J . Phys. Chem. 1987, 91,4464-4466
4464
Theoretical Vibrational Investigation of Hydrogen-Bonded Complexes: Application to ClWNH3, ClHwNH,CH,, and BrHwNH, Y. Bouteiller,* C. Mijoule, Laboratoire de Dynamique des Interactions MolPculaires,? UniversitP Pierre et Marie Curie, Tour 22, 75230 Paris Cedex 05, France
A. Karpfen, H. Lischka, and P. Schuster Institut fur Theoretische Chemie und Strahlenchemie der Universitat Wien A, 1090 Wien, Austria (Received: October 13, 1986; In Final Form: April 17, 1987) Previously reported ab initio calculations at the SCF and SCF + CI level are used for the infrared vibrational study of three closely related X-H-Y (X = C1, Br; Y = NH3, NH2CH3)hydrogen-bonded complexes. The force constants are computed up to the fourth order by means of a numerical procedure. A variational method, suitable in the case of strong coupling between two vibrations, is used to compute the vXH and v ~ ~stretching . . ~ modes as well as the corresponding deuteriated modes for the three complexes.
Introduction
The gas-phase reaction between NH3 and HCl has been the subject of several investigations and this interest is maintained by the possible role of this reaction in the stratosphere.' In the field of electronic calculations, since the historical work of Clementi et al.,273several theoretical studies have been performed on this complex."8 It has been recently shown8 that minimal basis sets lead to an overestimation of the interaction between the two monomers and that split valence basis sets erroneously predict an ion-pair structure (H,NH+-CI-), a conclusion which is reversed by polarization of each basis. In the work of Raffenetti and PhilipsS an a b initio calculation is carried out at the S C F C I level using a basis set with polarization functions. A significant result of this work is that C1H-NH3 is a neutral-type complex as in the case of S C F calculations using basis sets with polarization functions. More recent calculations performed at the S C F and S C F C I level using double { plus polarization functions' have been reported for CIH-NH, and closely related complexes. All these calculations lead to a single minimum determination of the potential energy surface except for the BrH-NH2CH3 complex which presents a very flat double minimum for proton transfer. The vibrational calculations reported up to now2S5 take into account only the quadratic force constants. The purpose of this paper consists of first obtaining an analytical determination of the potential energy curves for X H (X = C1, Br) monomers and the computation of the related uXH stretching modes. These calculations verify the quality of the electronic basis sets and contributing improvements of the CEPA method. The second part of the vibrational calculations includes the analytical determination of the potential energy surfaces for XH-Y (X = C1,Br; Y = NH,, NH2CH3) complexes and the computation of vXH and vXH.ystretching modes of the complexes. The vibrational calculations are performed for one or two dimensions by taking into account the mechanical anharmonicity effects by means of a variational method. In the case of one as well as two dimensions, previously scanned potential curves (or surfaces)' have been used.
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Vibrational Calculations A . Calculation of the vXH Monomers Stretching Modes. In
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the Schriidinger equation (p2/2p V(r))$(r) = E$(r) where 7' = mX-l + mH-l,the one-dimensional V(r) potential function is expanded as a polynomial up to the fourth order. The expansion coefficients are calculated by using the method of orthogonal polynomials. The Schrodinger equation is then solved by the variational method, the eigenfunctions $,(r) being taken as an 'Equipe de Recherches du C.N.R.S. No. 271. 0022-3654/87/2091-4464$01.50/0
TABLE I: Expansion Coefficients (in mdyn/kl) of the Potential and Vibrational Transitions (in em-') for CIH and BrH MonomersQ
CIH a2
a3 a4 YXH
SCF
SCF + CI
BrH SCF
2.863 -5.250 6.379 3084 3162b
2.665 -5.087 5.706 2949 (2885e) 305 1
2.314 -3.726 3.854 2755 (2506) 2829
V ( r ) = x p a f . bThe vibrational transitions on this line are given in the harmonic approximation, Le., a, = 0, a4 = 0. 'The numbers quoted in parentheses represent the experimental data.
expansion of the eigenfunctions of the harmonic oscillator. The expansion coefficients are shown in Table I for both monomers in the case of SCF and S C F C I calculations. Likewise, the related stretching modes are reported in Table I as well as the experimental data. It can be seen from the comparison between the S C F C I calculated value 2949 cm-' of the vCIH stretching mode and the 2885-cm-' experimental data that the 64-cm-' difference represents a relative error of about 2.2%. At the S C F level of calculation this relative error increases to 6.9% for ClH and 9.9% for BrH monomers. The contribution of the mechanical anharmonicity is of the same order of magnitude. At the S C F level the relative errors increase from 6.9 to 9.6% for ClH and from 9.9 to 12.9% for BrH monomers. For S C F C I calculation the relative error increases from 2.2 to 5.7% for CIH. It is expected from this brief analysis that vibrational transitions of ClH-NH, complex, calculated by taking into account the electronic correlation effects and the mechanical anharmonicity, may be of the same order (2%) of error as obtained for the vCIH stretching mode of the C1H monomer. B. Calculation of the v ~ ~Complexes . . ~ Stretching Modes. a. The Method. The vXH and uXH..y stretching modes have been calculated by using a previously reported variational m e t h ~ d . ~
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(1) Heicklen, J.; Luria, M. Int. Chem. Kinet. Symp. 1975, 567, 1 ; Proceedings of the Symposium on Chemical Kinetics f o r the Upper and Lower Stratosphere, 19-1 8 Sept. 1974. (2) Clementi, E. J . Chem. Phys. 1976, 47, 2323. (3) Clementi, E.; Gayles, J. W . J . Chem. Phys. 1976, 47, 3837. (4) Kollman, P.; Johansson, A.; Rothenberg, S . Chem. Phys. Lett. 1974, 24, 199. ( 5 ) Raffenetti, R. C.; Phillips, D. H. J . Chem. Phys. 1979, 71, 4534. (6) Latajka, Z.; Sakai, S.; Morokuma, K.; Ratajczak, H. Chem. Phys. Lett. 1984, 110, 464. (7) Brciz, A.; Karpfen, A,; Lischka, H.; Schuster, P. Chem. Phys. 1984, 89, 331. ( 8 ) Latajka, 2.;Scheiner, S.J. Chem. Phys. 1985, 82, 4131. (9) Lavenir, E.; Bouteiller, Y.; Mijoule, C.; Leclercq. J. M. Chem. Phys. Lett. 1985, 117, 427.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 17, 1987 4465
Vibrational Investigation of Hydrogen-Bonded Complexes
TABLE 111: Convergence of the Variational Method on CIH-NH3 (SCF + CI) size of the vibrational basis set transitions nm-n'm" 10 X 10 16 X 16 18 X 18 20 X 20 22 X 22
TABLE II: Expansion Coefficients"of the Potential for the Hydrogen-Bonded Complexes CIH-NH3, ClH..NH2CH3,and BrH-NH3
ClH.*NH, SCF SCF+CI
__ all
~ 0 2
a30 021
a12 a03 040
022 (104
CIH-NH2CH3 SCF
BrH-NH,
2.239 0.190 0.109 -5.309 0.805 -0.193 -0.160 4.917 0.668 -0.801 0.160 0.108
1.816 0.144 0.078 -3.765 0.566 -0.165 -0.106 3.098 1.069 -0.850 0.153 0.073
1.938 0.213 0.132 -4.503 0.510 0.004 -0.240 3.835 -0.188 -0.071 -0.344 0.249
2.382 0.197 0.106 -5.575 0.379 -0.459 -0.08 4.879 -0.188 -1.325 -1.153 0.143
----
SCF
00 01 00 02 00 03 00 04 00 05 00+06 00-07 4
00-08 00 09
V(r,R) = E~-oE~$,a&Rq. The results are given in mdyn/&'+q-l. Only a brief review of this method is presented here. The Schrainger equation H\k(r,R) = E\k(r,R) with !p
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10 11 12 13 14 15
201 39s 585 774 964 1159 1357 1560 1769
20 1 395 585 774 964 1159 1357 1560 1768
20 1 395 585 774 964 1159 1357 1560 1768
20 1 395 585 774 964 1159 1357 1560 1768
2262 2500 2726 2941 3149 3354
2257 2504 2724 2939 3146 3349
2253 2498 2724 2939 3146 3348
2251 2497 2724 2939 3146 3348
2249 2496 2724 2939 3146 3348
"nand m are the quantum numbers referring to the uCIH and Y vibrations, respectively.
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TABLE I V Vibrational Transitions' for ClH-NH,, CIH-NH2CH3, and BrH-NH2 Hvdrogen-Bonded Comdexes
m, dr aR
2p'
0000 00 000000-
20 1 395 585 774 966 1180 1395 1735
is solved for the internal degrees of freedom r and R when r is related to the X-H distance and R to the X-Y distance. The reduced masses are given by p-l = m;' + mH-I, p'-I = mx-l my-]. The eigenfunctions \ka(r,R) are written as an expansion of products of the eigenfunctions of the harmonic oscillator
ClH.sNH3 CIH**NH2CH, BrH-NH, SCF SCF+CI SCF SCF Harmonic Approximation
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n n
XH XH-Y(H) XD XD-Y(D)
2888 172 2072 162
XH XH-Y(H) XD XD-Y(D) XH/XD
2501 162 1876 156 1.333
2606 192 1873 180
2800 146 2007 139
2516 135 1779 126
Anharmonic Results In the Hamiltonian, the potential function is expanded as a polynomial in two dimensions N N-P
V(r,R) =
p=oq=o
apqrpRq
(3)
to the required order to ensure a good representation of V(r,R) with regard to the electronic calculations. The secular determinant lHjj - E6jjI = 0 is solved and provides the eigenvalues and the eigenvectors. b. Calculation of the Expansion Coefficients of the Potential Functions v(r,R). Grids of V(r,R)have been constructed involving a number of points depending on the complex considered. The 2 coefficients of the expansion 3, up to the fourth order, have been computed by using the method of orthogonal polynomials. The result are reported in Table 11. As the values of the coefficients of the expansion are dependent on the size of the grid, it is not easy to find a criterion for the choice of the grid. For each complex, the size of the finally chosen grid is such that the uppermost points involved in are at least 3/2hWX-H far from the minimum of the potential energy surface. Under these conditions, the mean size of displacement around the equilibrium position is 0.3 A for r and 0.3 A for R . The coefficients of the expansion are then used to restore the original data. The points of the potential energy surface are reproduced with an averaged accuracy which is always better than 10 cm-I. This represents sufficiently accurate result to undertake vibrational calculations. From Table I1 it is seen that the quadratic force constant azo is substantially decreased by passing from the S C F C I calculation for the ClH-NH3 complex. On the other hand the ao2force constant is increased by nearly a factor of 1.3. These changes are consistent with those observed for the equilibrium geometry.' Such trends have been previously observed for hydrogen-bonded complexes.lOJI
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a (10) Bouteiller, Y.;Allavena, A.; Leclerq. J. M. Chem. Phys. Lerr. 1981, 84, 361.
2249 20 1 1645 186 1.367
2365 144 1777 137 1.33 1
2084 144 1564 136 1.332
"The results are given in cm-I. The sets of force constants present similarities up to the constants a2' for the three closely related complexes at the level of S C F or S C F C I calculations. c. Calculation of the vXH and v X H . . ~Stretching Modes. For each complex the secular determinant has been solved for different sizes of the vibrational basis set to study the convergence of the variational method. For the C1H-NH3 complex at the S C F as well as at the SCF CI level the convergence is attained: In Table I11 the transitions are listed as an example for the S C F + CI level. From this table it is seen that the overtones of the vCIH+, transition, the vCIH transition, and associated combination bands vCIH + mvCIH..N converge in a range equal to or smaller than 2 cm-'. For the same size of the basis set (22 X 22) the convergence is very much slower for the ClH-NH2CH3 and BrH-NH3 complexes and stands in a range of 20 cm-'. An absolute convergence would be attained either by using a very much larger basis set or by improving the convergence with a potential energy surface fitted with a more adapted function than a polynomial. A sum of two-dimensional Morse functions would probably represent an answer to this problem. The results for the three complexes are listed in Table IV. As expected from the differences observed between the a20and ao2coefficients, the vCIH stretching mode of the ClH-NH, complex is lowered and the YCIH..NH, symmetric stretch is increased by passing from the S C F to the S C F C I level of calculation. These trends have been previously observed for hydrogen-bonded For the vCIH stretching mode the difference between the S C F and the S C F + C I calculation is greater than 250 cm-' which emphasizes the necessity of taking the electronic correlation effects into consideration. In the har-
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(1 1) Szczesniak, M. M.; Scheiner, S.; Bouteiller, Y . J . Chem. Phys. 1984, 81. 5024.
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J. Phys. Chem. 1987, 91, 4466-4470
4466
monk approximation, there is a good agreement with the Raffenetti calculation for the ClH-NH, complex. The S C F C I calculation of Brciz et al.' provides a value of 2606 cm-I for the uCIHtransition close to the value 2550 cm-' of Raffenetti. The anharmonicity effects, however, are quite important because they decrease this transition by an additional 357 cm-l. Another comparison is instructive. In the harmonic approximation, the SCF calculation gives a value of 2888 cm-' for the uCIHtransition of the ClH-NH, complex. The comparison with the value 2249 cm-' of the S C F C I calculation which includes the anharmonicity effects in the vibrational study shows that both electronic correlation effects and anharmonicity effects are responsible for a decrease of nearly 640 cm-' for this transition. At the level of experimental study the infrared spectra of ClH-NH, complex has been recorded for the first time by Ault and Pimentel12 in a nitrogen matrix at low temperature. More recently several author^'^-'^ have shown that the assignment of the infrared spectra is strongly dependent on the nature of the matrix. For the uCIH transition, the present result, which disregards the environmental effects cannot be compared to the experimental . . ~ stretch, however, seems to be less data. The v ~ ~symmetric sensitive to the matrix effects and the present values of 162 and 201 cm-' calculated a t the SCF and S C F C I levels may be compared to the values 166 and 130 cm-' recorded in Ar and N2 matrices, r e ~ p e c t i v e l y . ~A~ ~similar '~ analysis stands for both C1H-NH2CH3 and BrH-NH3 complexes. For BrH-NH,, the uBrHWNsymmetric stretch has been recently assigned at 110 cm-I by subtraction from an N H 3 rocking mode.16 The corresponding
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(12) Ault, B. S.; Pimentel, G. C. J . Phys. Chem. 1972, 77, 1649. (13) Schriver, L.: Schriver, A,; Perchard, J. P. J . Am. Chem. SOC.1983, 105, 3843. (14) Barnes, A. J.; Beech, T. R.; Mielke, Z. J . Chem. Soc., Faraday Trans. 2 1984. 80. 455. (15) Barnes, A. J.; Kuzniarski, J. N. S.; Mielke, Z. J. Chem. SOC.,Faraday Trans. 2 1984, 80, 465. (16) Barnes, A. J.; Wright, M. P.J . Chem. SOC.,Faraday Trans. 2 1986, 82, 165.
value, 144 cm-I, calculated in the present work confirms this assignment. The mechanical anharmonicity of this symmetric stretch is not very large because the first calculated overtone occurs at 297 cm-'. The present S C F calculation presumably overestimates this overtone mode by 30-50 cm-I. As a consequence, it is not obvious that the band located at 302 cm-I may readily be assigned to this overtone which may be a rocking or a bending mode. The final assignment of the uC1H-N symmetric stretching mode of methylamine-hydrogen chloride complex has not yet been made. The fundamental and the first overtone transitions have been calculated at 144 and 302 cm-I, respectively. Taking into account the overestimation due to the S C F calculation, this symmetric stretching mode is expected to lie in the range of 110-120 cm-'. On the other hand, the 220-cm-' band possibly corresponds to this overtone. Conclusion
It has been first c o n f i i e d that the differences observed between the S C F and S C F C I levels of calculation for the ClH-NH, complex are substantial and lead to a strong reduction of the vXH transition value. The second relevant point is the inadequacy of the harmonic approximation in describing the vibrational properties of such medium-strength hydrogen-bonded systems well. In Table IV, the differences calculated between the uXH transitions taking into account the whole set of coefficients of the potential energy and the um transitions in the harmonic approximation demonstrate that only a variational method leads to a correct description of coupled anharmonic vibrational modes. In most of the cases treated here, the perturbation method, even at the second order, is certainly not convergent.
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Acknowledgment. Y.B. and C.M. are indebted to the "Centre de calcul d'Orsay" for allowing them to make use of facilities on N A S 9080 and IBM 3090/200. Registry No. HC1, 7647-01-0; HBr, 10035-10-6; NH3, 7664-41-7; NHZCH,, 74-89-5; Dz,7782-39-0.
Calculated Circular Dichroism of the n-r* Transition In N-Acetylglucosamines Aaron H. Coben and Eugene S. Stevens* Department of Chemistry, University Center at Binghamton. State University of New York. Binghamton. New York 13901 (Received: January 16, 1987; In Final Form: May 4 , 1987)
The rotational strength of the amide n-r* transition of 2-acetamido-2-deoxy-~-glucopyranoses is calculated as a function of CI hydroxyl, C3 hydroxyl, and acetamido group orientations. The results explain features of the circular dichroism (CD) solvent dependence observed with a-GlcNAc-OMe and 0-GlcNAc-OMe, including a strong anomeric effect. The results are also relevant to the CD of glycosaminoglycans.
Introduction
Beychok and Kabat first reported carbohydrate Cotton effects near 220 nm and assigned them to the n-r* transition of acetamido gr0ups.l That assignment has been supported in subsequent work.2,3 In an early theoretical treatment of the circular dichroism (CD)4 of acetamido sugars it was shown that a major source of optical activity was coupling of the n-r* transition with the strong acetamido r-r* transition near 190 nm.j (1) Beychok, S.; Kabat, E. A. Biochemistry 1965, 4 , 2565-2574. (2) Stone, A. L. Biopolymers 1971, 10, 739-751. (3) Coduti, P. L.; Gordon, E. C.; Bush, C. A. Anal. Biochem. 1977, 78,
9-20. (4) Abbreviations used are a-GlcNAc, 2-acetamido-2-deoxy-a-~-glucopyranose; 8-GlcNAc, 2-acetamido-2-deoxy-~-~-glucopyranose; a-GlcNAcOMe, Omethyl-2-acetamidc-2-deoxy-a-~glucopyraide; p - G l c N A d M e , O-methyl-2-acetamido2-deoxy-~-~-glucopyranoside: CD, circular dichroism.
0022-3654/87/2091-4466$01 .50/0
There are now three reasons for reexamining and extending that early theoretical study. First, the solution properties of polysaccharides in general, and glycosaminoglycans in particular, have attracted increased attention as appreciation for their biological significance has Circular dichroism has proved a sensitive probe of polysaccharide conformation8 and the n-r* C D of glycosaminoglycans has been noted to display substantial ~ a r i a b i l i t y , ~but - ' ~the significance of that variability will remain ( 5 ) Yeh, C.-Y.; Bush, C. A. J. Phys. Chem. 1974, 78, 1829-1833. (6) Solution Properties of Polysaccharides; Brant, D. A,, Ed.: ACS Symposium Series 150; American Chemical Society: Washington, DC, 1981. (7) Molecular Biophysics of the Extracellular Matrix; Arnott, S., Rees, D. A,, Morris, E. R.,Eds.; Humana: Clifton, NJ, 1984. (8) Morris, E. R.,Frangou, S. A. In Techniques in Carbohydrate Metabolism; Elsevier: London, 1981; Vol. B308, pp 109-160. (9) Cowman, M. K.; Bush, C. A.; Balazs, E. A. Biopolymers 1983, 22, 1319-1 334.
0 1987 American Chemical Society
