J. Phys. Chem. 1991,95,4329-4332 proposedz3that with a rise in solvent polarity the energy gap between the TICT states and the low-lying triplets decreases and this accelerates the rates of nonradiative transitions from the TICT state to the triplets according to the energy gap law of nonradiative transitions42 This speculation is substantiated by the increase in the triplet yield with increase in solvent polarity.' According to the present calculation (Figure 7), with a rise in solvent polarity the S5 (TICT) energy approaches that of the triplet TI and the resulting enhancement in the rate of intersystem crossing to TI may be responsible for the decrease of lifetime and the yield of emission from the TICT state. 4. Conclusion
The present calculations suggest that the TICT process of DMABN involves more than two electronic states. First, the TICT state unequivocally corresponds to state S5 with a large dipole moment (18.656 D) and a perpendicular geometry (T = 90"). The (42) Avouris, P.; Gelbcrt, W. M.; Elsayed, M. A. Chem. Rev. 1977, 77, 793. (43) All the geometrical parameters were independently optimized without assuming any specific geometry of any group.
4329
"nonpolar" emission, however, is attributed to either or both of the states SIand Szhaving much lower dipole moments (5.48 and 8.66 D, respectively) and nearly planar geometries (minima at T = 30" and T = 0", respectively). Second, it has been shown that the TICT state becomes more stable than the "nonpolar" state at e > 2.2, explaining why the TICT emission is observed only in polar solvents. Third, notwithstanding the limitations of the semiempirical theories and the drawbacks of the continuum model, a reasonably good estimate of the energy barrier for the TICT process has been obtained, although the nature of the dependence of the barrier on rise in polarity could not be reproduced satisfactorily. Last, these calculations show that the rotation of the dimethylamino group is essentially barrierless in the ground state, the 0" and 90" conformations being rather close in energy. The energy difference between the TICT emission and the 'nonpolar" emission may be attributed almost exclusively to the energy difference between the two excited states. Acknowledgment. Our thanks are due to the Council of Scientific and Industrial Research, Government of India, for a generous research grant (No. 5( 136)/88-EMR-II). Registry No. DMABN, 1197-19-9.
Dynamic Polarizability of Haioforms: Experimental and ab Initio Theoretical Studies Shashi P. Kama, Eric Perrin, Paras N. Prasad,* Photonics Research Laboratory, Department of Chemistry, State University of New York at Buffalo. Buffalo, New York 14214
and Michel Dupuis Data System Division, Department 48B/MS 428, IBM Corporation, Neighborhood Road, Kingston, New York 12401 (Received: October 9, 1990)
Experimental study of polarizability dispersion for various haloforms is conducted using refractive index measurements. The results are compared with those calculated from ab initio time-dependent coupled perturbed HartretFock theory with a basis set that includes semidiffuse functions. For the wavelengths of study between 457.9 and 694 nm, a satisfactory agreement between the theoretical and experimental results is found.
Introduction Molecular systems have emerged recently as an important class of nonlinear optical materials for applications in the new technology of photonics. The main advantage lies in that the nonlinear optical response in these systems is determined primarily at the microscopic level. Hence one can use molecular engineering to tailor the molecular structure in order to optimize a particular nonlinear optical response at the microscopic level. In order to achieve this goal, an understanding of microscopic structureproperty relationships is of vital importance. Such an understanding at the microscopic level may be achieved through quantum chemical studies of the related properties. Unfortunately, like most other quantum mechanical properties, the linear and nonlinear optical properties of molecules are extremely sensitive to the methods and the technical details of the theoreticat approach used to evaluate them. In order to develop confidence in the predictive capability of a theoretical computation, a useful approach is correlation between theoretically computed values and those experimentally measured on model systems. This is the approach we have taken. In the past, ab initio methods have been used to calculate the polarizability and hyperpolarizability of organic molecular structures in the static limit, Le. in the presence of a static electric field (zero frequency limit) from analytically calculated energy
derivatives.I4 The measurements relevant to photonics are performed, however, at optical frequencies. Since the optical properties invariably show dispersion effects due to the presence of resonances, the correlation between the theoretical results and the experimental data is not always straightforward. In addition to the issue of this correlation between theory and experiment, an investigation of the dispersion effect on both the linear polarizability and the nonlinear hyperpolarizabilities is of great value for understanding the role of electronic resonances as well as designing specific device structures for photonics. The motivation for the present study is derived from these perspectives. The molecular systems selected for the initial study reported here are the various haloforms. The choice of these systems is based on the interesting large nonlinear optical response iodoform exhibits, presumably due to the presence of significantly polarizable iodine atoms.5 Also, some experimental and theoretical studies (1) Andre, J.-M.; Barbier, C.; Bodart, V.; Delhalle, J. In Nonlinear Optical properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J.. Eds.; Academic Press Inc.: London, 1987; Vol. 2, p 137. (2) Hurst, G. J. B.; Dupuis,M.; Clementi, E. J. Chem. Phys. 198&89,385. ( 3 ) Chopra, P.; Carlacci, L.; King, H. F.; Prasad, P. N. J. Phys. Chem. 1989. 93. 7120. (4) Perrin, E.; Prasad, P. N.; Mougenot, P.; Dupuis, M. J. Chem. Phys. 1989, 92, 4728.
0022-365419 112095-4329%02.50/0 0 1991 American Chemical Society
4330 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991
of nonlinear optical response of these systems have recently been reported.6 Measurements of molecular polarizability and hyperpolarizabilities at the wavelength of the sodium D line (A = 589 nm) and at 6 0 2 nm for CHC13, CHBr3, and CHI3 in solution have been reported recently.5 In particular, it has been observed that CHI, exhibits large second-order effects in various crystalline complexes and also displays a large value of the third-order nonlinear optical 1 , neat crystalline forms as measured by susceptibility, ~ ( ~ in femtosecond degenerate four-wave mixing (DFWM) experiments. A theoretical study of the static polarizability and first and second hyperpolarkabilities of the haloform series CHX, using an ab initio coupled perturbed Hartree-Fwk (CPHF) method and several basis sets has also been reported: It was found that the polarizability can be accurately calculated for these and similar molecules, provided that the basis set includes diffuse functions. For higher order polarizabilities, the agreement between experiment and theory was somewhat less satisfactory. In this paper, we report both the experimental and theoretical studies of the dispersion effect on the polarizabilities of various haloforms. The measurement of polarizability a ( w ) has been performed at a series of frequencies covering a wide range but always below the first electronic resonances of CHCl,, CHBr,, and CHI,. The frequency-dependent polarizability a ( w ) for the haloform series CHX3 (X = F, CI, Br, I) has been calculated by applying ab initio timedependent coupled perturbed Hartree-Fock theory.
Experimental Measurement The polarizability, a(w), is determined from the measurement of the refractive index, n(w), of solutions of various concentrations using an AbbC refractometer. Tetrahydrofuran (THF) is used as the solvent. The concentration ranges are 1.86.0 M for CHCI,, 1.6-4.0 M for CHBr3, and 0.25-2.0 M for CHI3. In the case of CHI, the concentration range is restricted by limits of solubility. Since the measurements are performed in the solution phase, only the orientationally averaged linear polarizability a(@)is measured for each compound. For a given frequency hw, the polarizability .(a) is calculated by using the Lorentz-Lorenz relationship for molar polarization PM,as given by eq 1:'
Karna et al. a detailed description of the implementation in the HOWW programg is given elsewhere."J In brief, the polarizability a ( w ) of a system perturbed by an oscillating electric field
E = E,,(&'
+ e-iwr)
(4)
with an interaction Hamiltonian
H' = -WE
(5)
is obtained from the first-order solution of the corresponding time-dependent Hartree-Fock (TDHF) equation
a
FC - i-SC = SCC at
(6)
subject to the orthonormalization condition
a
-CfSC = 0 at
(7)
In the above equations, p is the dipole moment operator, and F, S, C, and c are the perturbed Fock, overlap, molecular orbital (MO) coefficient, and Lagrangian multiplier matrices,respectively. The overlap matrix S is assumed to be independent of the perturbation, i.e. S = So, where So is the unperturbed overlap matrix. For a basis set that is independent of the external field, the above assumption is true. Expanding these matrices in a Taylor series of the field E, substituting the corresponding terms in eqs 6 and 7, and solving up to first order gives the first-order MO coefficient matrix C(')(fo) in terms of the zeroth-order coefficient matrix Co and a transformation matrix U(')(fw) as C(')(fw) = COU(l)(fw)
(8)
with (9)
where G(')(fw) = CofF(')(fw)Co
F(')(fw)
H(')(fw) + D(')(fw)(2J0 - K O )
(10) (11)
In eq 1 1 Jo and K O are the two-electron Coulomb and exchange integrals and are similar to the overlap matrix, independent of the applied field, and H(I)(h) is the dipole moment matrix. The first-order density matrix D(I)(fw) is obtained as
where PIM = %TNOaI(w)
(2)
D(')(fo) = C(')(iw)nCot+ ConC(')t(fw)
(3)
where n is the diagonal occupation number matrix with values of 2 for the occupied MOs and zero everywhere else. The polarizability tensor, a(@),is then calculated as
and P2M
y3rNOn2(w)
In the above expressions, Xs are the mole fractions of the solvent and the solute, n(w) is the refractive index of the solution measured at frequency w, p is the density of the solution, and No is the Avogadro number. The relationships assume that there is no interaction between solute and solvent molecules and that the molar polarizations are additive. The error estimate in the determination of a(w) is about 2%. The different wavelengths employed are 475.9, 488, and 514.5 nm obtained from a Spectra Physics (2020) Ar ion laser; 632 nm from an NRC He-Ne laser; and 673 nm obtained from a dye laser pumped by the Ar ion laser.
Theoretical Calculations The dynamic polarizability a ( w ) is calculated in the framework of the time-dependent CPHF theory. The formulation employed in the present work is similar to that of Sekino and Bartletts and (5) Samoc, A.; Samoc, M.;Prasad, P. N.; Williams, D. J. J . Phys. Chem.. submitted for publication. (6) Karna, S. P.; Dupuis, M.; Perrin, E.; Prasad, P. N. J . Chem. Phys. 1990,92,7418. Karna, S.P.; Dupuis, M. Chem. Phys. Lett. 1990,171,201. (7) Sauteret, C.; Hermann, J. P.; Frey, R.; Pradere, F.; Ducuing, J.; Baughm. R. M.; Chance, R. R. Phys. Reo. Lon. 1976, 436, 956.
(12)
a ( f w ) = - Tr [H(I)D(l)(fw)l
(13) where Tr stands for 'trace". The mean polarizability to be compared with the experimental value is calculated as a(w) =
73Xaji(w) i
(14)
Due to the coupled nature of eqs 8-12 an iterative solution is adopted. With the initial guess for fi')(fo)= H(I) and using the zeroth-order coefficient matrix Co,the corresponding equations are solved until the elements of U(I)(fw) have converged to within a threshold value of 10". With the final U(l)(fw) matrix, .(a) is calculated by using eqs 8, 12, and 13. For CHF3 and CHCI, two different basis sets have been used. The first basis set is a double-{ (DZ) Gaussian basis set" aug(8) Sekino, H.; Bartlett, R. J. J . Chem. P h p . 1986, 85. 976. (9) Dupuis. M.; Watts, J. D.; Villar, H. 0.; Hurst, G. J. B. Comput. Phys. Commun. 1989, 52,415.
(IO) Karna, S.P.; Dupuis, M.IBM Technical Report KGN-21 I , Jan 30, 1990, submitted for publication to J . Comput. Chem. ( I 1) Dunning, T. H., Jr.; Hay, P. J. In Modern Theorericol Chemistry; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 3, p 1 .
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4331
Dynamic Polarizability of Haloforms
TABLE I: Frequency-Depeodent Polarizabilities & for CHX, (X = F, Cl, Br, I).
CHF3
x
hw
457.9 488.0 514.0 589.0 632.0 673.0 694.3
2.707 2.540 2.412 2.105 1.962 1.842 1.786
CHCI,
CHBr3
CHI3
cxptl
calcd
exptl
Calcd
exptl
calcd
exptl
calcd
2.806
2.31 2.31 2.3 1 2.30 2.30 2.29 2.29
8.59 8.56 8.53 8.50 8.48 8.46
7.72 7.52 7.50 7.45 7.43 7.42 7.41
12.17 12.15 12.02 11.80 11.70
10.87 10.80 10.75 10.63 10.58 10.55 10.53
18.61 18.39 18.21 18.00 17.87 17.52
15.28 15.1 1 14.98 14.73 14.62 14.54 14.51
'Units are nm for A, eV for hw, and lom2'cm3 for a, bLundolr-Bornstein Zallenwerte und Functionen, Springer: Berlin, 1962; Band 11, Teil 8. 20,
TABLE II: Polarizability Dispersioa for CHX3 (X = F, Cl, Br, I)
diswrsion d417,9 &a dJl4
CHCI, calcd
exptl 1.5 1.2 0.8 0.5 0.2 0.0
489
d632 d673
CHBr3 exptl calcd
4.0 1.3 1.1 0.4
4.0 3.8 2.7 0.9
0.01 0.0
0.0
CHI3 exptl calcd
2.7 2.0 1.6 0.5 0.0
6.2 6.0 3.9 2.7 2.0
5.1 3.9 3.0 1.3 0.5
0.0
0.0
1
400
450
500
550
600
650
700
750
800
Wavelength (nm)
.
Figure 1. Experimental (disconnected symbols) and theoretical (connected symbols) polarizability dispersion for haloforms.
mented by polarization functions and is denoted as DZP. The second basis set is the effective core potential (ECP) basis set, which is essentially of double-{valence type with the core electrons represented by an effective potential.'* The ECP basis set was also augmented by the same polarization functions as used with the all-electron D Z Gaussian basis set. For the higher two members, CHBr3and CHI3, of the haloform family an ECP basis set augmented by polarization functions was used. This basis set is denoted as ECPP. The exponents of the polarization d functions are d(C) = 0.20; d(F) = 0.325; d(C1) = 0.155; d(Br) = 0.05967; d(1) = 0.03083. For hydrogen the polarization p function has an exponent of 0.1. These basis sets are extracted from larger basis sets used earlier6 for the calculation of static (hyper)polarizabilities of haloforms. Indeed, in our earlier work it was found that a basis set of this type with only one diffuse polarization function yields a static CY in good accord with the values obtained with the basis set containing several polarization and diffuse functions and in agreement with experiment within 12-20%. A similar accuracy for the dynamic polarizability a(@) is expected.
Results and Discussion The measured and calculated values of the mean polarizability n ( w ) are given in Table I. For CHF3and CHCl,, the all electron DZ + polarization (DZP) basis results are listed. The corresponding dispersion is shown in Figure 1. As expected, &(a) increases in the order CHC13 < CHBr, < CHI3 (see Table I). The calculated values of a(w) are about 1&22% lower than their experimental counterparts, with the largest error found for the heaviest member, CHI3, partly due to a large experimental uncertainty because of limited solubility of CHI3 and partly due to the neglect of electron correlation in the calculation, which may be more manifested for iodoform. The dispersion in the polarizability d, can be calculated as
n ( w ) - a(0)
d, = 100
n(w)
The experimental and calculated values of relative dispersion d, are listed in Table 11. The overall conclusion that emerges from (12) Stevens, W.J:; Bash, H.;Krauss. M.J . Chem. Phys. 1984,81,6026, and private communication.
Fnquancy (4
Figure 2. Polarizability dispersion for CHF, and CHCI, calculated by
using all-electron (connected symbols) and ECP (disconnected symbols) basis sets. 20 m i 18
E
$
'2
16
S
14
Y
.-b
:
'C
B
CHBr3 12 10 0.
I
1.000
2.000
3.000
4.000
/ 5.000
Fnquoncy (av)
Figure 3. Polarizability dispersion for CHBr, and CHI3 calculated by using the ECP basis set.
the dispersion data given in Table I1 is that the calculated dispersion effects are in reasonable agreement with experiment. As the frequency of the optical radiation increases, the polarizability increases and so does the dispersion. We also note that the dispersion increases from C1, to Br, and to I, except at X = 457.9 nm where the calculated dispersion of ru in CHBr3 is smaller than that in CHC13. Contrary to what was found for higher polarizabilities: CY can be calculated with a high level of accuracy even at the SCF level of theory as used here. It appears that dispersion effects can be accurately calculated as well. Whether this conclusion also holds for dispersion in higher polarizabilities of de-
4332
J. Phys. Chem. 1991, 95, 4332-4331
TABLE 111: PohriubiUty n ( w ) of CHF3 as Obtained from the DZP 8 d ECPP Set&
0
a(@) DZP ECPP
hw
X
(static) 0
911.3 759.4 694.3 673.0 632.0 589.0 569.4 514.0
1.360 1.632 1.786 1.842 1.962 2.105 2.177 2.412
2.280 2.288 2.291 2.293 2.294 2.297 2.300 2.301 2.306
2.240 2.243 2.246 2.249 2.251 2.253 2.254 2.255 2.269
a(w) X 508.9 488.0 457.9 227.8 151.9 113.9 101.2 96.94 94.92
hw 2.436 2.540 2.707 5.442 8.168 10.885 12.250 12.789 13.061
DZP ECPP 2.307 2.310 2.313 2.427 2.661 3.181 3.825 4.413 4.992
2.261 2.265 2.267 2.372 2.591 3.076 3.707 4.362 5.121
"See text for description of the basis sets. bunits are the same as in Table 1. localized 7r systems will be the subject of subsequent publications. The calculations were extended to yet higher frequencies to study the dispersion behavior of a in CHX3 near the first resonance. In Figure 2 the dispersions of a in CHF, and CHCl, obtained from the DZP as well as from the ECPP basis sets are shown. For CHBr, and CHI,, the dispersions of a obtained by using the ECPP basis set are shown in Figure 3. In the case of CHF, the difference in the values of a between the two basis sets is rather small (=2-3%). As a result, the dispersion curves for CHF3 for the two basis sets are hardly discernible from each other, especially at lower frequencies. For clarity, the corresponding values of n(w) for CHF3 are listed in Table 111. Both basis sets in the case of CHF, predict the first absorption to occur at ho = 13.3 eV. A small difference between the values of 43-775) obtained from the two basis sets is also noted in the case of CHCI,. The a values obtained by using the ECPP basis set for CHCl, are slightly higher than the corresponding value obtained from the all-electron DZP basis set. The difference (=3%) in the value of a obtained from the two basis sets is nearly constant up to ha = 5.5 eV but increases to about 5% near hw = 7 eV and about 7% near hw = 7.6 eV. Consequently, the ECPP calculation in CHCI, predicts the resonance to occur at a slightly lower frequency (hw = 7.7 eV) than the all-electron DZP basis set (hw = 7.9 eV). However, as can be noted, both basis sets predict nearly parallel a dispersion over a large range of frequencies below resonance where experiments are performed. This gives confidence in the results for CHBr3 and CHI3 when they are compared with the experimental values (Table I and Figure 1). A small error in the absolute value of a for CHBr, and CHI, is not expected to affect
the general observations regarding the comparison of the theoretical and experimental values discussed earlier. From the dispersion curves of CHBr, and CHI3 (Figure 3), one estimates the first resonance frequencies as: hw(CHBr3) = 5.442 eV and ho(CH13) 4.35 eV. Considering the level of theoretical approach used in the present study, these estimates for the first resonance frequencies are in reasonably good agreement with the corresponding experimental values, for example 5.53 eV for CHBr313and 4.06 eV for
-
Summary Molecular polarizabilities of CHC13, CHBr,, and CHI, at five optical frequencies have been obtained from refractive index measurements in T H F solution. The Lorentz-Lorenz relationship and linear additivity of the component polarizabilities were assumed. The measured polarizability dispersion increases in the order CHC13to CHBr3 to CHI3. Furthermore, in each system, the higher the optical frequency the larger is the polarizability dispersion. The polarizabilities of haloforms including CHF3 have also been calculated by the ab initio method in the framework of time-dependent Hartree-Fock theory. For the lowest member, CHF3, the all-electron basis set as well as the ECP basis set gives similar results for polarizability. A difference of about 3-7% is noted between the two basis sets for the polarizability in the case of CHCl,. For the higher two members, CHBr3 and CHI3, only the ECP basis set was used. The calculated polarizabilities are about 10-22% lower than their experimental counterparts, which could be due to the neglect of electron correlation in the present theoretical computation and/or incompleteness of the basis set. Since the present set essentially reproduces the a values (static) obtained from a more extended basis set that included several polarization d and f functions and diffuse s, p, and d functions on the heavy atoms,6 it may be concluded that the large part of the discrepancy between theory and experiment comes from the neglect of electron correlation in the present calculation. The trend in the calculated dispersion of the polarizability, however, is consistent with the experimental findings. Acknowledgment. We acknowledge many fruitful discussions with Drs. M. Samoc and A. Farazdel. The research a t SUNYBuffalo was supported by the Air Force Office of Scientific Research, Directorate of Chemical and Atmospheric Sciences and Polymer Branch, Air Force Wright Research and Development Center through Contract N. F49620-90-(2-002 1. (13) Kimura,
K.; Nagakura, S.Spectrochim. Ada
1961, 17, 166.
Structure, Bonding, and Relative Stabilities of Four-Membered Disiietane Rings Mark S. Gordon,* Theodore J. Packwood, Marshall T. Carroll: Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105
and Jerry A. Boatz Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12 (Received: October 22, 1990) Properties of the fully hydrogenated l-oxa-3-aza-2,4-disiletanefour-membered ring system are compared with the corresponding properties of the 3,4-disiletane isomer. The four-membered dioxa- and diazadisiletane rings also are studied. Of particular interest are the structure, strain, bonding, and energy of these molecules. Even though the Si-Si cross ring distance is unusually short in 1,3-dioxa-2,4disiIetane,an analysisof the electron charge density gives little evidence for the existence of an "unsupported r bond" between the silicons.
Introduction In a recent paper, Schmidt-Bame and Klingebiel reported the synthesis and crystal structures of the first four-membered 1-
oxa-3-aza-2,4-disiletanerings.' The actual synthesized compounds had N-trimethylsilyl and 2,2,4-tri-tert-butyl substituents and either tert-butyl or phenyl at the 4 position. In the present work, the
'Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellow.
(1) Schmidt-Baese, D.; Klingebiel, U. J . Organomer. Chem. 1989, 364, 313.
0022-3654191 12095-4332302.50/0
0 1991 American Chemical Society
