4216
J . Phys. Chem. 1987, 91, 4216-4218
-
change of D M in the time-resolved spectra (Figure 2a). These observations together with the inspection of time-resolved spectra may lead to the following conclusion. There exist two kinds of sites with respect to pyrene chromophores: monomer sites and dimer and/or aggregate sites. In the dimer sites, following a pulsed excitation, the fluorescence D is emitted from the excited ground-state dimer of pyrene, its decay being accompanied by a rise of the excimer fluorescence E*. The monomer emission M which originates from pyrene groups isolated along the chain backbone appears in a longer time region after the decay of the dimer fluorescence D. HPC is a rather hydrophobic polymer, with a Hildebrand solubility parameter of 10.7. The aqueous solubility of H P C is unusual. It is attributed to the formation of hydrogen bonds between water and the propylene glycol chains of the polymer. At temperatures above 0 OC in water HPC has a tendency to form aggregates and these become sufficiently extensive at elevated temperature to lead to phase separation above the lower critical solution temperature.I0 The formation of interpolymeric aggregates is enhanced in pyrene-labeled HPC. Unlike the polymer backbone pyrene groups cannot undergo hydrogen bonding with water. The number of hydrogen bonds between water molecules which are disrupted or distorted by the nonpolar pyrene groups is minimized if two or more pyrenes come in close proximity. The nonpolar dimers are then surrounded by a cage of highly organized
-
(10) Roberts, G. A. F.; Thomas, I. M. Polymer 1978, 19, 459
Ring Puckering Potential of Oxetane: TZ
water molecules tightly bound by hydrogen bonds. In this molecular environment surrounding the polymer, a pair of pyrene chromophores within a cage might be forced to make a metastable ground-state dimer. Similar behaviors of the dimer formation can be seen in silica ge15*6and zeolite’ surfaces, in LB films,8 and in cyclohexane matrix at 77 K.” Commonly to these cases, the pyrene excimer forms much faster (-0.1 ns) than in solution where the excimer formation is a diffusion-controlled process.[ The present study demonstrates furthermore another type of pyrene excimer which exhibits the fluorescence El with a peak at 420 nm which is characterized by a very fast rise and decay relative to the excimer Ez. This type of excimer has recently been reported in several different systems, viz., LB films,8 vapor deposited films,l2 and pyrene ~rysta1s.l~By reference to the bperylene single crystals reported by Matsui et al.,I4 this is expected to be of the one-center-type excimer in which the photoexcited molecule interacts simultaneously with several molecules situated around the excited molecules. Thermodynamical study will be needed to get an insight of the excimer conformation in addition to the time-resolved fluorescence study. (1 1) Mataga, N.; Torihashi, Y.; Ota, Y . Chem. Phys. Lett. 1967,1, 385. (12) (a) Mitsuya, M.; Taniguchi, Y.; Tamai, N.; Yamazaki, I.; Masuhara, H. ThinSolid Films, 1985,129, L45. (b) Taniguchi, Y.; Mitsuya, M.; Tamai, N.; Yamazaki, I.; Masuhara, H. Chem. Phys. Lett. 1986, 132, 516. (13) Matsui, A,; Mizuno, K.; Tamai, N.; Yamazaki, I. Chem. Phys. 1987, 113, 111. (14) Matsui, A. Mizuno, K.; Nishimura, H . J . Phys. SOC.Jpn. 1984, 53, 2818.
+ nP/MP4 (SDQ) Results
Harrell Sellers,* Jan Almlof, Minnesota Supercomputer Institute and Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
Svein Saeber, Department of Chemistry, Mississippi State University, Drawer CH, Mississippi 39762
and Peter Pulay Department of Chemistry, University of Arkansas, Fayetteville, Arkansas 72701 (Received: May 26, 1987)
The ring puckering potential of oxetane has been determined by the local correlation treatment of S a e b ~and Pulay employing basis sets of T Z + nP quality with n = 1-3 and Mdler-Plesset second-, third-, and fourth-order perturbation theory. The results show that the calculated values of the intramolecular dispersion interaction as well as the SCF potential are slowly convergent with respect to basis set size. The second-order perturbation results overestimate the correlation effects on the quadratic part of the potential by a factor of 2. Third-order PT corrects for this, and the fourth-order contributions are small.
Introduction Interest in the oxetane system stems primarily from the fact that the experimentally derived effective ring puckering potential possesses a small barrier to ring planarity.’-” Several theoretical ~~
~~~
( I ) Chan, S. I.; Zinn, J.; Fernandez, J.; Gwinn, W. D. J . Chem Phys
1960, 33, 1643. (2) Chan, S. I.; Zinn, J.; Gwinn, W. D. J . Chem. Phys. 1960, 33, 295. (3) Chan, S. I.; Zinn, J.; Gwinn, W. D. J . Chem. Phys. 1961, 34, 1319. (4) Chan. S. I.: Rogers. T. R.: Russell, J. W.: Strauss, H. L.; Gwinn, W. D. J.‘Chem. Phys. 19g6, 44, 1103. (5) Wieser, H.; Danyluk, M.; Kidd, R. A. J . Mol. Specrrosc. 1972,43, 382. (6) Foltynowicz, I.; Konarski, J.; Kreglewski, M. J . Mol. Spectrosc. 1981, 87, 29. (7) Creswell, R. A,; Mills, I. M. J . Mol. Spectrosc. 1974, 52, 392. (8) Makkinson, P. D.; Robiette, A. G. J . Mol. Spectrosc. 1974, 52, 413. (9) Creswell, R. A. Mol. Phys. 1975, 30, 217. (IO) Jokisaari, J.; Kauppinen, J. J . Chem. Phys. 1973, 59, 2260. (1 1) Kidd, R. A,; Wieser, H.; Kiefer, W. Spectrochim. Acta 1983, 39, 173.
0022-3654/87/2091-4216$01.50/0
studies have been performed on the oxetane system in attempts to reproduce and identify the physical origins of the barrier to ring p1anarity.l2-l6 In a recent work16 we reported results of local correlation calculations that show that the electron correlation makes a negative contribution to the quadratic potential constant of the ring puckering potential. The local correlation methodl7-l9 ( 12) Banhegyi, G.; Pulay, P.; Fogarasi, G. Spectrochim. Acta 1983, 39, 761. (13) Skancke, P. N.; Foragasi, G.; Boggs, J. E. J . Mol. Strucr. 1980, 62, 259. (14) Pulay, P.; Banhegyi, G.; Jonvik, T.; Boggs, J. E. Presented at the 9th Austin Symposium on Molecular Structure, 1982; paper TM4. ( 1 5 ) Sellers, H. Chem. Phys. Lett. 1984, 108, 339. (16) Sellers, H.; Saebm, S.; Pulay, P. Chem. Phys. Lett. 1986, 132, 29. (17) Saeba, S.; Pulay, P. Chem. Phys. Lett. 1985, 113, 13. (18) Pulay, P.; Saeba, S . In Geometrical Deriuatiues of Energy Surfaces and Molecular Properties; Jorgensen, P., Simons, J., Eds.; Reidel: Dordrecht, 1986: p 95.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 16, 1987
Letters
4217
TABLE I: Energies (in hartrees) of Oxetane
basis 6-31 1G**
ESCF+
7
0.0 0.32 0.72
6-61 lG4*
0.0 0.32 0.72
6-31 lG4*’ 6-3 1 lG4*+
19 1
-0.958 920 18 -0.958 556 82 -0.955 887 81 -0.965 848 76 -0.965 529 50 -0.962 950 72 -0.966 928 25 -0.966 67 1 88 -0.964 242 35 -0.968 742 94 -0.968 463 76 -0.965 952 09
0.0 0.32 0.72 0.0 0.32 0.72
MP2
MP3
MP4
-0.621 201 98 -0.621 471 35 -0.62271393 -0.653 924 87 -0.65421941 -0.65552961 -0.655 158 81 -0.655 474 56 -0.656 846 92
-0.65321081 -0.653 352 89 -0.654074 34 -0.684 432 97 -0.684 586 13 -0.685 340 80 -0.685 31664 -0.685 478 95 -0.686 261 82
-0.660 504 83 -0.660 647 40 -0.661 395 48 -0.690 748 63 -0.690 909 28 -0.691 705 18 -0.69 1 779 05 -0.691 954 93 -0.692 797 66
EtOta1+191 -1.61942501 -1.61920422 -1.61728329 -1.656 597 39 -1.656438 78 -1.654655 91 -1.658 707 30 -1.658 626 82 -1.65704001
TABLE II: Puckering Potential of Oxetane (in cm-’)
SCF basis
A
6-31 1G** 6-311G4* 6-31 lG4*’ 6-311G4*+ exptl
655 551 405 455 -84 (-238)
MP2
B 1214 1304 1412 1402 930
A 93 -68 -262
allows a chemically meaningful interpretation of the pair energies, and we observed from our previous workI6 that the negative contribution to the quadratic puckering potential constant is contained in the many weakly correlating (nonbonded) pairs. We also observed that the nonbonded interactions with the oxygen lone pairs are primarily responsible for this intramolecular dispersion energy. We concluded that this intramolecular dispersion energy and the vibrational modulation would ultimately account for the barrier in the puckering potential. Previous local correlation (ACCD) calculations performed with a basis of D Z P qualityI6 yielded a barrier of about 2 cm-’, much lower than the experimental value of 15 cm-I. Since the barrier is essentially an intramolecular van der Waals effect, it is reasonable to suspect from past experience with van der Waals potentials that the D Z + P quality basis is far from adequate. We have performed calculations of the oxetane puckering potential with basis sets from T Z P to TZ 3P quality accounting for electron correlation through the fourth order of Moller-Plesset perturbation theory. The results of these calculations, presented below, give valuable information regarding the level of accuracy one might expect from calculations at this level of similar potential functions in which a van der Waals contribution is important.
+
+
+
Calculations and Results Our MP4 (SDQ) calculations were performed with the basis sets 6-31 1G**,206-31 lG4*,21and a version of the 6-31 lG4* basis in which a diffuse set of d functions has been added to the oxygen (we will denote this basis as 6-31 lG4*’). We performed an additional set of S C F calculations with a version of the 6-31 lG4* basis (denoted 6-31 lG4*+) in which a diffuse set of d functions has been added to all the heavy atoms. All of the calculations presented here were performed on the CYBER 205 at the Minnesota Supercomputer Institute. Previous calculations showed that adding additional polarization functions to the hydrogens had no effect on the puckering potential.I6 The local correlation program described was used. In all the calculations presented here the local domain17assigned to a bicentric localized orbital consists of the AOs of the two atoms. The local virtual space for the pair correlation between orbitals i and j consists of the union of the domains of i and j projected against the internal orbitals. Excitations from the core orbitals were not included. By restricting the virtual space for orbital pair correlation as mentioned above, the basis set superposition error is reduced. As (19) Pulay, P.; Saebra, S. Theor. Chim. Acta 1986, 69, 3 5 7. (20) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 6 5 0 . (21) Pulay, P.; Lee, J.-G.; Boggs, J. E. J . Chem. Phys. 1983, 79, 3382.
MP3
B 1063 1188 1321
A 366 237 70
MP4
B 1067 1169 1286
A
B
367 221 41
1043 1158 1282
regards this application, it is difficult to overstate the advantage of the local correlation treatment. These calculations would require much more computer time if performed in the canonical basis. Following Banhegyi et al.,12we take the puckering coordinate to be half the sum (in phase) of the four ring torsions. We calculate the energy of oxetane at three values of the puckering coordinate (0,0.32, and 0.72 rad) and fit these values to a two-term potential expression. The other 23 internal coordinates were relaxed at each value of the puckering coordinate with the 5-31G* basis. We believe that the changes in the geometrical parameters arising from the changing puckering coordinate are accurately described at the S C F level. The integral neglect threshold and SCF convergence criterion were set to small values to ensure that no fortuitous artifacts would contaminate the results. Table I contains the energies of oxetane at the three values of the puckering coordinate obtained with the four basis sets employed. The values under the heading MPn are the correlation energies through nth order. The values in the column headed E total are the sum of the S C F and MP4 energies. The puckering potential can be compactly represented as a two-term expression, I/ = Ar2 Br4. For negative values of the quadratic constant the barrier height is given by A2/4B. In Table I1 we present potential constants obtained by fitting the S C F and correlation contributions to this functional form. The values in the columns headed MPn are the puckering potential constants (SCF + correlation contributions) through nth order. Since the experimental puckering potential contains the vibrational modulation, we have subtracted this contribution from the experimentally determined potential. The value in parentheses in the row labeled “exptl” is the quadratic potential constant before the vibrational modulation subtraction. The data of Table I1 and Figure 1 show that the S C F potential has not converged with respect to basis set size as previously thought.I6 The general trend is for the S C F potential to become more flat with the addition of polarization functions. The S C F potential obtained with the 6-31 1G4*’ basis is out of line in this trend, but in this basis the oxygen has three sets of d functions and the carbons have two. In the other three basis sets the carbons and oxygen have the same number of d functions. When the basis is changed, a slightly different slice of the potential surface is obtained; however, the fact remains that the Hartree-Fock energy difference between two different geometries of the same molecule is not constant to within 0.1 mE with respect to basis set size at the T Z + nP level. The changes at the S C F level are thought to be changes in bonded interactions. An opposite trend is seen in the correlation contributions to the puckering potential from the electron correlation. As the d space of the basis is improved, the intramolecular van der Waals potential becomes more curved.
+
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The Journal of Physical Chemistry, Vol. 91, No. 16, 1987
Letters
SCF P C T E N T I A L CIJRVES
THEORETICAL P O T E N T I A L CONTRIBUTORS 450
,
I
,
,
,
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Figure 3. The three components of the theoretical puckering potential (6-31 lG4*'): SCF, curve A; MP4, curve B; vibrational modulation, curve
C. / -
6-31 lG4*' basis and the vibrational modulation contribution, showing the three theoretical components of the puckering potential. Both the S C F and correlation trends with respect to basis set size are in the direction of the experimentally derived results. Once again we observe that the MP2 values overestimate (as judged by the MP4 results) the magnitude of the correlation contribution to the quadratic potential constant. The MP3 and MP4 results are seen to be very similar.
2
160
$
140
Conclusion
120
The calculations presented herein are the highest quality calculations performed to date on a system of this kind and size. As in our earlier calculations,16 we observe that the quadratic contribution to the puckering potential is primarily due to the intramolecular dispersion interactions involving the oxygen lone pairs. It is well-known that potentials of van der Waals complexes are difficult to describe accurately owing to the relative smallness of the interactions and the level of theory that must be employed. The results presented above of TZ + nP quality suggest that the same is probably true of such potentials in which an intramolecular van der Waals interaction is important.
w
2
'"Li 60
40
20
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- 5
- 4
- 3 - 2
-.l
8
1
.2
3
.4
5
6
7
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+
Figure 2. Total theoretical puckering potentials (SCF MP4 (SDQ) correlation the vibrational modulation contribution): 6-31 1G*". curve A; 6-31 1 G4*,curve B; 6-31 lG4*', curve C.
+
Figure 2 illustrates the basis set dependence of the total theoretical puckering potential (SCF + correlation through fourth order + vibrational modulation). Figure 3 is a plot of the S C F and fourth-order correlation potential contributions obtained with the
Acknowledgment. This work was supported by Grant 86PCR24 from the Control Data Corporation, by the Minnesota Supercomputer Institute, and the donors of the Petroleum Research Fund, administered by the American Chemical Society. H.S. thanks Mr. Roland Schweitzer of the ETA Corporation and Dr. Bruce Loftis of the Minnesota Supercomputer Center for valuable help with program adaptation.
