 M H z and 0.42. This shows that the xrl and '7 values are significantly influenced by methyl substitution on the nitrogen atom. The directions of the principal axes for these x tensors are shown in Table IV. The definitions of Ol and O2 are shown in Figure 4. The angle O , , which corresponds to the so-called lone-pair axis, is about 104' in all cases. For the inner-outer conformers of DMH, the direction of the x axis, denoted 8 2 , for the nucleus to which the outer methyl group is attached is 10' larger than that for the nucleus which has the inner methyl group. The value of e2 for the outer-outer conformer is intermediate between the two inequivalent values of the O2 angles for the inner-outer conformer.
Nuclear Quadrupole Coupling in DMH Analysis of the Observed Hyperfine Structures. The rotational transitions of the two stable conformers of D M H have recently been assigned.11J2 Almost all the assigned transitions have complicated hyperfine structures caused by the nuclear quadrupole coupling of the two nitrogen nuclei. As described in the preceding sections, the nuclear quadrupole coupling constants were calculated for both conformers by the 4-31G(N*) basis set at the optimized geometry. The hyperfine structures of the observed transitions were simulated by using the calculated coupling constants. The observed hyperfine structures were reproduced nearly completely by use of the calculated coupling constants, although splittings were overestimated by about 5%. Therefore, simulation of the (20) Murase, N.; Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Hamada, Y . ;Tsuboi, M.; Kuchitsu, K., to be published.
Nuclear Quadrupole Coupling Tensors for Hydrazines
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 831
TABLE IV: Calculated x Tensors for Hydrazine Derivatives (Coupling Constants in megahertz and Angles in degrees)
HY MH(1,i)‘ MWI) MH(O,o) MWO) DMH( I0,i) DMH(I0,o) DMH(O0,o)
XZ2
Vb
OIC
-5.78 -6.25 -5.83 -6.31 -5.78 -6.18 -6.28 -6.14
0.44 0.37 0.42 0.36 0.42 0.35 0.34 0.34
104 104 105 103 104 103 104 103
91 85 88 93 88 83 96 88
Xao
Xbb
Xcc
3.89 3.92 -0.50 3.71 2.92 3.25 2.38 2.97
-2.01 0.86 -0.13 0.81 -3.04 1.29 -4.86 0.27
-1.89 -4.79 0.63 -4.52 0.12 -4.54 2.48 -3.24
‘See caption of Figure 3. bDefined in eq 3. CidSeeFigure 4. TABLE V System
x Tensors (MHz) for DMH in Molecular Principal Axis r,
Figure 4. Principal axis system of the x tensor. The principal axes of the x tensor are denoted x, y, and z. The angle between the z axis and the N-N bond is denoted el, and O2 is the angle between the x axis and
the projection of the NLN bond on the xy plane.
hyperfine structures should, in general, be useful for the assignment of hyperfine transitions. The hyperfine splittings for the torsional excited states were found to be nearly equal, and, therefore, an analysis of the coupling constants was made only for the ground vibrational state of these conformers. The 1lo-Ow and 321-313 transitions for the inner-outer conformer and the 211-101and 322-414 transitions for the outerouter conformer, which have well-defined hyperfine splittings, were used for the determination of the coupling constants. A leastsquares analysis was made on these hyperfine transitions using the calculated coupling constants as initial values. As independent and xbb2were taken for the inner-outer parameters, xml,X b b l , b2, conformer and xooand X b b for the outer-outer conformer, since the two x tensors of the outer-outer conformer are equivalent. The calculated values are also useful for assignment of the two sets of the coupling constants to the two inequivalent nuclei of the inner-outer conformer. The frequencies of the nine hyperfine transitions of the two rotational transitions were simultaneously fitted for the inner-outer conformer and those for the ten hyperfine transitions for the outer-outer conformer. The coupling constants derived from the above analysis are shown in Table V and the results of these fittings are shown in Table VI. Typical examples of the observed and best fit theoretical hyperfine splittings are shown in Figure 5 . The determined coupling constants were found to reproduce all the observed hyperfine structures satisfactorily. The experimental details have been described in ref 11. The splittings and the intensities of the hyperfine transitions in the above analysis were calculated by evaluation of the nuclear quadrupole interaction by the first-order perturbation theory with representation by the coupling scheme2’ dethe ~(JI,)FlZ2FMF) fined as J + Il = Fl
xon
(IO#
Xbb
(I0,o)
xoa
(00,o)
xao
Xbb
Xbb
obsd 2.92 (30) 1.35 (32) 2.38 (33) -4.69 (35) 2.84 (30) 0.32 (43)
4-31G(N*) DZ+P 3.30 3.43 1.20 1.25 2.48 2.57 -4.94 -5.16 2.98 3.04 0.14 0.17
4-31G(N*) 3.25 1.29 2.38 -4.86 2.97 0.27
‘See caption of Figure 3. TABLE VI: Hyperfine Transition Frequencies (MHz) for 1,2-Dimethylhydrazine
rot transitions
assignt F’,F’l-F’’,F’’l Inner-Oute? 3,2-2,1 2,2-2,l 2,1-2,1 1,2-2,1 1,o-2,1 5,4-5,4 4,4-4,4 4,3-4,3 2,3-2,3
110-0,
321-313
obsd 22 254.99 22253.85 22 255.59 22 257.17 22253.24 39 131.46 39 129.72 39 732.12 39 732.67
Outer-Outerb 4,3-3,2 40 254.73 3,3-2,2 40254.33 3.2-2,l 40 253.37 2,l-1,l 40 256.30 2,3-1,2 40255.10 5,4-6,5 39 779.05 4,4-5,5 39 777.88 4,3-5,4 39 777.33 3,3-4,4 39 776.1 1 3.3-3,3 39 778.44
211-101
322-414
obsd calcd -0.02 0.00 0.01
-0.01 -0.01 0.01 0.00 0.01 -0.01
0.00
0.09 0.06 -0.06 -0.09 0.04 0.01 0.03
-0.13 0.04
-
‘Center frequencies of the llo-Ooo and 321-313 transitions are 22254.88 and 39 132.37 MHz, respectively. bCenter frequencies of the 2,,-lO1and 322-414transitions are 40254.51 and 39778.18 MHz, respectively. I ‘
’
’
’
’
‘ 1
+
Fl I, = F The coupling constants were used to derive accurate center frequencies of the transitions, from which accurate rotational constants and centrifugal distortion constants can be determined.” x Tensors Calculated at Experimental Geometry. Recently, the geometrical parameters have been determined precisely by a joint analysis of ED and M W data.” Therefore, the field gradients, q,,, were also evaluated a t these geometries. As shown in eq 2, q,, can be divided into the nuclear and electronic parts. Since the first nuclear term in eq 2 can be estimated accurately by using the known experimental geometry, the calculation based on the experimental geometry is useful for testing the basis set dependence of the second electronic term. The calculated values for the three tensors for the DMH conformers are summarized in Table V. The calculation was performed at the experimental ~
~~
(21) Thaddeus, P.; Krisher, L.; Loubser, J. J . Chem. Phys. 1964,40, 257.
Figure 5. Observed hyperfine structures of the (a) llo-Ow rotational transitions of the inner-outer conformer of DMH and (b) the 211-1~1 rotational transitions of the outer-outer conformer of DMH. The best fit hyperfine transitions obtained by a least-squares analysis are also shown, and the hyperfine envelope and hyperfine intensities are compared. Experimental details are given in ref 11.
geometry using the 4-3 lG(N*) and the DZ+P basis sets, and the results were compared with the coupling constants calculated in the preceding section. The calculated values are compared with
832 The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 TABLE VII: x Tensors (MHz) for 1,2-Dimethylhydrazine in the Principal Axis System
Yamanouchi et al. TABLE VIII: Observed and Calculated Nuclear Quadrupole Coupling Constants (MHz) for Hydrazine"
DZ+P-
r,
obsd" 4-31G(N*) DZ+P 4-31G(N*) 2.01 1.98 (IO,i)b xxx 1.98 1.94 4.17 xyI, 3.84 4.28 4.46 -6.44 -6.18 xZz -5.83 -6.12 Axc 0.40 0.351 qd 0.320 0.377 0.384 2.08 (I0,O) xxx 1.84 2.01 2.05 4.5 1 4.20 xyy 4.11 4.31 xrr -5.96 -6.32 -6.56 -6.28 Ax 0.09 0.374 0.336 7 0.380 0.365 2.04 (00.0)xxx 1.91 1.96 1.99 4.42 4.10 xyy 4.25 4.22 -6.44 -6.14 xrr -6.17 -6.18 Ax 0.28 0.379 0.335 I/ 0.379 0.366 Derived from the observed coupling constants and calculated ones evaluated at the r z structure using the DZ+P basis set (see Appendix 1). bSee caption of Figure 3. CDerivedfrom experimental values by using eq A14 in Appendix 1. dDefined in eq 3. the experimental values in Table V, where the differences in the x tensors calculated with different geometries are found to be small, probably because the geometry optimized by the 4-31G(N*) basis set is nearly equal to the experimental geometry in this case. Principal Values of the x Tensors. The nuclear quadrupole coupling constants determined by use of the observed hyperfine structure provide the diagonal elements of the x tensor expressed in the molecular principal axis system. The principal values of the x tensor, xrr,xyy,and xxx, can be estimated by use of the off-diagonal elements derived from the present calculation of the x tensor components. As shown in Table V, the calculated values are larger than the experimental values by 5-10%; the same trend has been pointed out by Ha6 in his S C F calculation of ammonia. Therefore, the off-diagonal elements of the x tensor were estimated from the calculated off-diagonal elements, xa;, xb;, and xc2,by an appropriate scaling, as described in the Appendix 1. The principal values estimated by the method described in the Appendix 1 using the DZ+P basis set are listed in Table VII. This table shows that the x tensor for the I4N nucleus to which an outer methyl group is attached (No) is closer to that for the outer-outer conformer than is the x tensor for the I4N nucleus to which an inner methyl group is attached. In the rz structure," the No-N,-C and N,-No-C bond angles of the inner-outer conformer are 114' and 11 1', respectively, and the N-N-C angle of the outer-outer conformer is 110'. Therefore, the principal values of the x tensor seem to depend on the local geometrical structure such as the N-N-C angle. On the other hand, the directions of the principal axes, such as O2 in Table IV, are sensitive to the change in the dihedral angle around the N-N axis. The scale parameter, k (see Appendix l ) , is about 0.90 for these three inequivalent tensors; therefore, it seems to be a general trend that the field-gradient tensor elements are overestimated by about 10% when the DZ+P basis set and the cmz, are used. nuclear quadrupole moment, Q = 1.93 X
Nuclear Quadrupole Coupling Constants for Hydrazine Analysis of Observed Hyperfine Structures. The nuclear quadrupole coupling constant for H Y has been reported by Kasuya2' to be -4.09 MHz. This value corresponds to the xlrn constant, but it should have a positive sign, as pointed out by Harmony and Baronz3 in their study of NzD,. The xlroand xbb constants for N z H 4 have never been reported. Therefore, the hyperfine structure for hydrazine was measured, and the coupling constants were determined (see Appendix 2). From the results for D M H given in the preceding sections, an a b initio calculation was also expected to give good estimates of the x tensor for hydrazine. Accordingly the x tensor for hydrazine (22) Kasuya, T. Sci. Papers Inst. Phys. Chem. Res. (Jpn.) 1962, 56. 1. (23) Harmony, M. D.; Baron, P. A. J . Mol. Strucr. 1977, 38, 1.
N2H4
Xoo Xbb
N2Ddb
Xee Xao Xbb Xce
obsd 4.14 (8) -2.15 (15) -1.99 4.23 (4) -1.98 ( 5 ) -2.25 (5)
4-31G(N*) 3.90 -2.02 -1.89 4.02 -1.89 -2.13
DZ+P 4.06 -2.09 -1.97 4.17 -1.97 -2.20
(SDCI)
3.83 -1.97 -1.87 3.94 -1.87 -2.07
"The ra structure derived in ref 15 was used for the calculations. bobserved values are those derived in ref 23. TABLE IX: Hyperfine Transition Frequencies (MHz) of the ll-Zn(A+) Rotational Transition for N,Hf F'J] '-F'',F1 " obsd obsd - calcd
1.1-2.2 2,l-3,2 3,2-3,2 2,2-3,3 3,2-4,3 1,2-2,3 1,o-2,1 1,o-0,l
31 060.76 31 061.31 31 062.24 31 062.77 3 1 064.02 3 1 064.76 31 065.86 31 066.55
-0.02 0.00
0.03 -0.03 0.03 0.03 -0.01 -0.03
"The center frequency of the 11-20(A+) transition is 31 063.18 MHz.
'6oI'
FREQUENCY(MHz)
'"
Figure 6. Observed hyperfine structure of the 1 l-20(A+) rotational transition of the normal species of hydrazine. The best fit hyperfine transitions obtained by a least-squares analysis are also shown, and the
resultant hyperfine envelope and hyperfine intensities are compared. was estimated by an ab initio calculation using the experimental geometry. The basis sets used for the S C F calculation were 4-31G(N*) and DZ+P. In the case of the DZ+P basis set a successive CI calculation was made with single and double excitations (SDCI), and the x tensor was derived by using the CI wavefunctions. The coupling constants for N2D4were also estimated under the assumption that the geometrical structure for the ground vibrational state was isotope independent. The calculated coupling constants are listed in Table VIII. The simulated hyperfine structure based on the calculated coupling constants, xnaand xbb, are nearly equal to the observed structures. Therefore, the hyperfine quantum numbers were readily assigned. A least-squares analysis on the hyperfine structures was then performed. The results of the fitting are summarized in Table IX. The derived coupling constants are compared in Table VI11 with the calculated values. The observed and best fit spectra for the ll-2,,(A+) transition are shown in Figure 6. In the evaluation of the intensities of the hyperfine components the spin weights of the two sets of equivalent hydrogen atoms were taken into account. In the case of HY, the calculated coupling constants with the DZ+P basis set in the S C F level agree well with the observed values. A successive SDCI calculation decreased the values by about 5%; this trend is consistent with the case of the x tensor of ammonia reported by Ha.6 The principal values of the x tensor for H Y were also estimated with the experimental coupling constants and the theoretical off-diagonal elements of the x tensor, as listed in Table X . Nuclear Quadrupole Coupling Constantsfor Methylhydrazine. The nuclear quadrupole coupling constants for the inner conformer
Nuclear Quadrupole Coupling Tensors for Hydrazines TABLE X: Principal Values of the
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
x Tensors (MHz) for Hydrazine rap
N2H4a
xxx XYY XZZ
AXC
1.38 4.48 -5.86 0.05
833
NZD4” 1.37 4.46 -5.83 0.05
DZ+P(SDCI) 1.28 4.15 -5.42
756
DZ+P 1.44 4.41 -5.85
4-31G(N*) 1.48 4.25 -5.73
4-31G(N*) 1.64 4.24 -5.87
4The theoretical x tensor derived by an SDCI calculation with the DZ+P basis set and observed diagonal elements of the x tensor in the molecular principal axis system in Table IX were used. braand re are the geometries used for the calculation. See footnotes to Table 11. CEstimated by eq A14 in Appendix 1. were derived by Lattimer and Harmony.24 Though the two x tensors in the inner conformer were inequivalent, the coupling constants for only one set of xuuand X b b were determined. The calculated x tensors for the inner and outer conformers of M H by the 4-31G(N*) basis set a t the optimized geometry are summarized in Table XI. The coupling constants expressed in the molecular principal axis system for the 14N nucleus with no methyl group for the inner conformer are found to be remarkably small. Therefore, the calculated results explain why the observed hyperfine structures can be simulated only by the constants for the I4N nucleus with the inner methyl group. The coupling constants for the outer conformer were recently determined by Murase et aLzoby analyzing the resolved hyperfine structures. The observed and calculated constants are compared in Table XI. The principal values of the x tensors for M H estimated by the method described in the Appendix 1 are also summarized in Table XI.
TABLE XI: Nuclear Quadrupole Coupling Constants (MHz) for Methylhydrazine
xo4 Xbb
xCc
5- 10%. As demonstrated for hydrazine derivatives, reasonable hyperfine structures can be estimated by use of the coupling constants based on an a b initio calculation if appropriate scaling factors are used. For a molecule with two or more quadrupolar nuclei, hyperfine transitions are in general very complicated. In such a case hyperfine structures estimated by this procedure can be used for the assignment of transitions. The method for estimating the principal values of the x tensor used in the present study provides a means for examining the electronic wavefunction at the quadruplar nucleus. For example, the influence of rotational isomerism or chemical substitution on the electronic structure can be evaluated by way of the nuclear quadrupole coupling constants.
4-31G(N*)
4.09 (3)b 0.69 (3) -4.78 (3)
3.92 0.86 -4.79
obsd
4-3 lG(N*)
xxx 4.43‘ xYy 1.88 xZr -6.31 Axd
4.30 1.96 -6.26
0.32
(1) x44
xbb XCC
3.7 (3)e 0.7 (4) -4.4
-0.13
xxx
-0.50 0.63
XYY
xzz
1.69 4.13 -5.83
3.71 0.81 -4.52
xxx 1.95 xYy 4.24 xiZ -6.19
2.02 4.29 -6.13
Ax
Summary The nuclear quadrupole coupling constants for the hydrazine derivatives in the molecular principal axis system were evaluated by an ab initio M O calculation with basis sets of the double-f type. The agreement of the calculated and observed values is satisfactory, except that the absolute values are overestimated by about
obsd (Wa
3.2 (3)e -2.5 (3) -0.7
2.92 -3.04 0.12
0.17
xxx 1.12 xYY 4.29 xzz -5.40 Ax
1.69 4.09 -5.78
1.16
“See caption of Figure 3. bDerived in ref 24. cObtained from the nuclear quadrupole coupling constants at the re geometry calculated with the 4-31G(N*) basis set and the observed coupling constants. See Appendix 1. Derived by eq A14 in Appendix 1. e Reference 20. A x tensor expressed in the principal axis system is defined as a symmetrical 3 X 3 matrix
X = (x,)
i , j = a, b, c
(‘41)
and an approximate estimate for X,denoted as X, represents the calculated x tensor expressed in the same system. The ith ( i = 1, 2, 3) eigenvalues, A, and A,*, and the associated eigenvectors, u, and vi*, for the matrices X and x*, respectively, are defined so that
xu,= x,u,
(‘42)
x*u,*= x,*u,*
(A31
and
Acknowledgment. W e are grateful to the Computer Center of the Institute for Molecular Science for making their M-200H computer available for the present calculations. K.Y. is grateful to Dr. P. Godfrey, Monash University, for his valuable comments on the hyperfine splittings for the hydrazine derivatives.
A matrix P, which has the diagonal elements of X and the scaled off-diagonal elements of P, is also defined so that PU,m
Appendix 1 The diagonal elements of the x tensor expressed in the principal axis system of a molecule, xaa,xbb, and xCc,can be derived from high-resolution spectroscopy. In order to obtain the principal values for the x tensor, xxx,x,,,,, and xzz, it is necessary to estimate off-diagonal elements. If the diagonal elements obtained from an a b initio MO calculation agree well with the corresponding observed values, it is reasonable to utilize the off-diagonal elements evaluated by the same calculation to estimate the principal values of the x tensor. By the method described below, the principal values of the x tensor and their errors can be estimated by combining the nuclear quadrupole coupling constants determined by experiment and those derived from a theoretical calculation. (24) Lattimer, R. P.; Harmony, M. D. J. Am. Chem. SOC.1972, 94, 351.
= X,mu,m
(A4)
where uImand Aim represent the eigenvectors and the eigenvalues respectively. of the matrix P, Operators D and b are introduced: A matrix DX has the same diagonal elements as those in matrix X , whereas all the off-diagonal elements in DX are zero. On the other hand, the matrix DX has the same off-diagonal elements as those in X,whereas all the diagonal elements are zero. By use of these operators, matrix P can be written as
P = DX+ k D P
(‘45)
where the scale parameter k is defined as
k =
C X , , X , ,J * / C ( X ~ j~=* )a,~b, c
(‘46)
so as to minimize the error in the estimation of the diagonal elements, CJ(xJJ- k ~ ~ , * If) the ~ . error in the estimation of the
J . Phys. Chem. 1987, 91, 834-837
834
off-diagonal elements, kDX* - DX, is denoted 6, (A4) can be rewritten as
(X+S)vim =
('47) Operation of vi from the left on both sides of eq A7 and the use of eq A2 lead to UisUim
Aimvim
= ( h i m - Ai)Zivim =
(Aim
- AI)
(AS)
where the following approximation is made: ijiuim
N
UimVim
= 1
(-49)
After taking the norm of both sides of eq A8, one finds that
[[SI1
'
lAim
-
Ail
(A101
where the norm of the matrix S = (sij) is defined here as
[[SI1 =
(cc(sij)2)1/2 i
l
(All)
Therefore, the diagonalized elements can be estimated as
xi =
f [[slj'
(A121
Though it is not easy to evaluate [[SI], it seems reasonable to assume that each of the 3 X 3 elements of matrix kX* has the same magnitude of error. Therefore, [[SI] can be estimated by using [ [D(kX* - X ) ] ] as
[[SI]
N
2'12[ [D(kX* - X)]]
(A131
In the present case of nuclear quadrupole coupling, the principal values of the x tensor, xxx, xyy, and xrr, correspond to A,, A2, and A3, respectively. Then, uniform errors in these principal values can be estimated by using eq A12 and A13 as follows:
where xJJand x,* represent the experimental and theoretical diagonal elements of the x tensor, respectively, expressed in the molecular principal axis system.
Appendix 2 The sample of NzH4 was obtained from the 40% aqueous solution of hydrazine. The sample pressure in the waveguide cell was about 3 mTorr. The ll-20(A+,A-) and 30-2,(A+,A-) transitions were observed. The microwave spectra were measured by a Stark-modulated spectrometer1' with a modulation frequency of 100 kHz. The absorption cell was a 3-m X-band waveguide cell. The microwave sources were an HP8627A synthesizer and an HP8690 microwave sweeper phase-locked to the synthesizer. The microwave frequency was swept through an HP-IB system controlled by an HP9835 desktop computer. The measured hyperfine transition frequencies are listed in Table IX. Registry No. HY, 302-01-2; DMH, 540-73-8; methylhydrazine, 6034-4.
A Classical Trajectory Study of Laser-Induced Dlssociation Dynamics in Triatomic Molecules W.-K. Liu,* Guelph- Waterloo Program for Graduate Work in Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3Gl
A. F. Turfs,+ Department of Chemistry, Temple University, Philadelphia, Pennsylvania 191 22
W. H. Fletcher, Chemistry Department, University of Tennessee, Knoxville, Tennessee 3791 6
and D. W. Noidt Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (Received: May 19, 1986; In Final Form: August 19, 1986)
The dissociation dynamics of the excited states of the nonbending model triatomic molecules H 2 0 and D 2 0 in the presence of a laser is studied classically. In particular, we are interested in quasi-bound, largely nondissociative, states whose energy levels lie above the dissociation limit of the molecule. dt is found that coupling of a laser field to the molecule initially prepared in such states would enhance the dissociation probabilities'and rates, although the energy absorbed by the molecule is very small.
1. Introduction
Intramolecular transfer of vibrational energy in isolated molecules has recently been the object of considerable attention.1.2 A number of classical studies have dealt with molecular excitation and dissociation by infrared lasers3 One of the first such studies4 addressed the multiphoton dissociation of a polyatomic system 'Present address: Research and Development, Integrated Ionics, Inc., Da ton, NJ 08810. YPresent address: Institute for Defense Analyses, 1801 N. Beauregard St., Alexandria, VA 22180.
0022-3654/87/2091-0834$01 SO10
(CD3C1) and elucidated the dissociation dynamics by demonstrating (1) that energy absorption is a sharply peaked function of the exciting frequency, (2) that the dissociation threshold depends upon the fluence of the laser rather than intensity, and (1) Noid, D. W.; Koszykowski, M. L.; Marcus, R. A. Annu. Reu. Phys. Chem. 1981, 32, 261. (2) Rice, S. A. Adu. Chem. Phys. 1981, 47, 117. (3) Gray! S. K.; Stine, J. R.; Noid, D. W . Laser Chem. 1985, 5. 209, and references cited therein. (4) Noid, D. W.; Koszykowski, M. L.; Marcus, R. A,: McDonald, J . D. Chem. Phys. Lerr. 1977, 51, 540.
0 1987 American Chemical Society
