CHAPTER 1
Part I
PHYSICAL ASPECTS OF PHOTOCHEMISTRY
1
Spectroscopic and Theoretical Aspects
The work reported in this section is categorized as in Volume 2 together with an additional section on Chemically Induced Dynamic Nuclear Polarization, a subject which is of increasing interest to photochemists. The restriction on the number of papers considered in Section 1 has been even more severe this year, and those selected for inclusion must inevitably represent a subjective selection by the authors from the very large number available. Nevertheless, it is hoped that those included are of interest to photochemists, and that those excluded on the grounds of space-saving are of less current general interest, although inevitably some of those excluded will have been of interest to particular groups and individuals working in the field.
1 Absorption Spectra and MO Calculations
The absorption spectrum of diatomic argon has been investigated in the 780–1080 Å region with a 6.65-m normal incidence vacuum spectrograph using the helium and argon continua as background sources. Nine discrete band systems were identified. The analysis shows that the ground state is stable, has a dissociation energy D00 = 76.9 cm-1, and six vibration levels, v= 0 — 5. A number of previous calculations of intramolecular potentials agree with these experimental results. Definite dissociation products are assigned for some of the upper states of these systems. A triplet potential surface for argon has been calculated, and Wanner-type impurity excited states in liquid rare gases reported.
It has been shown that the gross shifts in the spectrum of the Hg 3P1<- 1S0 transition of Hg in solid rare gases can be correlated by considering the difference in the interaction potential between the lattice and the Hg atom in the 3P1 and 1S0 states, providing the distortion of the lattice caused by the Hg atom is taken into account. In Ar, Kr, and Xe the spectrum can consist of three separate components. It was quantitatively shown that one component arises from relatively isolated Hg atoms, the other two from Hg atoms having nearest neighbour Hg atoms. This interpretation has been criticized, and an alternative suggested in which the two additional absorption components arise from splitting of the 3 P1 state of Hg by the asymmetry of the crystal field caused by a vacancy adjacent to the Hg atom. The latter interpretation is itself subject to several criticisms. The intensities of the two additional components relative to the main component depend on the Hg doping concentrations as predicted by the Hg–adjacent-Hg hypothesis but not by the Hg–vacancy hypothesis. In addition, there is no obvious reason why the equilibrium concentration of a Hg–vacancy complex should greatly exceed the fractional concentration of vacancies in pure rare gases at equilibrium. On energetic grounds the reverse would be more likely. Since the equilibrium mole fraction of vacancies is about 0.015 at the triple point of Ar and Kr, and since for Ar the equilibrium value of about 10-4 can be attained rapidly at 50 K, it would be surprising if the ratio of substitutional Hg to Hg -adjacent vacancy exceeded 0.1, whereas at least this fraction is necessary to explain the observed relative intensities.
A semi-empirical treatment has generated potential energy curves of the hydrogen molecule in the ground 1Σg and excited 3Σu states. A spectroscopic study of deuterium photolysis has been reported.
Hartree–Fock (HF) electronic transition moments have been calculated in both the position and momentum representations, and were presented as a function of the internuclear separation R for the BeH, MgH, OH, and SH (A–X) systems. The vibrational averages of these quantities were obtained and the results used to calculate some absorption band oscillator strengths. For the OH (A–X) system several independent experimental determinations of the 0–0 band oscillator strength have been reported in the literature, and the theoretical value of 20.6 x 10-4 differs from experiment by a factor of 2.5. Consideration of the united and separated atom limits and the region of the equilibrium internuclear separation for the states involved leads to an abbreviated discussion of the effect of correlation on the HF transition moments. HF transition moment calculations at a single value of R were also reported for the BH+, AlH+, HF+, and HCl+(A–X) systems.
By means of a photoelectrical technique, the absorption cross-section of the O2 continuum in the region 2350–1814 Å and the absorption cross-section of CO2 in the region 2160–1718 Å have been measured. The cross-section of the O2 continuum is 3.8 x 10-24 cm2 at 2350 Å; it slowly increases towards shorter wavelengths and reaches 10.7 x 10-24 cm2 at about 1980 Å, then increases very rapidly and reaches 7.1 x 10-22 cm2 at about 1814 Å. In the case of CO2, numerous discrete bands were found overlapping a weak continuum in the wavelength region below 1980 Å. The absorption cross-section of the CO2 continuum is about 2 x 10-24 cm2 at 2100 Å; it gradually increases toward the shorter wavelength side, and reaches about 4 x 10-24 cm2 at 2000 Å. The continuum rises rapidly at 2000 A and its value is 1.19 x 10-20 cm2 at 1718 Å.
Absorption coefficients of 1Δ gO2 have also been measured in the far u.v. Measured lifetimes of rotational and vibrational levels of electronic states of N2 have been reported. Vacuum-u.v. spectroscopy and photo -electron spectroscopy have been used to determine the electronic structure of NO2, and the results correlated with Gaussian orbital calculations. These results may be compared with those calculated by other workers.
It has been demonstrated by photofragment spectroscopy that the long -accepted assignment of the main I2 visible continuum as being almost entirely due to a transition to the B 0+u(3Π) state is incorrect. In reality, a transition to a 1u state, probably the 1u(3Π) is of at least comparable, if not greater, importance. An I2 molecular beam was crossed with pulses of polarized light from a laser-pumped tunable dye laser, and the distribution of recoiling I atoms measured with a mass spectrometer as a function of flight time and of recoil angle measured from the electric vector of the light. The observed B 0+u(3Π) <- X 0+g(1Π), and 1u<- X 0+g(1Π) transitions are clearly separated both by flight time and recoil angle, as shown in Figure 1.
The upper panel shows the results of photolysis in the main I2 visible continuum at 21 510 cm-1 with the polarization set so that the detector is at – 70° from the electric vector of the light in the laboratory (lab) co-ordinate system. This corresponds approximately to measurement perpendicular to the electric vector in a centre-of-mass (c.m.) co-ordinate system whose origin travels with the moving 12 molecule. To a good first approximation, the c.m. to lab transformation simply rotates the angular distribution by an angle Θ = arcsin c/u, in which c is the original speed of the I2 molecule and u is the c.m. speed of the recoiling I atom. The peak is at such short flight times that the dissociation must be to ground-state atoms, as all the photon energy available after breaking the I2 bond is expressed as translational energy of the atoms. The recoil of the atoms predominantly perpendicular to the electric vector of the light indicates that the transition dipole moment is perpendicular to the internuclear axis (i.e. ΔΩ = [+ or -] 1, and thus Ω = 1 in the upper state). The only 1u states correlating with ground-state atoms are the A 1u(3Π) and 1u(1Π). The A 1u(3Π) should lie lower and almost certainly corresponds, as in the usual assignment, to the weak long-wavelength bands and continuum. That this weak continuum indeed corresponds to a 1u state has also been confirmed by photofragment spectroscopy at 14405 cm-1. Thus, the peak shown in the upper panel is definitely due to a 1u state dissociating to ground -state atoms, and is probably due to the 1u(1]Π) molecular state.
The lower panel of Figure 1 shows the results of the same experiment with the detector at + 20° from the electric vector in the lab system, approximately corresponding to recoil along the electric vector in the c.m. system. A slower peak is seen, with flight time corresponding to dissociation to one ground-state (2P[??]) and one excited-state (2P1/2) atom. Since the atoms recoil parallel to the electric vector, the transition moment is parallel to the internuclear axis and ΔΩ = 0. The upper state must therefore be B 0+u(3Π), the unique 0+u state correlating with 2P[??] + 2P1/2 atomic states.
Spin-generalized SCF wavefunctions for water, OH, and atomic oxygen have been developed, and excited states of the HCN+ ion described. The effect of low temperatures and high pressures of inert gas upon the 1780 Å band of carbon suboxide has been reported.
Methylene continues to attract much attention. Ab initio SCF calculations using a slightly extended basis set have been carried out on the low-energy electronic states. The equilibrium geometries and energies of these states determined, and potential curves for each state obtained, are shown in Table 1 and Figure 2 respectively.
Recent e.s.r. work on CH2 in solid matrices and theoretical calculations suggest strongly that CH2 is bent in its triplet ground state. The e.s.r. results strongly point to a large deviation from linearity, viz. an HCH angle of 136°, in striking agreement with the results of the theoretical work mentioned. On the other hand, the study of the vacuum-u.v. absorption spectrum of gaseous CD2 seems to suggest equally strongly that in the triplet ground state methylene is 'linear or nearly linear'. In view of the diverging results it is perhaps worth pointing out that there is a possibility of reinterpreting the vacuum-u.v. spectrum in terms of a bent form of the radical.
The absorption band of CD2 at 1416 Å certainly has the structure of a Σu- - Σg- band of a linear molecule. However, such a band structure would also arise for the K' = 0 <- K" = 0 sub-band of an A2 -B1 transition of a bent molecule. But other sub-bands, K' = 1 <- K" = 1, etc. would be expected in such a transition unless the rotational constant A is so large that the intensities of these other sub-bands are small compared to the 0–0 sub-band on account of a small Boltzmann factor. It was on this basis that the earlier conclusion 'linear or nearly linear' was drawn, where nearly linear was intended to imply that the angle must be larger than 150°.
There is another reason why the apparent intensities of the other sub-bands could be small, namely predissociation. In 1960 there was no reason to make such an ad hoc assumption, but in view of the discrepancy which has arisen one is forced to consider it. If the A2 upper state were subjected to heterogenous predissociation by a B2 state it is readily seen that, on account of the selection rules, levels with K= 0 would be the only levels not affected and thus such a predissociation, if sufficiently strong, could account for the lack of observation of sub-bands with K greater than zero: the 1–1, 2–2, etc. sub-bands would have to be assumed to be so broadened by predissociation that they escaped detection.
For CH2, unlike CD2 , there is a strong predissociation of the 0–0 sub-band. This predissociation is probably homogeneous and has nothing to do with the predissociation invoked above.
The considerations given point strongly toward the bent structure of the triplet ground state (3B1) of CH2, as first suggested by the e.s.r. work and the ab initio calculations. This conclusion does, however, require the ad hoc assumption of a strong predissociation in the upper state of the vacuum-u. v. bands such that only the K = 0 sub-band is observed.
Chemical evidence has been given that the energy difference between the singlet and triplet (ground) states of methylene lies between 4.2 and 8.4 kJ mol-1. Collision-induced intersystem crossing in methylene has been described and a theoretical explanation of the results given. The process is characterized by the small-molecule limit. In this situation, 'preparation' of the molecular system in a non-stationary state of the total Hamiltonian of the system (by photolysis to give 1CH2, for example), the effect of spin–orbit coupling is to cause the system to oscillate between almost degenerate zeroth-order singlet and triplet vibronic states. Therefore, collisional deactivation of the vibrationally excited triplet state is required for irreversible intersystem crossing in the gas phase (see discussion on anthracene, Part I, Chapter 4).
Kinetically the overall process may be described by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where X are inert gas atoms or molecules, and k1 and k-1 are pseudo-rate constants. Steady-state analysis yields
d[3CH2]/dt = k1k2/ k1 + k-1[X] [1CH2][X] (3)
Therefore, the rate of formation of 3CH2 is bimolecular if k-1 >> k2 [X], and independent of [X] (unimolecular) if k-1<< k2 [X].
It is necessary to derive a formula for the intramolecular radiationless transition probability in order to compare the orders of magnitude of k1 and k-1 with k2. The hamiltonian is written in the form
H = H0 + V
where H0 is the zeroth-order (non-relativistic) molecular hamiltonian and the perturbation V is the spin-orbit interaction operator. It is assumed that the zeroth-order wavefunctions can be described as
Sψ = SΦSX for 1A1
TψσT ΦσTX, σ = 1, 0, -1 for 3B1(3Σg-)
where Φ are electronic wavefunctions, X vibrational and rotational wave-functions; S, T refer to singlet and triplet states, respectively, and sigma represents the quantum number for the z-component of total spin.
Assuming that only one singlet vibronic state and one (triply degenerate) triplet vibronic state are almost degenerate, and hence interactions with other vibronic states are negligible, the zeroth-order almost-degenerate perturbation theory can be applied with the following notation for the matrix element
VS, σ = < Sψ| V |Tψ>, Vσσ' = < Tψσ|V |Tψσ' (4)
In C2v symmetry, Vσσ' = 0 for all σσ' and Vs,σ' = 0 for σ = 0 from the selection rules. Hence the secular equation may be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where ES and ET are the zeroth-order singlet and triplet energies (electronic and vibrational) of the molecule.
Without loss of generality, the zeroth-order electronic wavefunctions can be taken as real ; the VS,0 are then purely imaginary. Using the relation VS,-1 = VS,1*, the following eigenvalues and eigenfunctions are obtained,
E1 = E-, E2 = E+, E3 = E4 = ET
with
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
with
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
By use of equations (7) Sψcan be expressed in the form
Sψ = C22 ψ1- C12 ψ2/ C11C22 - C12 C21 (8)
On introducing the time factors the time-dependent wavefunctions below are generated.
SΨ = C22ψ1exp[-(i/h)E1t] - C22ψ2 exp[-(i/h)E2t/ C11 C22 - C12C21 (9)
with SΨ = Sψ at time t = 0. If ψ1 and ψ2 in equation (9) are again expressed in terms of Sψ Tψ1 and Tψ-1 by use of equations (7), SΨ is obtained as a linear combination of 8t/s, Sψ, Tψ and Tψ-1. The squared modulus of the coefficient of 8t/sgives the probability PS(t) that the system will be in the singlet state Sψ at a subsequent instant t. The probability PT(t) = 1 - PS(t) that the system will be in the triplet state is given by
PT(t) = K sin2[(2 | V1,S|2 + δ2)1/2 t/h] (10)
where
K = 2 |V1, S|2/ 2 V1, S|2+ δ2
The | V1, S|2 may be approximately by
| V1, S|2 = | V1, S(e)|2 Q (11)
where
| V1, S(e) | = | < 2 Φ | V | T Φ1> |
and Q is the Franck–Condon factor. For numerical work below, | V1, S(e) | = 14 cm-1 and Q= 0.01.
Two limiting cases can be distinguished. (a) Near accidental degeneracy Sψ and Tψσ(δ ≈ 0):
PT(t) = sin2[[square root of (2)] | V1, S(e)| Q1/2 t/h ≈ sin2 (5 x 1011 t)
and (b) δ ≈ 10 3 cm-1 [much greater than] | V1, S|2:
PT(t) = (2 |V1, S|2/δ2 sin2 (δt/h) ≈ 4 x 106 sin 2 (2 x 1015 t)
On the other hand, the number of collisions per second of an average-sized molecule under standard conditions is the order of 109. For either case (a) or (b) above, the oscillatory frequency in PT(t)is then at least 102 times larger than the collision frequency. This allows use of the time-averaged transition probability which is determined essentially by K in equation (10). Therefore, for case (a) the intramolecular crossover is fast, resulting in the rapid establishment of an approximately 1 : 1 equilibrium ratio of singlet : triplet* methylene. Hence, referring back to equation (3), the condition k-1 k2 [X] is fulfilled and the overall intersystem crossing process would be bimolecular. For case (b), δ >> V1,S, the transition probability is very small, and the overall process is most likely unimolecular, (k-1<< k2 [X]), although collisional deactivation can be a very inefficient process for small molecules.
