J . Phys. Chem. 1990, 94, 3313-3316 mogeneous liquid (Figure 2e) are ascribed to random noise as discussed below. As a further test of the significance of the observed fluctuations, we plotted the histogram for our data, Le., the fraction of time that a particular signal is recorded vs the signal (Figure 3). While there is always a statistical spread in any measurement, the distributions shown in Figure 3b-d do not look like any simple one. In the case of a purely random source of noise, as, for example, noise from the laser and detection systems, one expects a Poisson distribution of the data.I3 In Figure 3a,e, the line corresponds to a Poisson distribution centered at the average measured signal. The fits to the data are excellent and thus support our contention that the noise in the data at these coverages is random noise. Furthermore, it is obvious that such a distribution will not fit Figure 3b-d. However, it looks like these data can be fitted by a linear combination of the fits to Figure 3, a and e. This is consistent with the interpretation noted previously, that at 150, 300, and 600 A2/molecule we are looking at a heterogeneous surface that consists of liquidlike and gaslike regions. We can also calculate the autocorrelation for each set of data. In Figure 4 is shown (AI(0)AI(t))vs time for the different surface coverages. The data for 150, 300, and 600 A2/molecule show a monotonic decay in the correlation function, which can be fitted to an exponential. All three sets of data give approximately the same correlation time of 6 f 1 s. Since the high signals obtained for measurements at 150, 300, and 600 A2/molecule, Le., in the coexistence region, are of the same magnitude as the signal obtained for the pure liquid state, e.g., at 75 A2/molecule, we conclude that the clusters are comparable in size with our incident beam. With this we make the plausible assumption that there is at most one cluster in the region of observation. We then determine the diffusion constant of the cluster from the measured correlation time and find a value of about lo-* cm2/s. ( I 3) Cova, S.; Longoni, A. In Analytical Laser Spectroscopy; Omenetto, N., Ed.; Wiley: New York, 1979; Vol. 50.
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The above estimate on the size of the clusters is smaller than what is estimated by ellipsometry8 and light scattering," which also differ from each other in the gas-liquid region. The differences observed can be due to differences in the method of preparation as well as the presence of P N P in the subphase. We believe that the fluctuations in the S H signal in Figure 2b-d are similar in origin to those observed by other technique^.**^^" However, in our measurements, we are able to adjust the time resolution; this enables us to analyze the fluctuations and extract a decay constant for their time correlation. This time constant of approximately 6 s is much faster than any time dependence indicated from measurements of ellipsometry* and surface potential,9 but slower than that obtained from light-scattering experiments." This discrepancy could possibly be due to differences in size of the clusters as previously mentioned.
Conclusions We have shown that fluctuations in the second harmonic signal can be utilized in the study of a heterogeneous surface, such as phase coexistence in two dimensions, as exemplified by the gasliquid coexistence in the spread monolayer of palmitic acid. Furthermore, we have illustrated a means of examining timedependent phenomena related to diffusion at the surface, which could be applied to other heterogeneous surface coverages. The observed fluctuations in the S H signal has a correlation time of 6 f 1 s for the three coverages (1 50, 300, and 600 A2/molecule) that are inside the gas-liquid coexistence region. We attribute this to the motion of the liquidlike clusters. If their motion is diffusive, we estimate a diffusion constant for the clusters of about IO-* cm2/s. Acknowledgment. We thank Prof. B. Whaley for the helpful discussions. We gratefully acknowledge support from the National Science Foundation, the Air Force Office for Scientific Research, and the donors of the Petroleum Research Fund, administered by the American Chemical Society.
A Theoretical Study of the Proton Affinities of Some Phosphorus Compounds Robert G.A. R. Maclagan Department of Chemistry, University of Canterbury, Christchurch, New Zealand (Received: December 18, 1989)
The proton affinities of PN, PO, PS,and HCP have been calculated in good agreement with values obtained from photon-transfer experiments. The effect on the calculated proton affinity of the basis set, level of theory, basis set superposition energy correction, and zero-point vibrational energy correction were studied. Protonation at the P atom is not preferred.
Introduction The observation by Turner and Bally' and Ziurys2 of P N in interstellar space has stimulated interest in the chemistry of other phosphorus-containing molecules that may exist in interstellar space. PH3 has been observed in the Jovian atmosphere. The reactions of the ions PH,' ( n = 0-4) with various neutral molecules have been studied by Thorne, Anicich, and Huntress3 and Smith, McIntosh, and Adams4 Maclagad has carried out a b initio calculations on the ion C2H2P+formed in some of these reactions. Recently the proton affinity of PN, PO, PS, and HCP E.;Bally, J. Astrophys. J . 1987, 321, L75. (2) Ziurys, L. M. Astrophys. J . 1987, 321, L81. (3) Thorne, L. R.; Anicich, V. G.;Huntress, W. T. Chem. Phys. Lett. 1983, 98, 162. (4) Smith, D.; McIntosh, B. J.; Adams, N . G.J . Chem. Phys. 1989, 90, 6213. ( 5 ) Maclagan. R. G . A. R Chem. Phys. Lett., in press. ( 1 ) Turner, B.
0022-3654/90/2094-3373$02.50/0
have been measured by Adams, McIntosh, and Smith.6 In this paper ab initio calculations of these proton affinities are reported in very good agreement with the measured values of Adams, McIntosh, and Smith. Except for HNP' and POH', ab initio calculations at different levels of theory and with different basis sets have been previously reported for these molecules and their protonated forms. The aim of this study is to obtain as reliable an estimate of the proton affinity using the same large basis set and high level of theory. Recent calculations include the study of Ahlrichs et al.' on PN, the studies of P O by Lohr and Boehm8 and Bruna and Grein? the study of HPO' by Nguyen, Hegarty, Ha and Brint,lo the study (6) Adams, N. G.;McIntosh, B. J.; Smith, D. Astron. Asrrophys., in press. (7) Ahlrichs, R.; Bar, M.; Plitt, H. S.; Schnockel, H. Chem. Phys. Lett. 1989, 161, 179. ( 8 ) Lohr, L. L.; Boehm, R. C. J . Phys. Chem. 1987, 91, 3207. (9) Bruna, P. J.; Grein, F. J . Phys. E : At. Mol. Phys. 1987, 20, 5967.
0 1990 American Chemical Society
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Letters
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
TABLE I: Calculated Energies for Various Phosphorus-Containing Molecules E. hartrees H FJ H FJ MP2 J SDecies level of theory 6-31G*' 6-31 IG**" 6-31 IG**' PN HF -395.12575 -395.15804 -395.149 70 -395.423 35 -395.593 94 -395.600 12 MP2(FU) MP4SDQ -395.414 35 -395.456 18 -395.458 89 MP4SDQ( BSSE) -395.417 17 -395.458 35 -395.464 80 -395.44607 -395.483 75 -395.478 67 PNH+ H F -395.72663 -395.907 45 -395.91 1 59 MP2(FU) -395.725 12 -395.771 57 -395.779 46 MP4SDQ -395.273 05 NPH+ HF -395.588 15 MP2(FU) -395.57905 MP4SDQ -415.54833 -415.58596 -41 5.585 43 PO HF -415.83672 -416.02286 -416.02445 MP2(FU) -415.833 59 -415.88995 -415.891 38 MP4SDQ MP4SDQ( BSSE) -415.83561 -415.897 56 -41 5.898 96 -415.83802 -415.88309 -415.881 81 POH+ HF -4 I 6.106 8 I -41 6.304 91 -416.306 IO MP2(FU) -416.11065 -41 6.178 7 1 -41 6.179 75 M P4SDQ -415.788 17 OPH+ HF -416.03763 MP2(FU) MP4SDQ -416.05256 PS HF -738.22069 -738.25843 -738.25039 MP2( FU) -738.426 98 -738.69681 -738.71680 MP4SDQ -738.436 1 I -738.482 33 -738.495 13 MP4SDQ( BSSE) -738.452 35 -738.500 76 -738.50203 PSH' HF -738.491 81 -738.53699 -738.535 76 -738.704 18 -738.988 04 -738.99066 MP2( FU) -738.7 15 88 -738.776 21 -738.777 49 MP4SDQ -738.486 31 SPH+ HF MP2(FU) -738.694 57 -738.708 14 MP4SDQ -379.10530 -379.13801 -379.135 45 HCP HF -379.359 21 -379.533 57 -379.535 78 MP2(FU) MP4SDQ -379.358 22 -379.405 73 -379.407 08 -379.38960 -379.42043 -379.420 21 H2CP+ H F -379.61 5 62 -379.793 31 -379.793 52 MP2(FU) MP4SDQ -379.62947 -379.68028 -379.680 53 HCPH' H F -379.30291 MP2(FU) -379.557 90 MP4SDQ -379.559 16
TABLE 11: Calculated Energies for the Process AH+
Various PhosDhorus-Containing Molecules
~
AE (incl ZPVE) AE + (incl scaled ZPVE) (incl BSSE) AE + (incl ZPVE) + (incl scaled ZPVE)
HFJ 6-31G* PN 815.9 783.1 786.7 808.5 775.7 779.3
AE (incl ZPVE) AE + (incl scaled ZPVE) (incl BSSE) + (incl ZPVE) + (incl scaled ZPVE)
calculation
-
A+
+ H+for
AE, kJ mol-' HFJ MP2J 6-311G** 6-311G** expt" 842.6 810.2 813.8 826.4 794.1 797.6
841.7 809.3 812.9 826.1 793.8 797.4
799
PO 727.4 700.2 703.2 722.1 694.9 697.9
758.1 730.9 733.9 738.2 710.9 713.9
757.1 729.9 732.8 737.2 710.0 713.0
982
LE (incl ZPVE) AE (incl scaled ZPVE) (incl BSSE) AE + (incl ZPVE) + (incl scaled ZPVE)
PS 734.4 712.3 714.8 691.9 669.7 672.2
77 1.6 750.1 752.5 723.2 701.7 704.1
741.3 719.8 722.2 723.2 701.7 704.1
699
AE (incl ZPVE) AE + (incl scaled ZPVE)
HCP 712.2 688.2 690.8
720.8 697.6 700.2
717.9 694.7 697.3
699
+
(I
Reference 6.
P-
N-H
P-
0
/H
N-P-
0 -
H
I
P
'Geometry optimized at this level of theory.
of PS by Bruna and Grein,9 the study of HPS' and HSP' by Nguyen," the studies of Lehmann, Ross, and Lohr'* and Nguyen and H a i 3 on HCP, and the study of H C P and H2CP+by Lohr, Schlegel, and M 0 r u k ~ m a . I ~
P-
Description of Calculations All calculation were done using the GAUSSIAN 82 program.Is Initially the geometries of all species were optimized at the HF/6-3 1 G* level of theory and harmonic vibrational frequencies and MP2 to MP4SDQ energies calculated at these optimized geometries, using the same basis set. This procedure was repeated with a 6-31G** basis set for the unprotonated species and the lowest energy isomer of the protonated species. Since there could be significant correlation effects on geometry, the geometries of the unprotonated species and the lowest energy isomers of the protonated species were optimized at the MP2/6-311G** level of theory and H F t o MP4SDQ energies calculated at this geometry. The MP4SDQ energies quoted do not include core interactions, whereas the MP2 energies do so. In order to take into account the basis set superposition energy correction, MP2 to
P-
(IO) Nguyen, M. T.;Hegarty, A. F.; Ha, T.-K.;Brint, P. Chem. Phys. Lett. 1985, 98, 447.
( 1 1 ) Nguyen, M. T. Chem. Phys. Lett. 1987, 117, 91. (12) Lehmann, K . K.; Ross, S. C.; Lohr, L. L. J . Chem. Phys. 1985,82, 4460. (13) Nguyen, M. T.; Ha, T.-K. J. Mol. Struct. (THEOCHEM) 1986,139, 142. (14) Lohr, L. L.; Schlegel, H. B.; Morukuma, K. J . Phys. Chem. 1984,88, 1981. (15) Binkley, J. S.; Frisch, M. J.; Del-rees, D. J.; Raghavachari, K.; Whiteside, R. A.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie-Mellon University: Pittsburgh, 1983.
d
C
\H
s-
H-C-P-
P
H
Figure 1 . Structures of protonated forms of PN, PO,PS, and HCP.
MP4SDQ energies were calculated for PN, PO, and PS at the optimized PX distance with a hydrogen basis set located relative to X as in the corresponding optimized PXH+ structure. Some calculations were also performed with the 6-31 1+G** and 63 1 1 +G(2df) basis sets to determine the effect of diffuse functions and an extended set of polarization functions on the value of the calculated proton affinity. Results and Discussion The calculated total energies of the various species at the different levels of theory and with different basis sets are given in Table I . The proton affinity at 0 K is calculated by PA = AE(MP4SDQ) + AE(ZPVE)
In calculating AE(MP4SDQ), the energy of PX with or without the correction for the basis set superposition energy can be used. In calculating AE(ZPVE), the calculated zero-point vibrational energy (ZPVE) can be scaled by the factor of 0.89 suggested by DeFrees and McLean.16 The values of AE(MP4SDQ) and PA for the various species at the different levels of theory and with (16) DeFrees, D. J.; McLean, A . D. J . Chem. Phys. 1985, 82, 333.
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3375
Letters TABLE 111: Optimized Geometric Parameters
distance, A species PN PNH' NPH' PO POH, OPH' PS PSH' SPH' HCP H2CP' HCPH'
calculation
PX
H F/6-3 I G* HFj6-31 IC** MP2/6-31 IG** HF/6-31G1 HF/6-31 IG** MP2/6-31 IC** HF/6-3 IG* H F / 6 - 3 1 G* HF/6-31 IC** MP2/6-31 IG** HF/6-31G* HF/6-3I IG** MP2/6-31 IC** HF/6-3 1 G* HF/6-3 IG* HF/6-31 IG** MP2/6-3I IC** HF/6-3 1 G * HF/6-31 IC** MP2/6-31 I G * * HF/6-31G* HF/6-3 1 G * HF/6-31 IG** MP2/6-31 IC** HF/6-3 1 G* HF/6-31 I C * * MP2/6-31 IC** HF/6-31G*
1.455 1.451 1.527 1.431 1.428 1.482 1.446 1.456 1.448 1.468 1.526 1.515 1.545 1.527 1.960 1.956 I.944 1.987 1.985 1.930 1.976 1.515 1.513 1.558 1.612 1.603 1.606 1.485
XH
U YD ,,A'
PH
angle, deg
PN PN H+
1.002 1.003 1.019 1.404
180.0 180.0 180.0
NPH+ PO
180.0
POH' OPH+ PS
0.965 0.957 0.978 1.41 1
126.3 129.5 126.0 94.0
PSH+ SPH' HCP H2CP+
1.336 1.345 1.350 1.406 1.063 1.064 1.075 1.086 1.087 1.099 1.067
100.5 99.6 91.5 94.6 180.0
180.0 180.0
1.386
122.0 122.0 122.2 180.0
different basis sets are given in Table 11. The structures of the protonated species studied are shown in Figure I . The optimized geometric parameters are given in Table 111. The uncorrected harmonic vibrational frequencies and zero-point vibrational energies are given in Table IV. Increasing the size of the basis set increases the value of the calculated proton affinity. The change varies from 8.6 kJ mol-' for H C P to 37.2 kJ mol-' for PS. This is less when the BSSE correction is taken into account. Inclusion of correlation energy lowers the calculated proton affinity except in the case of PS. The geometries optimized at the MP2 level gave slightly lower values of the calculated PA. Except for PS without a BSSE correction this was only about 1 kJ mol-'. Including a value of the zero-point vibrational energy is essential to obtain a value comparable with experimental values. Including the basis set superposition energy correction lowered the value of the calculated PA. The lowering varied from 7.4 kJ mol-' for PN to 42.5 kJ mol-' for PS. For HCP there i s not an obvious way to calculate the BSSE as is the case for the diatomic molecules. For this reason it was not calculated. The larger number of centers should decrease the size of any BSSE correction. With the exception of PO, the values of the proton affinity calculated at the MP4SDQ/6-31 lG**//MP2/6-311G** level of theory with basis set superposition energy and scaled ZPVE corrections included were within experimental error of 8.4 kJ mol-' (2 kcal mol-'), of the experimental values of Adams, McIntosh, and Smith.6 The poor agreement in the case of PO cannot be ascribed to the use of a U H F zero-order wave function as ( S 2 ) = 0.767 and 0.765 for PO and POH' in the MP4/6-31 1G**/ /MP2/6-31 IC** calculations. In order to see whether better agreement is possible in the case of PO, we have investigated two of the corrections suggested by Pople et al." in their GI procedure. The inclusion of diffuse functions was tested for PO by MP4SDQ/6-31 I+G**//MP2/6-311G** calculations. The energies for PO, without and with BSSE correction, and POH' were -415.901 48, -415.907 19, and -416.18487 hartrees, respectively. This gave a value for the proton affinity calculated including BSSE and scaled ZPVE corrections of 704.8 kJ mol-'. This is a lowering of 8.2 kJ mol-' due to the use of diffuse functions. The effect (17) Pople, J . A,; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtis, 1989, 90. 5622.
L. A . J . Chem. Phys.
TABLE IV: Harmonic Vibrational Frequencies species basis set harmonic vibrational frequencies, cm-I
HCPH+
6-31G* 6-311G** 6-31G* 6-31 IC** 6-31G* 6-3 1 G* 6-31 lG** 6-31G* 6-31 IC** 6-31G* 6-31G* 6-31 IG** 6-31G* 6-31 IG** 6-3 1 G* 6-31G* 6-31 1G** 6-3 I G*
( u ) 1589
(a) 1600
793
(a) 1624
(a) 3870
(a)777
( u ) 1633 (a)1585
(a) 3818 (a)2598
(a') I172
(a') 3877 (a') 3947 (a') 2535
(7r)
(T)195i
( u ) 1404
(a) 1416
(a') 899 (a') 839 (a') 912
(a') 1188 (a') 1035
(6)547
( u ) 526
(a') 537 (a') 517 (a') 543
(a') 886 (a') 845
(a') 2834
(a') 849
(a') 2575
(T)832
(a) 1473
(a)818
( u ) 1473
(a) 3575 (a) 3518 (a,) 1096 (b2) 3337 (a,) 1107 (b2) 3278 (a) 1557
(b2) 533 (a,) 1484 6-311G** ( b d 478 (a,) 1455 6-31G* (a)455i (a) 2716
(b,) 1026 (a,) 3246 (bi) 998 (a,) 3190 (T)837
(a) 3551
(a') 2757
9.5 9.6 42.4 41.9 25.0 8.4 8.5 35.6 35.7 26.8 3.3 3.1 25.5 24.6 23.7 40.1 39.6 64.1 62.8 56.8
of an extended set of polarization functions was tested by MP4SDQ/6-311 +G(2df)//MP2/6-31 IC** calculations. The energies for PO, without and with BSSE correction, and POH+ were -415.97697, -415.977 65, and -416.244 52 hartrees, respectively. This gave a value of 676.4 kJ mol-' for the proton affinity calculated including BSSE and scaled ZPVE corrections. This is a further lowering of 28.4 kJ mol-' due to the use of the extended set of polarization functions. This value is now within the experimental error quoted by Adams, McIntosh, and Smith. To check whether a similar large correction occurs for other species, these calculations were repeated for P N . The MP4SDQ/6-31 l+G(2df)//MP2/6-31 IC** energies for PN, without and with BSSE correction, and PNH+ were -395.518 17, -395.5 18 64, and -395.827 25 hartrees, respectively. This gave a value of 78 1.5 kJ mol-' for the proton affinity calculated including BSSE and scaled ZPVE corrections, which is just outside the experimental error limits. The lowering in this case is only 15.9 kJ mol-' compared with the 36.5 kJ mol-' for PO. For proton affinities the GI method" "higher level correction" is zero but the residual correlation effects correction appears to have the opposite sign to that due to the inclusion of diffuse functions and that due to the use of an extended set of polarization functions. The results at 298 K are not much less than at 0 K, being less by 0.4, 1.3, 1.3, and 0.6 kJ mol-' for PN, PO, PS, and HCP, respectively. Protonation at X is preferred over protonation at the P atom. Lohr and Boehm's8 MP3/6-3 1+G** calculations found that the H P O 'A' state was 31.3 kJ mol-' lower in energy than that of the POH 3A" isomer. However, the POH' isomer is lower in energy than the HPO' isomer. Nguyen" also found that Sprotonation is preferred over P-protonation with PS. Nguyen's best calculation gives a difference of 27.7 kJ mol-' compared with the 18.8 kJ mol-' obtained from the MP4SDQ/6-3IG*//HF/ 6-31G* calculations. This is much less than the 144.7 kJ mol-' calculated for POH+/OPH+. The results of the calculations with the 6-31G* basis set agree with those reported by Lehmann, Ross, and Lohr'* and Lohr, Schlegel, and Morukuma14 for H C P and by Lohr, Schlegel, and Morukuma for H2CP', and HCPH'. Lohr, Schlegel, and Morukuma also found that HCPH' is not a local minimum. This is in contrast to the situation with HCN, but in agreement with the result for the isoelectronic H$Si and HCSiH studied by Hoffmann, Yoshioka, and Schaefer.'* Except for PS bonds, correlation effects lead to an increase in predicted PX bond lengths. Correlation effects lead to an increase (18) Hoffmann, M . R.; Yoshioka, Y.;Schaefer, H. F. J . A m . Chem. SOC. 1983, 105. 1084.
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J . Phys. Chem. 1990, 94, 3376-3379
in all XH bonds. The increase in basis set size from 6-31G* to 6-31 IG** leads to a decrease in all bond lengths.
Conclusion These calculations support the experimental values of Adams, McIntosh, and Smith6 for the proton affinities of PN, PO, PS,
and HCP. Protonation is not favored at the P atom. In order to get theoretical values close to the experimental values, a large basis set. the inclusion of basis set superposition error corrections, and zero-point vibrational energies are necessary. Acknowledgment. I acknowledge the exchange of correspondence with Professor David Smith which stimulated this study.
Photochemical Hole Burning of Porphine in Amorphous Matrices In-Ja Lee, Gerald J . Small, and John M. Hayes* Ames Laboratory, US.Department of Energy and Department of Chemistry, Iowa State University, Ames, Iowa 5001 I (Receiced: January 9 , 1990)
Polarized hole and antihole spectra for tetraphenylporphine in a polystyrene matrix are presented. It is shown that, consistent with the photochemical nature of the hole, the antihole is polarized oppositely to the hole and is distributed throughout the inhomogeneous distribution of absorbers. However, there is also a pronounced asymmetry of the antihole which is interpreted as being due to the amorphous nature of the lattice. A correlation between the site energy distribution functions for the Q, and Q, states is also demonstrated
Introduction It is well-known from N M R studies of porphine solutions that these molecules undergo facile tautomerization involving a double proton transfer.1,2 Although the dark ground-state processes monitored by N M R cease at cryogenic temperatures, the tautomerization can still occur photochemically, even at temperatures
