O–H bond fission in 4-substituted phenols: S1 state predissociation
viewed in a Hammett-like framework.
Tolga N.V. Karsili, Andreas M. Wenge, Stephanie J. Harris, Daniel Murdock,
Jeremy N. Harvey, Richard N. Dixon and Michael N.R. Ashfold
School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, UK
No. of tables:
2
No. of figures:
5
Electronic supplementary information: 8 pages including 6 Tables.
Author for correspondence:
mike.ashfold@bris.ac.uk
Tel: +44 (117) 928 8312
Fax: +44 (117) 925 0612
1
Abstract
The photofragmentation dynamics of various 4-substituted phenols (4-YPhOH, Y = H, MeO,
CH3, F, Cl and CN) following π*π excitation to their respective S1 states have been
investigated experimentally (by H Rydberg atom photofragment translational spectroscopy)
and/or theoretically (by ab initio electronic structure theory and 1- and 2-D tunneling
calculations). Derived energetic and photophysical properties such as the O–H bond
strengths, the S1–S0 excitation energies and the S1 predissociation probabilities (by tunneling
through the barrier under the conical intersection between the S1(11ππ*) and S2(11πσ*)
potential energy surfaces in the RO–H stretch coordinate) are considered within a Hammettlike framework. The Y-dependent O–H bond strengths and S1–S0 term values are found to
correlate well with a simple descriptor of the electronic perturbation caused by the aromatic
substituent Y (the Hammett constant, σp+). We also identify clear correlations between σp+
and the probability of a photochemical process (predissociation). Such a finding is
unsurprising, given that Y substitution will perturb the entire potential energy landscape, but
appears not to have been demonstrated hitherto. The predictive capabilities of this approach
are explored by reference to existing energetic data for larger 4-substituted phenols like 4ethoxyphenol, tyramine, L-tyrosine and tyrosine containing di- and tri-peptides.
2
Introduction
The Hammett equation (1) has long been used by physical organic chemists to rationalize,
and to predict, the effect of a given substituent on reaction rates and reactivities.1,2
𝐾
𝑘
log 𝐾  log 𝑘 = 𝜎𝜌
0
(1)
0
The equation is a linear free energy expression that relates the logarithmic ratio of the
equilibrium constant, K, or the rate constant, k, of a reaction involving a substituted derivative
to that for the unsubstituted molecule (K0 or k0) in terms of just two parameters – a
substituent (or Hammett) constant, σ, and a (reaction-type dependent) reaction constant, .
The original σm and σp (i.e. m = meta and p = para) substituent constants were derived from
the ionization constants of benzoic acids in aqueous solution,1 but numerous subsequent
modifications have been introduced to account for additional electronic effects which, though
not affecting the ionization of benzoic acids, are important for other reacting systems. For
example, σ and σ+ constants, derived from the ionization constants of substituted phenols 3,4
and cumyl chlorides,5 were developed in order to correct for observed deviations from
linearity in the case of strongly withdrawing (σ) or strongly donating (σ+) substituents in
reactions where the substituent can lead to resonance stabilization of the reaction centre.
Previous studies have considered the correlation of various energetic properties of substituted
phenols, such as the OH bond dissociation energy
6-10
and the phenoxyl radical stability,11
with σp+. Here we explore the extent to which a Hammett-like approach can usefully be
extended to predict not just energetics, but also the relative decay rates – specifically the
probabilities of OH bond fission – of a range of gas phase 4-substituted phenols (henceforth
4-YPhOH) following UV photoexcitation to their respective first excited singlet states.
Photoinduced X–H bond fission in heteroaromatic molecules (i.e. X = N, O, S, etc.) is
attracting much current interest, both because of its potential importance in determining the
photostability of biological systems 12 and as a test-bed for exploring interactions between the
optically ‘bright’, bound * states and ‘dark’ * states (states that are dissociative with
respect to extension along the X–H bond length, RX–H).13 X–H bond fission processes have
thus been studied in some detail in phenol,14-17 thiophenols,18 aniline 19-21 and pyrrole,22 and
in heteroaromatics of greater biological relevance like imidazole
(building blocks for nucleotides).
3
23-25
and adenine
26,27
In the specific case of phenols, Pino et al.15 demonstrated a correlation between the 11*
state lifetime and the energy separation between the 11* and the 11* potential energy
surfaces (PESs) in the vertical Franck-Condon (FC) region. [For compactness, we will
henceforth use the respective labels S0, S1 and S2 to describe the diabatic ground, 11* and
11* states.] Such lifetime measurements cannot distinguish the various possible
depopulation paths from the S1 state, but these authors concluded that O–H bond fission by
tunneling through the barrier under the conical intersection (CI) between the S 1 and S2 PESs
was likely to be a significant contributor to the total decay rate. Analysis of the translational
energies of the H atoms formed following excitation to the S1 state of phenol,14 and a number
of substituted phenols,28 and femtosecond pump-probe measurements of the H atom
formation process
16
serve to reinforce this conclusion. The measured translational energy
distributions are typically bimodal – displaying a structured, high kinetic energy component,
and an unstructured component at low kinetic energies.
In the case of bare phenol (henceforth PhOH), the structured part of the total kinetic energy
release (TKER) spectrum indicates formation of phenoxyl (PhO) products, in their ground (
~
X 2B1) electronic state, as a result of H atom loss by tunneling under the S1/S2 CI. These PhO
radicals are formed in a limited sub-set of the many vibrational levels that are accessible on
energetic grounds; the identities of the populated levels are generally understandable on FC
grounds, but all involve an odd number of quanta in 16a. Such activity in 16a (an out-ofplane ring puckering vibration) is understood by recognizing that (i) 16a is the lowest energy
mode of PhOH with the appropriate symmetry to promote non-adiabatic coupling between
the S1 and S2 PESs,28 and (ii) the frequency of this mode drops considerably, then recovers,
during the evolution from the S0 to S1 to S2 states of the molecule and ultimately to the
ground state PhO radical. The ultrafast study 16 showed the tunneling rate to be insensitive to
the choice of excitation energy within the S1 state. This can be understood by recognizing that
excitation populates FC active vibrational levels within the S1 state. These parent vibrations
are typically orthogonal to the dissociation coordinate, and thus tend to carry through into the
eventual phenoxyl radical fragment. As such, they are of little help in moderating the barrier
to tunneling. Excitation at much shorter wavelengths populates the S2 state directly, enabling
~
direct dissociation to H + PhO( X ) products. As shown later in this paper, analysis of
structured TKER spectra recorded at both long and short excitation wavelengths (if available)
provides the most certain route to determining the O–H bond strength in any given phenol.
4
The present study explores, experimentally and/or computationally, the effect of 4substitution on the O–H bond strength in a range of phenols and the relative predissociation
probabilities (by tunneling) following excitation to the v=0 level of their respective S1 states.
The experimental studies return a binary outcome: the rate of O–H bond fission in any given
4-YPhOH molecule either is, or is not, sufficiently fast relative to other competing population
loss processes from the S1(v=0) level to allow observation of structure in the TKER spectrum
attributable to H + 4-YPhO products. The computational studies comprise two parts. The
first involves ab initio calculation of potential energy cuts (PECs, along RO–H) through the S0,
S1 and S2 PESs of each of the 4-YPhOH molecules of interest. The resulting PECs then form
the basis for 1- and 2-D calculations of the tunneling probability following excitation to the
respective S1(v=0) levels. These serve to extend the (binary) experimental findings by
providing a more quantitative measure of the effect that a particular Y substituent has on the
OH bond fission probability. Finally, we consider the possible utility of viewing these
predissociation rates within a Hammett-like framework, thereby allowing prediction of the
OH bond fission rates in other 4-substituted phenols without the need for extensive
electronic structure and tunneling probability calculations.
Methodology
Experimental
The experimental work involved measurement of one or more of the following: resonance
enhanced two photon ionisation (i.e. 1+1 REMPI) spectra of the chosen jet-cooled 4-YPhOH
molecules at wavelengths around their S1–S0 origins; ‘action’ spectra for forming H atom
products following excitation in the same wavelength range; and time-of-flight (TOF) spectra
of the H atom products formed when exciting various of the resonances identified in the
parent excitation spectra. The H Rydberg atom photofragment translational spectroscopy
(PTS) apparatus and procedures have all been detailed previously.22 Samples of PhOH, 4fluorophenol (4-FPhOH), 4-methoxyphenol (4-MeOPhOH, also known as mequinol) and 4cyanophenol (4-CNPhOH) – all supplied by Sigma Aldrich, with quoted purity >99% – were
heated to, respectively, ~50°C, ~50°C, ~150°C and ~200°C in order to generate sufficient
vapour pressures and seeded in ~1 bar Ar prior to expansion into the source region of the
spectrometer, and passage through a skimmer en route to the laser interaction region.
5
Electronic structure calculations
Initial geometry optimisations on the phenols, and the corresponding phenoxyl radicals and
phenol cations were carried out using density functional theory with the B3LYP functional
together with the Gaussian 03 computational package 29 at the B3LYP/6-311+G(d,p) level of
theory. The (anharmonic) normal mode vibrational wavenumbers computed at the optimised
structures and listed in Tables S1-S6 in the electronic supplementary information (ESI) were
used to correct the calculated bond energies and ionization potentials for zero-point effects.
Ab initio PECs were calculated with MOLPRO Version 2010.1,30 in the Cs point group, using
the complete active space self-consistent field (CASSCF) method in conjunction with second
order perturbation theory (CASPT2), and Dunning’s augmented correlation consistent basis
sets of triple ζ quality: aug-cc-pVTZ (AVTZ). In the case of 4-chlorophenol (4-ClPhOH), an
additional tight d function was added to the chlorine atom, i.e. the aug-cc-pV(T+d)Z basis
was used. In all of the rigid-body scans (see below) two additional sets of even-tempered
diffuse s and p functions were included on the O atom in order to describe the Rydbergvalence coupling more effectively.31,32
The choice of active space was motivated by the need to describe all significant static
correlation effects in the ground and excited states in as even-handed a way as possible across
the PES at the minimum practicable computational expense. Test calculations were
performed using a variety of active spaces to explore how to meet these constraints; the
optimum active space was found to be Y-dependent. For PhOH, 4-FPhOH, 4-ClPhOH and 4MePhOH, the active space comprised 10 electrons in the following 10 orbitals: 3 ring centred
 orbitals and their * anti-bonding counterparts, the OH centred px orbital (which supports a
lone pair of electrons that conjugates with the phenyl centred  system), a hydroxyl oxygen
centred 3s Rydberg orbital, and the  and * orbitals localised on the OH bond. The choice
of active space for 4-MeOPhOH and 4-CNPhOH was less trivial, and required consideration
of the out-of-plane substituent-centred orbitals. For 4-MeOPhOH, all of the above orbitals
plus the occupied px orbital centred on the methoxy O atom were included in the orbital
space, resulting in an active space consisting of 12 electrons in 11 orbitals (12/11). In 4CNPhOH, the extra orbitals consisted of the out-of-plane and * orbitals centred around the
CN group, resulting in a (12/12) active space.
6
The CASSCF method was first used to find the optimized structure of the S 0 state of each 4YPhOH molecule. PECs along RO-H for the S0, S1 and S2 states were then calculated using
CASPT2 with a CASSCF reference wavefunction obtained by state-averaging over the four
lowest-energy singlet states (i.e. the S0, 11*, 11* and 21* states) by progressively
extending the O–H bond without changing the C-O-H angle or the C-C-O-H dihedral angle,
or any other internal coordinate of the phenoxyl partner. Test calculations for the S0 and
11* states using state-optimized CASSCF reference wavefunctions led to modest
differences in the calculated PECs, but calculations for the 1* excited states proved hard to
converge using state-optimized orbitals. An imaginary level shift of 0.5 a.u. was used in the
CASPT2 part of the calculation to encourage convergence. A further set of single point
‘relaxed‘ CASPT2 calculations were carried out on ‘relaxed’ structures at a few selected RO-H
values with the same active spaces and basis sets as for the rigid body (or ‘unrelaxed’)
calculations in order to assess the impact of structural relaxation in the Franck-Condon region
and during dissociation.
Tunneling calculations
The probability of O–H bond fission from the S1(v=0) level is sensitively dependent upon the
details of the barrier to tunneling under the S1/S2 CI, so it was necessary to establish a
consistent protocol for deriving this barrier as described below. The tunneling probability, T,
was then estimated using the Brillouin-Kramers-Wentzel (BKW) method which, for low
tunneling probabilities, gives
 Ro 2mV ( R)  E )  
dR  .
T  exp  2 
2
 Ri

(2)
The integral in eq. (2) runs from the inner (Ri) to outer (Ro) limits of the 1-D potential barrier
V(R) in RO–H at a total energy, E – the energy of the starting vibrational level in the S1 state.
For simplicity, we take m as the mass of the H atom. Strictly, it should be the appropriate
reduced mass, but this introduces negligible error if the partner mass is taken to be that of the
4-YPhO radical.
Results and Discussion
Ab initio potentials and calculated energetics.
7
Figure 1 shows unrelaxed PECs along RO–H for PhOH, 4-CNPhOH and 4-MeOPhOH at
planar geometries, plotted so that the minimum of each S0 PEC is at zero energy. The energy
of the S/S2 CI is well above the minimum of the S1 state in all three cases, but the height
(and the width) of the barrier in these unrelaxed potentials through which an S1(v=0)
molecule would have to tunnel in order to dissociate to ground state products is clearly Y
dependent.
Notable features of these PECs include:
i) The close similarity of the diabatic S0 PECs for these and all other 4-YPhOH molecules
investigated. This can be understood by recognizing that the primary effect of any
substitution at the 4-position will be on the π-electron density, and that such substitutions will
~
thus have minimal effect on the bonding interaction between the 4-YPhO( A ) radical (i.e. a
radical with a singly occupied pσ orbital orthogonal to the π-system) and the H(1s) atom.
ii) Substituting an electron donating (MeO) or withdrawing (CN) group in the 4-position
~
clearly lowers/raises the energy of the X state radical (which has a pπ-hole, and is thus
stabilized/destabilized by donating/withdrawing π electron density). Any shift in the energy
~
of the X state radical maps through into the relative energy of the long range part of the S 2
potential.
iii) The long range part of the various S2 PECs are essentially parallel to each other – as
expected, given that the repulsive in-plane interaction between an H(1s) atom and a 4-YPhO
radical with a doubly occupied pσ orbital should be rather insensitive to the nature of a Y
substituent on the opposite side of the ring. At shorter RO–H, however, the three S2 PECs show
obvious differences. The detailed shape of the S2 PEC (along RO–H) in these molecules is
sensitively dependent upon the extent of Rydberg (3s)/valence (*) mixing – often termed
Rydbergisation.13,33 Quantum defect considerations dictate that any factor which stabilizes
the ground state parent cation should also stabilize Rydberg states belonging to series
converging to that ionization limit. Adding an electron donating group (EDG) in the 4position is one such factor (for the same reason that such substitution stabilizes the ground
state 4-YPhO radical), which has the effect of boosting the 3s contribution to (and lowering
the vertical excitation energy of) the S2 state in the vertical FC region. This can be clearly
seen by comparing the PECs of the S2 states of PhOH and 4-MeOPhOH shown in fig. 1.
Substituting an electron withdrawing group (EWG) will destabilize the parent cation, and the
associated Rydberg states, and will thus be expected to have the opposite effect – reducing
8
the 3s contribution to (and raising the vertical excitation energy of) the S2 state, as seen for
the case of 4-CNPhOH in fig. 1.
iv) The S1S0 origins for all of the 4-YPhOH molecules investigated are red-shifted relative
to that of PhOH. This can be understood by considering how the various substituents affect
the energy gap between the highest occupied and lowest unoccupied molecular orbitals (i.e.
the HOMO/LUMO separation). In the case of MeO, the additional  electron density donated
to the ring by the O(2p) lone pair destabilises the HOMO, but has little effect on the energy
of the LUMO – resulting in a substantial red shift. Conversely, in the case of 4-CNPhOH, the
HOMO is stabilised by a weak interaction between the phenol  system and a CN-centred 
orbital, but the LUMO gains greater stabilization from the strong overlap of the anti-bonding
CN orbital and the * system of the ring – again causing a (smaller) red-shift of the S1S0
origin (cf. PhOH).
Table I includes a summary of the following energetic properties for the 4-YPhOH molecules
studied in this work: (i) the calculated unrelaxed (CASSCF) and relaxed (CASPT2) S1S0
excitation energies, together with the corresponding experimental term values, T00(S1S0);
(ii) the calculated D0(4-YPhOH) values returned by the relaxed single point calculations
(after zero-point energy (zpe) correction) and (iii) the calculated (zpe corrected) first I.P.s
returned by the relaxed single point calculations – again with the corresponding experimental
quantities in each case.
The unrelaxed PECs in fig. 1 and the contents of Table I clearly show that 4-substitution with
an EWG like CN increases D0(4-YPhOH) and the energy of the S2 PEC. The S1 origin also
shows a small red shift, so the net effect is an increase in the height (and the width) of the
barrier to tunneling. The O–H bond fission rate by tunneling from the S1(v=0) level should
thus be reduced by substituting an EWG in the 4-position. Adding an EDG like MeO lowers
D0(4-YPhOH), and the S1 origin, and the energy of the S1/S2 CI, and thus might have been
expected to cause a comparable increase in tunneling rate (cf. that in phenol). But the relative
stabilisations of the S1 and S2 states in this case are comparable, so the height (and width) of
the barrier under the S1/S2 CI – and thus the tunneling probability from the S1(v=0) level – is
actually similar to that in PhOH. Most of the other substituents considered in this work (e.g.
CH3, or a light halogen atom like F) are typically viewed as σ- rather than π-perturbers, and
consequently also have relatively minor effect on quantities like D0(4-YPhOH) or the I.P.
Before attempting to quantify such effects, we first consider pertinent experimental data.
9
H atom photofragment translational spectroscopy
Figure 2 shows TKER spectra derived by measuring the TOFs of H atoms formed following
excitation of 4-MeOPhOH, 4-FPhOH, PhOH and 4-CNPhOH at their respective S1S0
origins and, in each case, at one wavelength corresponding to an energy above the S 1/S2 CI.
We calculate the energy splitting between the syn and anti rotamers of 4-MeOPhOH in the S0
state to be negligible (ΔEsyn-anti ~10 cm-1). Resonances attributable to both rotamers are
readily identifiable in the 1+1 REMPI spectrum (obtained by monitoring the parent ion yield
as a function of excitation wavelength), however, and in the excitation spectrum for forming
H atom products – as a result of the much larger (~100 cm-1) syn-anti splitting in the S1 state.
34,35
The respective I.P.s of the two rotamers also differ by ~100 cm-1 (Table I), implying that
the splitting is mainly a consequence of the asymmetric distribution of the remaining electron
in the π HOMO. The TKER spectrum shown in fig. 2(a) was recorded at  = 297.066 nm, the
S1S0 origin of the syn-rotamer. The spectrum obtained when exciting at the origin of the
anti-rotamer (at  = 297.932 nm) was essentially identical. The structure in this spectrum is
reminiscent of that observed when photolysing at the S1 origins of 4-FPhOH ( = 284.768
nm, fig. 2(b)), PhOH ( = 275.113 nm, fig. 2(c)), or 4-MePhOH 28 and, as in those cases, can
be assigned to population of radical modes 16a and 18b (the C–O in-plane wag). In none of
these cases is the TKER spectrum sensitive to the relative alignment of the polarization
vector () of the photolysis laser radiation and the TOF axis, indicating that the H atom
products have isotropic recoil velocity distributions (consistent with their formation via a
tunneling process occurring on a timescale that is much longer than the parent rotational
period).
The energy of the S1 origin of 4-CNPhOH is less than half that of the first I.P. (Table I),
which precludes straightforward observation by one color 1+1 REMPI spectroscopy. The
S1S0 origin has been identified by laser induced fluorescence, however, at  = 281.31 nm,36
and the excited state lifetime estimated from linewidth measurements ( = 10.6±3 ns,36 cf. 
=2.2±0.1 ns for PhOH 15). This origin wavelength was confirmed in a two colour 1+1' mass
analysed threshold ionisation (MATI) spectroscopy study, which also yielded a precise value
for the first I.P.37 As fig. 2(d) shows, no fast, structured features were discernible in TKER
spectra obtained when exciting 4-CNPhOH at its S1 origin. Spectra such as that shown in fig.
10
2(d), maximizing at low TKER values, are often observed when exciting on comparatively
long lived parent resonances and are variously ascribed to unimolecular decay following
radiationless transfer to high vibrational levels of S0 and/or (unintended) multiphoton
excitation processes. 14,16
Figures 2(e)-2(h) show TKER spectra obtained from the same four phenols when exciting at
wavelengths above the respective S1/S2 CIs. The relative intensities of all four spectra are
greater when  is aligned perpendicular to the detection axis; analysis returns recoil
anisotropy parameters in the range –0.25    –0.5 (i.e. preferentially perpendicular, though
non-limiting, recoil anisotropy). Each spectrum shows partially resolved vibrational structure
which, in the cases of 4-FPhOH and PhOH (figs. 2(f) and 2(g)), has been subject to previous,
detailed analysis.14,38 As noted in the Introduction, such analyses only yield internally
consistent (i.e. photolysis wavelength independent) values for the O–H bond strengths in
PhOH,14 4-FPhOH 38 or 4-MePhOH
39,40
(or of the corresponding O–H bond in phenol-d5 41)
if the fastest radical products formed at long (e.g. figs. 2(b) and 2(c)) and short wavelengths
(i.e. at energies above the S1/S2 CI, as in figs. 2(f) and 2(g)) carry one quantum of 16a and
16b, respectively. Such product energy disposals have been rationalised by invoking q16a as
the ‘branching-space’ coordinate 42 that facilitates tunneling under the S1/S2 CI, and 16b as a
mode that promotes direct excitation to the (low oscillator strength) S2 state by vibronic
coupling with the higher lying, ‘bright’ 21ππ* state.28 4-CNPhOH shows no structure
attributable to O–H bond fission by tunneling under the S1/S2 CI, so any D0(4-CNPhO–H)
value derived from analysis of TKER spectra like that shown in fig. 2(h) inevitably depends
on how one chooses to assign the fastest peak. Since the calculated S2S0 oscillator strength
is small (as in PhOH), and the same non-rigid (G4) molecular symmetry restrictions apply in
both cases, we choose to assign the fastest peak in fig. 2(h) to population of 4CNPhO(16b=1) products. The recoil anisotropy parameter measured for these products ( ~ –
0.5) is consistent with that expected if dissociation involves an a1 (in G4) vibronic transition
moment (which points along the CO bond) and subsequent prompt O–H bond fission on the
S2 PES.
As with PhOH, photolysis of 4-MeOPhOH at energies above and below the S1/S2 CI yields
structured TKER spectra. Spectra obtained at long excitation wavelengths (e.g. fig. 2(a)) are
rotamer specific, whereas those recorded at short wavelength (e.g. fig 2(e)), where the parent
absorption spectrum is continuous, are necessarily superpositions of contributions from both
11
rotamers. Given the very small energy splitting between the syn- and anti- rotamers in the S0
state this should not degrade the product state resolution. In marked contrast to PhOH,
however, analysis of all TKER spectra from photolysis of 4-MeOPhOH return a common
‘effective’ value for the O–H bond strength. Unlike CH3, F, Cl or CN, substituting a MeO
group in the 4-position necessarily lifts the torsional tunneling degeneracy – as evidenced by
the ease with which the syn- and anti-rotamers can be distinguished in the S1 state. MeO
substitution must therefore also lift the non-rigid G4 molecular symmetry restrictions that
provided a rationale for the deduced role of q16a in the tunneling mechanism in PhOH. For the
specific case of syn-4-MeOPhOH, therefore, we have calculated S1/S2 2-D coupling matrix
elements in the space defined by qO–H and each of the more probable branching-space
coordinates of a symmetry (including q16a). Given these relaxed symmetry restrictions, OH
torsion (OH) is deduced to have the largest interstate coupling constant (~2.5 larger than
that for qO–H/q16a coupling) – consistent with the early (non-G4 symmetry restricted)
theoretical analysis of S1/S2 coupling in PhOH.43 OH is a ‘disappearing mode’ upon O–H
bond fission, but its participation would satisfy the symmetry requirements for coupling
between the S1(1A') and S2(1A) states. The experimental D0(4-MeOPhO–H) value listed in
Table I is obtained by attributing the fastest peak in TKER spectra obtained with this
molecule to radical products with v=0.
Tunneling calculations
As noted previously, the tunneling probability from any given 4-YPhOH S1(v=0) level will
be very sensitive to the area of the barrier under the S1/S2 CI and, as fig. 1 showed, this is Y
dependent. Inspection of Table 1 shows that the relaxed single point calculations of
E(S1S0) consistently underestimate the experimental T00(S1S0) term value, while the
unrelaxed PECs shown in fig. 1 substantially overestimate D0(4-YPhO–H). Both deficiencies
will impact on any estimate of the area of the barrier under the S1/S2 CI.
‘Tuning’ the potentials: We start by using the available experimental data to ‘correct’ the ab
initio rigid body PECs (henceforth defined as S0(calc), S1(calc) and S2(calc)) in a mutually selfconsistent manner. To ensure that there is no ambiguity about signs, we define S2(calc) >
S1(calc) > S0(calc) in the vFC region (R = 0.95 Å), and reference all energies to that of the S0
potential minimum.
12
(i) Correcting S1(calc): The ab initio S1(calc) potential is shifted in energy to match the
experimental T00 value using the relationship
T00 = S1(calc) + S1(zpe) – {S0(calc) + S0(zpe)} + S1(shift)
 S1(shift) = T00 – [S1(calc) + S1(zpe) – {S0(calc) + S0(zpe)}] ,
(3)
where all quantities are calculated at the respective minimum energy geometries. Calculating
these zero-point energy (zpe) terms is a source of possible ambiguity. Ideally, the zpe
associated with all modes of the S0 and S1 states should be used. In the case of PhOH, the
former can be calculated using Gaussian (S0(zpe) = 22302 cm-1, anharmonic) and seen to
agree well with the experimental value: S0(zpe) = 22262 cm-1 (ref. 44). All bar two of the S1
state wavenumbers are also listed by Bist et al.45 The two missing modes are a C–H stretch
and a C–C stretch vibration, both of b2 symmetry. We adopt the S0 (anharmonic) values for
these two missing vibrations and thus estimate S1(zpe) = 21031 cm-1. These values result in a
small positive value for S1(shift) (eq. (3)) which is applied to the S1(calc) values at each R to
yield the final S1(shifted) PEC, i.e.
S1(shifted)(R) = S1(calc)(R) + S1(shift).
Lacking the same detailed information about the S1 vibrations of the various 4-YPhOH
molecules we regard the various Y substituents are spectators to the ring deformation
accompanying π*π excitation and use the same (zpe) = S1(zpe) – S0(zpe) = –1231 cm-1 (–
0.155 eV) in all cases.
(ii)
Correcting De: The experimental quantity D0(4-YPhO–H) links to the ab initio
quantities via:
D0 = S2(calc)(R = ) + R0(zpe) – {S0(calc) + S0(zpe)} + D(shift),
where R0(zpe) is the zero point energy of the radical calculated at its minimum energy
geometry and S0(zpe) is the parent zero point energy. Both of these quantities can be
calculated (anharmonic values) for all modes of all 4-YPhOH molecules and all 4-YPhO
radicals with Gaussian. The difference in zero point energies in each case is essentially what
would be expected given the three disappearing modes on O–H bond fission. Rearrangement
yields a value for D(shift)
D(shift) = D0 – [S2(calc)(R = ) + R0(zpe) – {S0(calc) + S0(zpe)}]
13
(4)
which is the larger (always negative) correction that needs to be applied to the S 2(calc) value at
R =  in order to match experiment. The ab initio S2(calc) PEC is essentially flat by R = 3 Å,
and we take this as the R =  value when applying this correction.
(iii) Correcting S2(calc): The shift applied to S2(calc) is R dependent. The necessary shift at R =
 (3 Å) is the D(shift) value from eq. (4), while at R = 0.95 Å we elect to shift S2(calc) by the
same amount as S1(calc), i.e.
R  0.95 Å:
S2(shifted) = S2(calc) + S1(shift)
R  3 Å:
S2(shifted) = S2(calc) + D(shift)
Between these limits (i.e. 0.95 < R < 3 Å), the required shift in S2(calc) is assumed to scale
linearly with R, thereby yielding the final S2(shifted) PEC for each 4-YPhOH.
The legitimacy of this approach was checked by comparing the S1(shifted) and S2(shifted) PECs
for PhOH with the ‘relaxed’ ab initio PECs,28 and the tunnelling probabilities derived from
each using model 1 (see below). The latter comparison gives T(relaxed)/T(shifted) ~ 0.88 –
an insignificant difference given the one or more order of magnitude variation in T upon
changing Y.
(iv) Correcting S0(calc): This correction is included for completeness; it is not important for
the tunneling calculations that follow but is necessary for illustrating the S0/S1 CI. S0(shift) is
determined as the difference between the unrelaxed and relaxed ab initio S0 diabatic potential
energies calculated at R =  (3 Å). The rigid body S0(calc) PEC is then corrected by assuming
S0(shifted) = S0(calc) when R < 0.95 Å, S0(shifted) = S0(calc) + S0(shift) at R > 3 Å, and that the
correction interpolates linearly in the intervening range 0.95  R  3 Å. S0(shift) is a small
correction, ~ 0.04 eV in the case of PhOH.
Figure 3 illustrates the effect of each of the above corrections to the ab initio PECs of PhOH
and the consequent reduction in the area of the barrier to tunneling under the S1/S2 CI.
Refining the tunneling calculations: Table II lists Rx (the RO–H value at which the shifted S1
and S2 PECs cross) and the corresponding energy (E(S1/S2 CI)), the maximum height (h) and
the base width (w) of the barrier under the S1/S2 CI (defined relative to E(S1(v=0)) after
correcting the unrelaxed PECs for each 4-YPhOH molecule, along with the respective barrier
areas and the respective tunneling probabilities, TY, returned by three different sets of 1-D
14
BKW calculations. Model 1 assumes a barrier V(R) given by V = S1(shifted) in the range Rx 
RCI, and V = S2(shifted) for Rx  RCI and starts from an S1 energy E = {S1(shifted) + S1(zpe′)},
where S1(zpe′) is the 1-D quantity 0.5OH – i.e. tunnelling starts from the vOH = 0 level in the
S1(shifted) PEC.
As noted above, dissociation of PhOH(S1) molecules by tunneling under the S1/S2 CI at
planar geometries is symmetry forbidden, but enabled by motion along q16a. The wavenumber
~
associated with normal mode 16a doubles as the system evolves from PhOH(S1) to PhO( X )
~
and, experimentally, the PhO( X ) products formed in the dissociation are found to have v16a
 1. Model 1 must therefore return upper limits to the tunneling probabilities, and two
improvements to the model have thus been explored.
Model 2 uses effective 1-D potentials, where the S1(shifted) PEC has been raised by the zeropoint energy of 16a in the S1 state (i.e. by ~93 cm-1 (ref. 45)) and the S2(shifted) PEC raised by
~560 cm-1 (i.e. by 1.5 quanta of 16a in the ground state radical). The effect of these changes
on Rx, E(S1/S2 CI), E(S1(v=0)), h, w and A for each 4-YPhOH molecule, along with the
respective TY values starting from the S1(vOH = 0) level, are shown (in italics) in Table II.
Recognizing the role of motion in q16a in this way has the effect of increasing the barrier area
(and thus reducing the rates of dissociation by tunneling) for all 4-YPhOH molecules, though
we note that the assumption implicit in this approach – that the 16a wavenumber in the S2
state at the S1/S2 CI is as large as in the asymptotic radical – means that the values of A and
TY from this model are likely to be, respectively, upper and lower limits.
Model 3 employs a plausible 2-D potential. i.e. the same R dependent S1(shifted) and S2(shifted)
potentials as in model 1, plus a harmonic potential in q16a (with force constants for the S1 and
S2 surfaces equal to 0.469 and 2.236 aJ rad-2, respectively), which are also coupled by a nonadiabatic function H12 = V12 q16a with V12 = 2500 cm-1 rad-1. The tunnelling probability, T, is
then calculated at the energy of 0.5OH for a range of q16a displacements. Each T(q16a) is then
weighted by the normalised integrand function of this S1/S2 coupling matrix element
w(q16a) = [S1(v16a=0)H12(q16a)S2(v16a=1)],
(5)
where S1(v16a=0) and S2(v16a=1) are, respectively, the initial and final state wavefunctions
(in q16a). As Table II shows, the total tunnelling probability, given by T (q16a )w(q16a ) , after
normalising to ensure that
 w(q16a )  1 , is typically ~60% that returned by model 1. Such
15
an outcome is unsurprising, given the symmetry requirement in G4 systems like phenol that w
is zero at q16a = 0 – where S1(v16a=0) has maximum amplitude. More significantly in the
present context, Table II shows that models 1, 2 and 3 all return similar relative tunneling
rates (i.e. similar TY/T0 values, where T0 is the tunneling rate calculated for bare phenol) for
any given 4-YPhOH molecule.
A final caveat is in order here. All three model comparisons assume that all of the phenols
exhibit the same dissociation dynamics but, as noted previously, 4-MeOPhOH is not
constrained by G4 symmetry and can thus dissociate to v=0 radical products. Torsion is
assumed to drive the non-adiabatic coupling at the S1/S2 CI in this latter case. Tunneling
probabilities as a result of this alternative coupling mode (when operative) were estimated via
a further set of tunneling calculations. These followed the spirit of model 3, but assumed OH
torsion as the orthogonal coupling coordinate. V12 in this calculation was held at 2500 cm-1
rad-1, but H12 was scaled to match the experimental wavenumber for OH torsion in the S1
state of phenol (634.7 cm-1 [ref. 45]), with associated force constants for the S1 and S2 PESs
equal to 0.044 and 0.123 aJ rad-2, respectively. The tunneling probabilities returned by these
calculations were all less than, but within 5% of, those returned by Model 1, suggesting that
the tunneling probability in 4-MeOPhOH will be comparable to that in phenol itself.
The tunneling rates of interest cannot be measured directly, but could be estimated given
reliable S1 state lifetimes and quantum yields for H atom product formation. Unfortunately,
as noted previously, PTS experiments give a binary outcome: relative to the sum of the rates
of all S1 population loss processes, the predissociation rate either is, or is not, sufficient to
give a measureable yield of H atom products from the tunneling pathway. Lacking
quantitative yield data, we content ourselves by noting that the trends in calculated tunneling
probability are broadly consistent with the available excited state lifetime data. The reported
S1 state lifetimes, , for PhOH,15 4-MePhOH,15 4-FPhOH
15
and 4-ClPhOH
46
are all in the
range 1    2.2 ns, whereas that for 4-CNPhOH is 10.6  3 ns.36 In all but the last case, the
lifetimes of the corresponding 4-YPhOD isotopologues have also been reported: PhOD ( =
13.3 ns
47
), 4-MePhOD ( = 9.7 ns
48
), 4-FPhOD ( = 3.2 ns
49
), 4-ClPhOD ( = 1.6 ns 46).
These S1 state lifetimes are the reciprocal of the total population loss rate constant, k, which
includes contributions not just from tunneling (ktunn) but also, potentially, from internal
conversion to S0 (kIC), intersystem crossing (kISC) and radiative decay (krad). As noted
previously, kinetic isotope effects will ensure that the tunneling probability from the S1(v=0)
16
level of PhOD must be ~103 lower than that for the corresponding H atom loss process in
PhOH.28 O–D bond fission by tunneling is thus unlikely to make any significant contribution
to the k values for the deuterated isotopologues, and the reduction in measured lifetime upon
switching from O–D to O–H (particularly in the cases of PhOH and 4-MePhOH) suggests
that tunneling is a substantial contributor to the total S1 decay rate.
However, the
observations of an unstructured slow component within the H atom TOF spectra, and of
vibrationally excited CO products following excitation of PhOH at 248 nm
50
(i.e. at an
energy just below the threshold for populating the S2 state directly) reminds us that at least
one alternative radiationless decay pathway (IC, yielding highly vibrationally S 0 molecules
which subsequently fragment) is also operative.
Energetics and tunneling probabilities viewed in a Hammett framework
Figures 4(a) and (b) show the respective first I.P.s and O–H bond strengths of PhOH and the
4-substitued phenols listed in Table I in the form of Hammett plots, i.e. as plots of the ratios
I.P.(4-YPhOH)/I.P.(PhOH) and D0(4-YPhO–H)/D0(PhO–H) versus σp+. Both show good
linear correlations (R2 = 0.97 and 0.96, respectively) – as reported previously in an extensive
review of published D0(4-YPhO–H) values
51
– and serve to validate the choice of Hammett
parameter. Both ratios increase with increasing p+, reflecting the destabilisation of the 4YPhOH+ cation and the 4-YPhO radical caused by attaching a more strongly electron
withdrawing substituent at the 4-position.6,9-11
As noted above, all Y substituents cause some red shift of the electronic origin relative to that
for PhOH; thus the T00(S1S0) term values do not vary linearly with p+. Nonetheless, the
Hammett-like representation (fig. 5(a)) and the illustrative shaded regions) is useful in
highlighting the apparent break at p+ ~0.3. EDGs like MeO and NH2 reduce T00(S1S0) far
more than EWGs like CN or NO2. The tunneling barriers (and probabilities) are sensitive not
just to the stabilisation (or otherwise) of the radical (and thus of the diabatic S2 PEC) that
results from Y-substitution, but also to any shift in the S1(v=0) term value. The former scales
linearly with σp+ (fig. 4(b)), but the latter does not (fig. 5(a)). The obvious break in the log
(TY/T0) versus σp+ plot (fig. 5(b)) is an inevitable consequence of the latter. Thus we conclude
that electron donating substituents in the 4-position will typically cause only modest changes
in tunneling rate (relative to phenol itself), but that 4-substitution with a strongly electron
withdrawing group like CN (or NO2) will reduce the tunneling probability from the S1(v=0)
level by several orders of magnitude. Support for the former conclusion is provided by the
17
available lifetime data for the S1 states of 4-MeOPhOH (1.2    9.8 ns 52) and 4-H2NPhOH
( = 2.2 ns 53).
We recognise that the quantum yield for OH bond fission by tunneling under the S1/S2 CI in
any given 4-YPhOH will be determined by the tunneling rate relative to the rates of all
population loss processes from the S1 state. The maximum tunneling probability (~10-5 in the
case of PhOH) implies a tunneling rate ~109 s-1 – consistent with previous conjectures that
predissociation by tunneling is a substantial contributor to the total decay rate – and the ns
lifetime – of phenol(S1) molecules. Such a view is further reinforced by recent suggestions
that O–H bond fission is the dominant primary photodissociation process following 275 nm
photoexcitation of PhOH in an Ar matrix at 15 K 54 and the observed slow build-up of
phenoxyl products following 267 nm photoexcitation of PhOH in a weakly interacting
solvent (cyclohexane).55,56
The proposed Hammett-like approach to excited state photophysics (rather than ground state
energetics) offers a route to predicting the effect of substituents in cases where the necessary
data is unavailable. Relevant spectroscopic (i.e. T00(S1S0) and I.P.) data for several other 4substitued phenols – mostly from jet-cooled excitation spectroscopy and from mass analysed
threshold ionization spectroscopy – are included in Table I. The S1–S0 term values for 4ethylphenol and 4-n-propylphenol,57,58 for example, are very similar to those of 4methylphenol, and those for syn- and anti-4-ethoxyphenol 59 are barely distinguishable from
those for the corresponding isomers of 4-methoxyphenol. In both cases, one can predict that
the O–H bond strengths and the rates of O–H bond fission by tunneling from the S1 state will
be similar to that of the lighter analogue. Gas phase laser induced fluorescence excitation
and/or REMPI spectra have also been reported for 3-(4-hydroxyphenyl)propionic acid,60
tyramine 61 and tyrosine.62 Each reveals S1S0 band origins for several different conformers,
but all show the expected (small) red-shift relative to that of PhOH. A (non-conformer
specific) I.P. value of 8.46 ± 0.1 eV has also been reported for tyrosine.63 Notwithstanding
the large uncertainty, the appropriate Hammett plot (fig. 4(a)) implies σp+ ~0 (0.1), implying
an O–H bond strength in tyrosine ~29650 (170) cm-1 (fig. 4(b)). None of the conformers of
tyrosine exhibit G4 symmetry. O–H bond fission by tunneling following excitation at its
S1S0 origin is thus likely to be facilitated by OH torsion (as in 4-MeOPhOH), but the
foregoing analysis suggests that the predissociation rate is likely to be similar to that in PhOH
18
or 4-FPhOH. Again, the available fluorescence lifetime data for tyrosine(S1) molecules (
~3.4 ns in aqueous solution
64
) is sensibly consistent with such expectations. 1+1 REMPI
spectra of di- and tri-peptides containing a tyrosine (Tyr) chromophore (e.g. Gly-Tyr or AlaTyr, where the glycine (Gly) or alanine (Ala) is attached to the N-terminus of tyrosine) reveal
S1S0 origins very close to that of bare tyrosine,65,66 encouraging the view that, even in these
larger systems, O–H bond fission is likely to occur on a nanosecond timescale.
Conclusions
The photodissociation dynamics of several 4-substituted phenols (4-YPhOH) in their
respective S1 states have been studied experimentally (by HRA-PTS methods) and
theoretically (by ab initio electronic structure and 1- and 2-D tunneling calculations).
Relative to bare phenol, the probability of tunneling through the barrier under the S1/S2 CI is
relatively insensitive to substituting a (non-symmetry breaking) EDG in the 4-position, but
can be reduced by one or more orders of magnitude by substituting an EWG. Tunneling
under the S1/S2 CI requires a coupling mode of appropriate symmetry. PhOH (and 4-YPhOH
molecules with Y = CH3, F, CN, etc.) are best described within the non-rigid molecular group
G4, wherein 16a is the lowest frequency parent mode of appropriate (a2) symmetry to couple
the S1 and S2 states – thereby explaining the finding that all PhO products from dissociation
of PhOH(S1) molecules are formed in levels with 16a = odd.14,28 The vibrational energy
disposal in the 4-MeOPhO products formed in the dissociation of 4-MeOPhOH(S1)
molecules implies subtly different fragmentation dynamics in this case. MeO substitution in
the 4-position lowers the overall symmetry, lifts the degeneracy of the two rotamers and
introduces a marked asymmetry in the electron density remaining in the π HOMO. We
conclude that such relaxation of the symmetry constraints allows OH torsion to promote S1/S2
coupling – thereby accounting for the observation of H + 4-MeOPhO(v=0) products when
exciting the 4-MeOPhOH(S1) state.
The O–H bond strengths determined for a range of 4-YPhOH molecules, and the I.P. values
available in the literature, show good linear correlations with the appropriate σp+ parameter.
The present work explores the value of extending the Hammett concept to consideration of
T00(S1S0) term values and (calculated) tunneling probabilities from the S1(v=0) level. As
might be expected, both quantities show more complex variations with σp+, but Hammett-like
plots of both nonetheless offer some predictive capability. For example, the reported I.P. and
19
T00(S1S0) values for the amino acid L-tyrosine
62,63
(figs. 4(a) and 5(a)) imply a σp+ value
~0 for the side-chain, suggesting that the O–H bond strength and tunneling probability in Ltyrosine(S1) will be similar to that in 4-FPhOH or PhOH. The present work relates to excited
state predissociations, but serves to highlight yet again the potential importance of H atom
tunneling processes – even when occurring on long (nanosecond) timescales – in situations
where there are no more probable competing reaction pathways.
Similar analysis could be developed for 3-substituted phenols, though the nodal properties of
the π HOMO suggest that any variations in tunneling probability as a result of introducing a
π-donor or π-acceptor at the 3-position will be less marked. Greater variability can be
anticipated in the case of 2-substitutions, however, in light of the additional influences of
steric crowding and possible intramolecular H-bond formation.67
Acknowledgements
The authors gratefully acknowledge financial support from EPSRC (Programme Grant
EP/G00224X) and the Marie Curie Initial Training Network ICONIC (contract agreement no.
238671). MNRA is also very grateful to the Royal Society for the award of a Royal Society
Leverhulme Trust Senior Research Fellowship.
20
Table I
Energetic properties of selected 4-YPhOH molecules, including those studied in the present
work. Column 1 lists calculated (non-zero-point corrected) excitation energies to the S1 state
along with the experimental T00(S1S0) term values (in italics). Columns 2 and 3 show zeropoint corrected bond strengths, D0(4-YPhOH) from the relaxed single point calculations,
and first I.P.s (calculated using Gaussian 03), again with the corresponding experimentally
determined values again shown in italics. Hammett p+ values are also listed where available
(from ref. 2). Quantities predicted on the basis of the present analysis are shown in square
brackets.
E(S1S0) / cm-1
D0(4-YPhOH) / cm-1
Y
Unrelaxed Relaxed
H
MeO
syn:
anti:
CH3
F
Cl
Unrelaxed
I.P. / cm-1
p+
0
Relaxed
36550
34030
36348 14
32420
29950
30015 ± 40 14
67160
68625 ± 4 68
34130
33940
33679 34
33573 25
35910
34350
40
35333
35420
34030
35116 38
35360
33420
38
34811
31260
28820
28620 ± 50 52
60600
62308 ± 5 35
62202 ± 5 35
64030
65918 ± 5 69
67320
68577 ± 5 70
66540
68104 ± 5 71
0.78
32530
29630
29320 ± 50 40
32620
29730
29370 ± 50 38
32390
30010
29520 ± 50 38
Br
CN
HO
syn:
anti:
EtO 59
syn:
anti:
C2H5
0.07
0.11
0.15
34794 38
35770
34320
35548 74
29790 ± 100 72
33630
30620 ± 50
68718 ± 80 73
70950
72698 ± 5 37
33535 75
33500
[28430]
64051 76
63998
33647
33550
28576
61670
61565
[66150]
0.66
0.92
0.81
[29260]
35503
n-C3H7
trans:
gauche-A:
gauche-B:
NH2 78
0.31
0.30
57
0.29
35501 58
35453
35441
[29270]
[27910]
31395
NO2
[30690]
21
65283 ± 5 77
65385 ± 5
65369 ± 5
1.31
58829
0.78
73400  400
79
HOOCCH2CH2
3-(4-hydroxyphenyl)
propionic acid
H2NCH2CH2
tyramine
H2NCH(COOH)CH2
L-tyrosine
35368 60
28846
35466 61
[0.61]
64370 ± 400 80
29649
35491 62
22
0
68240 ± 800 63
Table II
Properties of the barrier under the S1(shifted)/S2(shifted) CI for each 4-YPhOH molecule, assuming models 1 (normal font), 2 (italics) and 3 (bold),
along with the calculated tunneling probabilities, TY, and the corresponding Hammett parameters, σp+. Rx and E(S1/S2 CI) are, respectively, the
RO–H value and energy at which the S1(shifted) and S2(shifted) PECs intersect, h, w and A are the height, base width and area of the barrier defined by
reference to E(S1(v=0)), the energy of the S1(shifted)(vOH = 0) level, and the numbers in parentheses in the TY column are the relative tunneling
probabilities scaled to that of PhOH.
MeO
E(S1(v=0))
/ eV
4.551
4.562
h / cm-1
1.169
1.182
E(S1/S2 CI)
/ eV
4.987
5.062
Me
1.184
1.195
5.298
5.364
F
1.192
1.205
H
Y
Rx / Å
w/Å
A
3514
4032
0.474
0.516
/ 10-20 J m
0.849
0.985
4.758
4.770
4357
4798
0.495
0.533
0.991
1.12
5.322
5.384
4.731
4.743
4768
5171
0.483
0.529
0.971
1.10
1.182
1.194
5.427
5.488
4.884
4.895
4379
4776
0.424
0.463
0.817
0.877
Cl
1.211
1.218
5.360
5.421
4.693
4.705
5377
5777
0.554
0.600
1.20
1.29
CN
1.234
1.245
5.601
5.662
4.785
4.796
6580
6986
0.629
0.680
1.48
1.61
23
TY /107
903 (0.71)
202 (0.31)
537 (0.52)
189 (0.15)
45.1 (0.07)
111 (0.11)
235 (0.19)
59.3 (0.09)
140 (0.14)
1270 (1.00)
661 (1.00)
1023 (1.00)
19.4 (0.02)
6.93 (0.01)
13.1 (0.01)
0.93 (310-3)
0.21 (310-4)
0.58 (610-4)
p+
0.78
0.31
0.07
0
0.11
0.66
Figure captions
Figure 1
Calculated unrelaxed S0, S1 and S2 PECs along RO–H for PhOH (black), 4-MeOPhOH (red)
and 4-CNPhOH (blue), plotted so that the minimum of each S0 PEC lies at zero energy.
Figure 2
TKER spectra of the H + (4-Y)PhO products resulting from photolysis of jet-cooled 4MeOPhOH at  = (a) 297.066 nm and (e) 250.0 nm, 4-FPhOH at  = (b) 284.768 nm and (f)
228.0 nm, PhOH at  = (c) 275.113 nm and (g) 225.0 nm, and 4-CNPhOH at  = (d) 281.31
nm and (h) 222.0 nm, with  aligned perpendicular to the TOF axis in each case. The vertical
arrow in each right hand panel indicates the fastest peak identified in the various shortwavelength TKER spectra.
Figure 3
Expanded view of the unrelaxed ab initio S0, S1 and S2 (black) PECs and the corrected
S0(shifted), S1(shifted) and S2(shifted) (blue) PECs of PhOH.
Figure 4
Hammett plots showing (a) first ionization potentials, I.P., and (b) dissociation energies,
D0(4-YPhO–H), each referenced to the corresponding quantity in phenol, as functions of p+
(from ref. 2). Solid symbols indicate experimentally determined quantities for substituents
with known p+ value. Half-open circles represent substituents where the quantity has been
determined experimentally and p+ deduced by fitting to the line of best-fit in (a), while open
symbols show quantities predicted on the basis of p+ values derived in (a).
Figure 5
(a) Experimental T00(S1S0) term values and (b) logarithm of the calculated tunneling
probabilities (TY in Table II) through the barrier under the corrected S1/S2 CI (assuming
models 1, 2 and 3) relative to the corresponding tunneling probability in PhOH (T0), both
plotted against p+. The key for solid, half-open and open symbols is as for fig. 4 and, again,
the substituent is typically labeled on just one or other plot to avoid clutter.
24
Figure 1
25
Figure 2
26
Figure 3
27
Figure 4
28
Figure 5
29
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