J. Phys. Chem. 1987, 91, 37-41 and the object of the argument. Our purpose here has been to clarify the source of the density-functional correlation effect and to delineate its limits. It is a characteristically molecular effect, intimately involved with the separated-atom asymptotic limit and with the different response of H F and density functional Ham-
37
iltonians to the ionic character of determinantal molecular-orbital wave functions.
Acknowledgment. This work was supported in part by a grant from the National Science Foundation.
Ab Initio Calculations on Imine-Carboxyl Complexes L. Fugler, C. S. Russell, Department of Chemistry, City University of New York, City College and Graduate Center, New York, New York 10036
and A. M. Sapse* Department of Chemistry, City University of New York, John Jay College and Graduate Center, New York, New York 10036, and Rockefeller University New York. New York 10021 (Received: March 7 , 1986)
Ab initio (Hartree-Fock) calculations are performed in order to investigate the methylene imine complexes with formic acid. The basis sets used are STO-3G and 6-31G. It is found that the proton resides on the carboxyl and no second minimum is found for the charge pair complex. Calculations are also performed on the allylimine-carboxyl complex using complete optimization and a very shallow minimum is found for the charge pair complex using the 6-31G basis set.
Introduction The aldimine or Schiff base moiety (-HC=N-) appears in the prosthetic group of many proteins and is implicated in the mechanism of many enzymatic reactions. Iminium cations are good electron sinks and have been invoked in the mechanism of action of, for example, amino acid decarboxylases, acetoacetate decarboxylase,' and L-2-keto-3-deoxyarabonatedehydrase.2 Protonated Schiff base structures (-HC=NH+-) participate in the photocycles of rhodopsin (visual pigment protein) and bacteriorhodopsin (the proton pump of the purple membrane of H a l o b a ~ t e r i u m )and ~ , ~are invoked in mechanisms for enzyme reactions involving Schiff base intermediates. Extensive spectroscopic, synthetic, and theoretical studies have addressed the role that the protonated species plays in the properties and mechanism of action of retinals7 proteins. In particular, the nature of the counterion to the aldiminium cation (-HC=NH+-) and the nature of its interactions with the chromophore were investigated. A candidate for an anionic counterion is the carboxylate group of an aspartic or glutamic acid residue from the apoprotein. Several analogue and model systems that mimic the natural chromophore to varying extents have been studied by many forms of spectroscopy and with various levels of theoretical calculation^.^^^ Some of the results are applicable to systems that do not contain the retinal Schiff base chromophore but may still have an imine-carboxyl interaction. Indeed, such interactions might be expected whenever an imine might require protonation or reversible proton exchange as part of its participation in catalysis. Ab initio calculations have been used in order to understand model systems for the protonated Schiff base retinal chromophore in rhodopsin and bacteriorhodopsin. Zuccarello and his col( I ) Tagaki, W.; Westheimer, F. Biochemistry 1968, 7, 891. (2) Portsmouth, D.; Stoolmiller, A,; Abeles, R. J . Bioi. Chem. 1967, 242, 275. (3) Balogh-Nair, V.: Nakanishi, K. In New Comprehensiue Biochemistry; Tamm, Ch., Ed.; Elsevier: New York, 1982; Vol. 3. (4) Smith, S . 0.; Mathies, R. A. Biophys. J . 1985, 47, 251. ( 5 ) Bagley, K. A,; Balogh-Nair, V.; Croteau, A. A.; Dollinger, G.; Ebrey,
T. G.; Elsenstein, L.; Hong, M. K.; Nakanishi, K.; Vittitow, J. Biochemistry 1985, 24, 6255. (6) Lewis, A. Methods Enzymol. 1982, 88, 561 and references therein. (7) Narva, D.; Callender, R. H. Photochem. Photobiol. 1980.32, 273 and
references therein. (8) Schiffmiller, A,; Callender, R. H.; Waddell, R.; Kakitani, H.; Honig, B.; Nakanishi, K. Photochem. Photobiol. 1985, 41, 563. (9) Wisenfeld, J. R.; Abrahamson, E. W. Photochem. Photobiol. 1968, 8, 487.
0022-3654/87/2091-0037$01.50/0
leaguesI0 studied the model system allylimine-ammonium complex, which featured a double minimum of comparable energy using the short basis set STO-3G. HodoSEek and Hadii" studied a similar model, N-methylallylimine-formicacid complex, as well as the desmethylretinal N-methyl Schiff base-formic acid complex. For the STO-3G level, only a slight inflection resulted for the proton transfer. The charge pair complex was found to be much higher in energy than the neutral-neutral complex. The 4-3 1G basis set results showed two minima, much closer in energy but still favoring the neutral-neutral complex. These calculations were performed with limited optimization. Scheiner and Hillenbrand presented a thorough analysis of the proton-transfer reactions for these types of systems.I2 Also, charge distributions for methylene imine (H2CNH) have been reported.13 In our previous work on amine-carboxyl interaction in the gas phase, the most stable complex had the proton set on the carboxyl forming a neutral-neutral complex rather than a charge pair c0mp1ex.l~ In a nonpolar solvent, the N-methylallylimine-formic acid complex was shown" to have the proton residing on the carboxyl, forming a neutral-neutral complex. In another model system, the guanidinium ion-formate complex14in the gas phase, the most stable complex was shown to be the charge pair complex. Those differences can be attributed to the proton affinities of the different subsystems. The guanidinium ion features a fairly high proton affinity of 264 kcal/mol; methylamine shows only 23 1.1 kcal/mol. Even though they are both much smaller than that of the HCOO- ion (357.9 kcal/mol), the difference between them is good enough to stabilize the charge pair complex vs. the neutral complex for the guanidinium. It should also be noted that in the carboxylate ion as well as in methylamine the differences between the proton affinities predicted by the 6-31G and the 6-31G* calculation are insignificant (about 1%). In this study both the charge pair complex and the neutralneutral complexes for methylene imine-formic acid and Nmethylmethylenimine-formic acid are investigated in order to determine (a) their stability and (b) the proton-transfer energetics. The imine-carboxyl interactions studied do not feature the allyl group attached to the carbon. The purpose of omitting the allyl (10) Zuccarello, F.; Raudino, A,; Buemi, G. THEOCHEM 1984, 107, 215. (11) HodoSEek, M.; Hadii, D. Can. J . Chem. 1985, 63, 1528. (12) Scheiner, S.; Hillenbrand, E. A. J . Am. Chem. SOC.1985, 107, 7690. (13) Bruna, P. J.; Krumbach, V.; Peyerimhoff, S. D. Can. J . Chem. 1985, 63, 1594. (14) Sapse, A. M.; Russell, C. THEOCHEM 1986, 137, 43.
0 1987 American Chemical Society
38 The Journal of Physical Chemistry, Vol. 91, No. 1. 1987
Fugler et al.
IA
3A
\
\
I B. 38
\
01
I
\ \ \
/c2, 02
H5
Figure 1. (A) Single hydrogen bond neutral-neutral complex formed by the complexation of methylenimine with formic acid. (B) Single hy-
drogen bond charge pair complex formed by the complexation iof methyleniminium ion with formate ion.
f2\ H,
02
Figure 3. (A) Neutral-neutral complex formed by N-methylmethylenimine and formic acid. (B) Charge pair complex formed by the complexation of N-methylmethyleniminiumion and formate ion. 4
H
\ / ”
H
V
Figure 2. Double hydrogen bond neutral-neutral complex.
group in our model was to separate the effect of this group on the imine-carboxyl interaction. Calculations are also performed with the allylimine-zarboxyl system using full optimization in order to assess its effect on the complexation energetics. Since a carboxyl ion can form a double hydrogen bond with the guanidinium ion, it seemed appropriate to investigate the possibility of the formation of a double hydrogen bond system in our model shown in Figure 2. The complexes investigated are the following: (1) The single hydrogen bond neutral-neutral complex formed by the complexation of methylenimine with formic acid (Figure 1A); (2) The single hydrogen bond charge pair complex formed by the complexation of methyleniminium ion with formate ion (Figure 1B); (3) The double hydrogen bond neutral-neutral complex (Figure 2); (4)The neutral-neutral complex formed by N-methylmethylenimine and formic acid (Figure 3A); (5) The charge pair complex formed by the complexation of N-methylmethyleniminium ion and formate ion (Figure 3B); (6) N-methylallylimine-formic acid (Figure 4).
Methods and Results The method of calculation is the ab initio self-consistent-field (Hartree-Fock) method using Gaussian basis sets, as implemented by the GAUSSIAN-80 computer program.15 The basis sets used are STO-3G16 and 6-31G.l’ Some calculations are also performed ~
(15)
~
~
DeFrees, D. J.; Schlegel, H.B.; Topiol. S.;Kahn, L. R.; Pople, J. A.
Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA 15213. (16) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51,
GAUSSIAN-BO,
2657
H
\ \
, H,
\0
I’ /c2\ 02
’H,
Figure 4. N-Methylallylimine-formic acid.
with 3-21G and 6-31G* basis sets. The optimization method is the gradient method (Berny optimization method).18 In previous work by Hadii and HodoSEek” on the desmethylretinal N-methyl Schiff base-formic acid and N-methylallylimine-formic acid complex it was shown that a significant difference exists between the STO-3G calculations and 4-3 1G basis set under conditions of partial optimization. Consequently, we use STO-3G and 6-31G basis sets to investigate any such differences arising in our model and we repeat the calcultion on the N-methylallylimine-formic acid complex using complete optimization and 6-31G basis set. The calculations on the N methylallylimine-formic acid complex are performed for four N l H l distances, starting the optimization at N l H l = 1.77 8,and N l H l = 1.03 A and keeping it frozen for the values N l H l = ~~
~
~
(17) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem Phys. 1972, 56, 2256. (18) Schlegel, H. B. J . Comput. Chem. 1982, 3, 214
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987 39
Imine-Carboxyl Complexes
TABLE I: Energies (au) and Geometrical Parameters (Bond Lengths (A) and Angles (deg)) of the Subsystem in the 6-31G Basis Set
E ClNl C1H3 C1H4 NlHl N1H2 HlNlCl fH2NlCl LH3ClNl L H ~ 1CN 1 C2N1 LC2N 1C 1 c202 c201 OlHl H5C2 LOlC201 LH 1 01C2 LH5C202
H&=NH
[H2C=NH21+ _ _ --
H,C=NHCH,
[H,C=NHCH,l+ _ -.
HCOOH
HCOO-
-93.9814 1.261 1.077 1.077
-94.3476 1.271 1.072 1.072 1.002 1.002 120.2 120.2 122.2 122.2
-132.9924 1.258 1.073 1.083
-133.3716 1.269 1.071 1.072 1.004
-188.6655
-188.0952
1.204 1.345 0.956 1.073 124.4 114.9 126.0
1.257 1.257
1.007 115.8 124.7 115.8
118.6 119.4 124.0 1.464 120.5
TABLE II: Energies (au) and Geometrical Parameters (Bond Lengths (A) and Angles (deg) of Structures 1A and 1B (NlH1 = 1.03 A), Obtained through the Use of the 6-136 Basis Set 1A 1B angle a a = 0.0 a = 45.0 a = 90.0 a = 0.0 E -282.6706 -282.6677 -282.6491 -282.6525 NlCl NlHl N1H2 C1H3 C1H4 OlHl c201 c202 C2H5 NlOl LClNlHl LClNlH2 LH3ClNl LH4ClNl fH101C2 LOlC202 L02C2H5
1.264 1.731 1.004 1.073 1.078 0.988 1.323 1.216 1.077 2.719 116.3 117.5 118.7 123.6 115.2 124.9 112.1
1.262 1.751 1.005 1.073 1.078 0.985 1.327 1.214 1.076 2.736 119.4 117.2 119.f 123.7 116.5 125.1 111.8
1.261 1.787 1.005 1.073 1.078 0.981 1.329 1.211 1.076 2.768 127.0 116.5 119.4 123.5 117.9 125.6 111.4
1.267 1.03 0.997 1.078 1.073 1.525 1.276 1.254 1.084 2.555 118.2 123.0 116.0 121.4 105.5 124.7 116.7
1.4 8, and N l H l = 1.2 while the other parameters are optimized. The STO-3G basis set calculations are important to examine because for larger systems such as retinal they are the only ones possible and as such they should be studied for their limitations when systems like these are concerned. The 3-21G basis set is known to predict reliable geometries but overestimate binding energies; therefore only a few calculations were performed with this basis set. Our previous results did not show significant differences between 6-31G and 6-31G* calculations. Neither the geometries of the subsystems and the complexes nor the binding energies are very different. Therefore we limit the 6-31G* calculations in this paper to some essential ints such as the search for a minimum around N l H l = 1.03 The subsystems in this study (1) methylenimine, (2) methyleniminium, (3) N-methylmethylenimine, and (4) N-methylmethyleniminium have been geometry-optimized with STO-3G and 6-31G basis sets. The formic acid and formate ion parameters have been completely optimized with the STO-3G and 3-21G basis sets. The 6-3 1 G basis set results were taken from another study.14 The systems were set planar except for the N-methyl group in N-methylmethylenimine. Table I shows the data for these subsystems for the 6-31G calculations. The complex shown in Figure 1A is optimized, subject to the following constraints: the angle formed by the plane of the imine and the plane of the formic acid, a,is set a t three different values, a = Oo, 45O, and 90°, where the a = Oo condition sets 0 2 cis to H3. For each of these, the rest of the parameters are optimized with the exception of N l H l O l , which is kept linear. The N l H l bond length has been
120.4 120.4 1.482 126.2
1.111 130.1 115.0
TABLE 111: Energies (au) and Geometrical Parameters (Bond Lengths (A) and Angles (deg) of Methylenimine-Formic Acid Complex (NlH1 is Frozen at 1.03 A) in the 6-31G Basis Set 3A 3B E -321.68 17 -321.6679 NlCl N1C3 NlHl C1H3 C1H4 HlOl 01c2 02c2 H5C2 C3H6 NlOl LC3N 1C 1 LHl N l C l LH3ClN1 LH4C 1N 1 LH6C3N 1 LH 101C2 LO 1c 2 0 2 LH5C201
1.261 1.465 1.718 1.073 1.08 1 0.991 1.323 1.216 1.075 1.082 2.709 121.7 114.7 119.0 123.7 110.3 125.0 112.0 115.8
1.265 1.463 1.03 (set) 1.077 1.074 1.531 1.279 1.249 1.085 1.079 2.561 126.8 116.2 116.5 121.1 109.5 107.6 124.7 116.0
TABLE IV: Proton Affinities of the Subsystems at 6-31G Level of Calculation (kcal/mol)
proton subsystem H2C=NH H2C=NHCH3
affinity 230 237
subsystem H2C=CHC=NCH3 HCOO-
proton affinity 250 358
set at the initial value of 1.02 A and the O l H l distance at 1.6 A. When the optimization is completed the values indicate the proton to be covalently bound to the formate oxygen and hydrogen bonded to the imine nitrogen resulting in the formation of a neutral-neutral complex. To calculate the lowest possible energy for the charge pair complex (shown in Figure lB), the N l H l bond length was frozen at 1.03 A and all the other parameters were optimized. (Y was kept at Oo. These results are shown in Table 11. The double hydrogen bond complex shown in Figure 2 is allowed to relax its geometry through full optimization subject to the planarity constraints. The N-methylmethylenimine-formicacid complexes shown in Figure 3 have been geometry-optimized subject to the following constraints: (a) the angle formed by the plane of the imine and the plane of the formic acid, a,is set at two different values, Oo and 90°; (b) the rest of the parameters were optimized except the N l H l O l bond, which was kept linear. The charge pair complex has been geometry-optimized whereby the N1 H1 bond is kept at 1.03 A. The results are shown in Table 111 for the 6-31G calculations.
40
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987
Fugler et al.
between 0 2 and H 2 when 0 2 is cis to H2. In the charge pair complex (Figure 1B) the N l H l bond is frozen at a typical NH bond length (1.03 A), where the N H bond E is involved in hydrogen bonding. The rest of the parameters in NH, 8, STO-3G 6-31G the complex are varied in order to obtain the lowest possible energy 1.03 -278.9892 -282.6525 (within the constraint of planarity and keeping the N l H l O l bond 1.2 -279.0045 -282.6577 linear). The 6-3 1G results show this structure to have a minimum 1.3 -279.0332 -282.6585 energy at a stationary point with positive eigenvalues of the 1.4 -279.0434 -282.6653 second-derivative matrix. However, this is not a true local min1.5 -279.0493 -282.6682 imum since N 1H1 was kept frozen at 1.03 8, and only the other 1.7 -279.0543 -282.6706 parameters of the molecule have been optimized. The STO-3G results differ in that a minimum could not be found even after TABLE VI: Binding Energies (kcal/mol)" an exhaustive search. The results of the calculation predict a 1A 1B 3A 3B structure totally lacking physical significance. A simple explanation is that the STO-3G basis set is not adequate for this system. STO-3G 0 8.4 8.55 The STO-3G calculation exaggerates the difference in proton 45 7.6 affinity between the carboxylate ion and the imine. While 6-31G 90 7.0 calculations predict it to be 128 kcal/mol, STO-3G brings it to 21 9 kcal/mol. Experimentally, the difference between an amine 6-31G group and a formate ion is only 130 kcal/mol, which makes the 0 14.9 3.5 18.3 6.28 6-31G results much more reliable. The 3A structure is adequately 45 13.1 90 11.8 described by both STO-3G and 6-3 1G basis sets. In Table V, when the proton is transferred from the imine to the formic acid, at all calculated levels including 6-31G* no minimum is found for the charged pair complex. This result Table IV shows the proton affinities of the subsystem discussed, contradicts the results of HodoSEek and Hadii, who find a barrier at the 6-3 1G level of calculations. The energy path of the proton to the proton transfer for the N-methylallylimine-formicacid transfer has been studied in the following way: the N l H l distance complex.]' This difference can be explained by the fact that the has been kept frozen at 1.2, 1.3, 1.4, and 1.5 A. The rest of the double bond of the allyl group stabilizes the charge pair complex parameters in the complex have been optimized subject to planarity and produces a second minimum. An argument in favor of this and to the linearity of the H-bond constraints. The energy deexplanation is the higher proton affinity of N-methylallylimine pendence on the value of the N l H l bond length is shown in Table as compared to the N-methylmethylenimine. We have calculated V. The binding energies of the complexes are calculated by the proton affinities with the 6-31G basis set and found 250 subtracting the energies of the separate systems from the energy kcal/mol for N-methylallylimine and 237 kcal/mol for N of the complexes according to the following formula: methylmethylenimine. However, this difference in proton affinit is too small to account for a large difference in the energetics of E = Ecomp~ex- (Eimine + EHCOOH) complexation. Part of the latter is due to HodoSEek and Hadii The binding energies are displayed in Table VI. lack of complete optimization. When we repeated their calculation, using the 6-31G basis set and optimizing the systems Discussion completely, we found a very shallow minimum at N 1H 1 = 1.07 It is clear from Tables I1 and I11 that the neutral-neutral A. The difference between the energy of the neutral-neutral complexes are more stable than the charge pair complexes. In complex and the charge pair complex is only 4 kcal/mol. This the case of structures 1A and 1B the difference is 11.3 kcal/mol value is smaller than the 11 kcal/mol found by HodoZek and while structures 3A and 3B differ by 8.7 kcal/mol at the 6-31G Hadii without complete optimization. The barrier found around calculation level. N l H l = 1.2 A is very small (below 0.5 kcal/mol), as opposed The geometries of the complexes do not exhibit any surprise to 11 kcal/mol found by HodoSEek and Hadii. These differences features. The STO-3G basis set predicts, in general, longer bond show that complete optimization is essential in these systems. In lengths than 3-21G or 6-31G. For the formic acid at STO-3G particular, HodoSEek and H a d 5 seem to keep the N l O l distance our results are in agreement with Del Bene.I9 The angles preconstant for the charge pair and neutral-neutral complexes. dicted by STO-3G are quite similar to the other two basis sets However, the N l O l distance, upon optimization, shortens from results with the exception of the H101C2 angle, which is much 2.719 A for the neutral-neutral complex to 2.555 A for the charge smaller. As mentioned before, these results are also similar to pair complex. The relaxation of the subsystems in the complex the description of the anion provided by the 6-3 lG* c a l c ~ l a t i o n . ~ ~ may also contribute to the difference in results even though the The O l H l bond is similar in length for both basis sets. The differences in geometries due to complexation are small. It can parameters of the subsystems do not show a significant difference be concluded that even though the allyl group stabilizes somewhat upon complexation except for an elongation of the O l H l bond the charge pair complex it does not predict a significant barrier in formic acid. The O l H l bond in 6-31G is elongated from 0.96 to the proton transfer. A to 0.98 8,. The STO-3G predicted the O l H l bond length to As seen in Table VI, the binding energies are larger for the stay constant upon complexation at about 1.0 A. 6-3 1G calculations than for the STO-3G. STO-3G is not adequate The double hydrogen bond complex shown in Figure 2 does not for the description of the charge pair complex; it shows it to be represent a minimum in energy. When optimization is attempted unbound when compared to the neutral subsystems. Some calit reverts to the single hydrogen bond neutral-neutral complex, culations with the 3-21G basis set predict an overestimated binding featuring a linear N l H l O l bond with 0 2 cis to H2. This energy, probably due to the superposition error.2o In the STO-3G structure is less stable by 0.0007 au than the l a complex. This basis set, also found in other hydrogen bond systems,*' there might fact suggests that the positioning of 0 2 cis to H 3 is more stable be an error cancelation. The large superposition error inherent than to H2. Simple electrostatic attraction between the negatively in a minimal basis set is compensated by a decrease in the most charged 0 2 and the positive H 3 may account for this effect. important component of the binding energy which is electrostatic. Indeed, even though H 2 is more positive than H3, the distance The minimal basis sets predict smaller charge separation and as between 0 2 and H3 when they are cis is smaller than the distance TABLE V Energies (au) of the Proton Transfer for the Single Bond Complex
~
(19) Del Bene, J. E.; Worth, G . T.; Marchese, F. T.; Conrad, M. E. Tbeo. Chim. Acta 1975, 36, 195
~
~
~~~
(20) Boys, S . F.; Bernardi, F. Mol. Phys. 1970, 19, 553 (21) Sapse, A. M ; Fugler, L.; Cowburn, D. Int J Quantum Chem. 1986, Vol XXIX, 1241.
J . Phys. Chem. 1987, 91, 41-46 a result a smaller positive charge on H1 and a smaller negative charge on 0 1 is found. Thus the STO-3G method may give a fair estimate of the binding energies for the neutral-neutral complex. When the angle a is varied, the highest binding energy is obtained for a = Oo. The decrease in energy with the increase in a is probably due to the fact that (a) the dipole moment of the formic acid and of the imine are not coplanar and (b) the electrostatic stabilization due to the proximity of 0 2 and H 3 is removed. However, there is substantial binding energy even for cy = 90°, since the O l H l bond is not displaced. Consequently in an environment where the imine and the carboxyl are set perpendicular to each other they will still hydrogen bond. The presence of the methyl group on the nitrogen increases slightly the binding energy for the neutral-neutral complex. This effect has several probable causes. One explanation pertains to the fact that while the net atomic charge on the nitrogen is smaller in the methylated system, the change in charge from the N-methylmethylenimine to the complex is mu .h larger (0.17 eu vs. 0.1 1 eu). The positive charge on the methylene group also increases from the subsystem to the complex. Therefore one can assume that the polarization component of the binding energy is larger. Another explanation can be found by examining the H O M O which contains mostly the lone pair on the nitrogen. The HOMO also shows bonding between the in-plane p orbital of the methyl carbon and the lone pair on N. This bond is slightly increased in the complex. Obviously, this effect could not be found in the absence of the methyl group.
41
It can be concluded, for the methylenimine-formic acid and
N-methylmethylenimine-formic acid complexes, that (a) species found in the gas phase will exist as a neutral-neutral complex, (b) no barrier is found in the transfer of the proton, (c) the STO-3G basis set is not adequate for the description of the charge pair complex but predicts the correct trend in energy, and (d) even though the allyl group stabilizes somewhat the charge pair complex, the differences between the allylimine-carboxyl and methylenimine-carboxyl interaction are minimal. Outlook. All the above calculations are performed in the gas phase. However, in the methylamine-acetic acid complexz2it was shown that a polar solvent such as water stabilizes the charge pair complex preferentially. Therefore, it is to be expected that solvation may alter these results substantially. The experimental ~ ~allylimine-formic ,~~ results of Bissonnette and c o - w ~ r k e r sfor acid in chloroform and in methanol support this expectation. A future study will examine the effect of solvents on the neutralneutral and the charge pair complex through the use of a corrected Born equation.2z
Acknowledgment. A.M.S. thanks CUNY for Grant 666275. Registry No. Methylenimine, 2053-29-4; formic acid, 64-18-6; Nmethylmethyleniminium ion, 51943-18-1;N-methylallylimine, 5281336-2. (22) Gersten, J. I.; Sapse, A. M. J . Am. Chem. SOC.1985, 107, 3786. (23) Bissonnette, M.; Vocelle, D. Chem. %ys. Left. 1984, L l l l , 506. (24) Bissonnette, M.; Thanh, H. L.; Vocelle, D. Can. J . Chem. 1985, 63, 1480.
Theoretical and Experimental Studies of High-Resolution Inverse Raman Spectra of N2 at 1-10 atm M. L. Koszykowski,* L. A. Rahn, R. E. Palmer, Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550
and M. E. Coltrin Laser and Atomic Physics Division, Sandia National Laboratories, Albuquerque, New Mexico 87185 (Received: May I , 1986)
Theoretical spectra of the N2 Q branch at 295 K, from quasi-classical scattering calculations of the S-matrix elements, are compared to high-resolution inverse Raman spectra at 1, 5, and 10 atm. At 1 atm the spectrum consists of essentially isolated lines, whereas above 1 atm the spectrum collapses into one collisionally narrowed line as contributions from off-diagonal elements in the S matrix become important. The theoretical spectra are in excellent agreement with experimental spectra measured with a resolution of 0.003 cm-' and with an absolute frequency calibration of 0.001 cm-'. In particular, the theory accurately predicts the collisional contribution to the line widths of isolated lines at low pressure, as well as collisional narrowing at pressures up to 10 atm. A new scaling law with three parameters is introduced that agrees much better with the experimental data than either a power law or a simple exponential-gap model. The scaling law also predicts the temperature dependence of the diagonal elements of the S matrix calculated from quasi-classical scattering theory and is in agreement with preliminary experimental data.
I. Introduction Coherent Raman spectroscopies have become increasingly important tools as nonintrusive probes in hostile environment^.'-^ For example, coherent anti-Stokes Raman spectroscopy (CARS) has proven to be an important diagnostic technique in applications ranging from studies of state-specific chemical reactions to studies of internal combustion engines. However, to interpret fully the results of these CARS studies, it is necessary to have accurate (1) Phlat, M.; Bouchardy, P.; Lefebvre, M.; Taran, J.-P. Appl. Opt. 1985, 24,
1012.
(2) Hall, R. J.; Eckbreth, A. C. In Laser Applicafions; Ready, J. F., Erf, R. K., Eds.; Academic: New York, 1984; Vol. 5 , pp 213-309. (3) Druet, S. A. J.; Taran, J.-P. E. Prog. Quant. Electron 1981, 7, 1.
models for the Raman spectrum of the species being probed. For instance, to make accurate temperature measurements, one must first know the temperature dependence of the line shapes of the molecule being probed in a particular environment with a given set of collision partners. In general, this information is not well known, and the approximate model of Hall4 is widely used in practical applications; this model was fit to the limited data available at the time and is based on parabolic-path perturbation theory result^.^ Raman spectroscopy of molecular nitrogen is a widespread tool for determining gas temperatures in combustion devices and other (4) Hall, R. J. Appl. Spectrosc. 1980, 34, 700. (5) Robert, D.; Bonamy, J. J . Phys. 1979, 10, 923.
0022-365418712091-0041$01 .SO10 0 1987 American Chemical Society
