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 Hammett-like

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 4-ethoxyphenol,

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

log KK0

log kk0

=σρ (1)

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 OH 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 OH 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 23-25 and adenine 26,27 (building

blocks for nucleotides).

3

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 S1 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 S 1/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-of-

plane 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 4-

substitution 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

OH bond fission probability. Finally, we consider the possible utility of viewing these

predissociation rates within a Hammett-like framework, thereby allowing prediction of the

OH 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, 4-

fluorophenol (4-FPhOH), 4-methoxyphenol (4-MeOPhOH, also known as mequinol) and 4-

cyanophenol (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 Rydberg-

valence 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 4-

MePhOH, 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 OH 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 4-

CNPhOH, 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 S0 state of each 4-

YPhOH 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

T= exp[−2∫

Ri

Ro √ 2m (V ( R )−E ))ℏ2 dR ]

. (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 S2

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 4-position 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 the 3s

8

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 S1S0 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 S1S0

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) S 1S0

excitation energies, together with the corresponding experimental term values, T00(S1S0);

(ii) the calculated D0(4-YPhOH) 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-YPhOH) 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-YPhOH), 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-YPhOH) 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 S1S0

origins and, in each case, at one wavelength corresponding to an energy above the S1/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

S1S0 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

S1S0 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.

2(d), maximizing at low TKER values, are often observed when exciting on comparatively

10

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) S 2 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 S2S0

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 4-CNPhO(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 CO 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

rotamers. Given the very small energy splitting between the syn- and anti- rotamers in the S0

11

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(S1S0)

consistently underestimate the experimental T00(S1S0) 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 self-

consistent 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.

(i) Correcting S1(calc): The ab initio S1(calc) potential is shifted in energy to match the

experimental T00 value using the relationship

12

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 D e: 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)}] (4)

which is the larger (always negative) correction that needs to be applied to the S2(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.

13

(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

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 0.5OH – i.e. tunnelling starts from the vOH = 0 level in the S1(shifted)

PEC.

14

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 zero-

point 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 non-

adiabatic function H12 = V12 q16a with V12 = 2500 cm-1 rad-1. The tunnelling probability, T, is

then calculated at the energy of 0.5OH 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

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

15

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) 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–

16

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 S0 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 4-

YPhOH+ 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(S1S0) 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(S1S0) 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 S 2 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

available lifetime data for the S1 states of 4-MeOPhOH (1.2 9.8 ns 52) and 4-H2NPhOH

( = 2.2 ns 53).

17

We recognise that the quantum yield for OH 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(S1S0) and I.P.) data for several other 4-

substitued 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 4-

ethylphenol and 4-n-propylphenol,57,58 for example, are very similar to those of 4-

methylphenol, 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 S 1 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 S1S0 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

S1S0 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

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 Ala-

18

Tyr, where the glycine (Gly) or alanine (Ala) is attached to the N-terminus of tyrosine) reveal

S1S0 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(S1S0) 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

T00(S1S0) values for the amino acid L-tyrosine 61,62 (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 L-

tyrosine(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

19

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(S1S0) term values (in italics). Columns 2 and 3 show zero-

point corrected bond strengths, D0(4-YPhOH) 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.

YE(S1S0) / cm-1 D0(4-YPhOH) / cm-1

I.P. / cm-1 p+

Unrelaxed Relaxed Unrelaxed Relaxed

H 36550 34030 36348 14

32420 29950 30015 ± 40 14

6716068625 ± 4 68

0

MeOsyn:

anti:

34130 3394033679 34

33573 25

31260 28820 28620 ± 50 52

6060062308 ± 5 35

62202 ± 5 35

0.78

CH3 35910 3435035333 40

32530 29630 29320 ± 50 40

6403065918 ± 5 69

0.31

F 35420 3403035116 38

32620 29730 29370 ± 50 38

6732068577 ± 5 70

0.07

Cl 35360 3342034811 38

32390 30010 29520 ± 50 38

6654068104 ± 5 71

0.11

Br34794 38 29790 ± 100 72 68718 ± 80 73

0.15

CN 35770 3432035548 74

33630 30620 ± 50

7095072698 ± 5 37

0.66

HOsyn:anti:

33535 75

33500[28430] 64051 76

63998

0.92

EtO 58

syn:anti:

3364733550

28576 6167061565

0.81

C2H5

35503 56[29260] [66150] 0.30

n-C3H7

trans:gauche-A:gauche-B:

35501 57

3545335441

[29270] 65283 ± 5 77

65385 ± 565369 ± 5

0.29

NH2 78

31395 [27910] 588291.31

NO2[30690] 73400 400 79

0.78

21

HOOCCH2CH2

3-(4-hydroxyphenyl) propionic acid

35368 59

H2NCH2CH2

tyramine 35466 6028846

64370 ± 400 80[0.61]

H2NCH(COOH)CH2

L-tyrosine 35491 61 29649 68240 ± 800 62

0

22

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.

Y Rx / Å E(S1/S2 CI)/ eV

E(S1(v=0))/ eV

h / cm-1 w / Å A/ 10-20 J m

TY /107 p+

MeO1.1691.182

4.9875.062

4.5514.562

35144032

0.4740.516

0.8490.985

903 (0.71)202 (0.31)537 (0.52)

0.78

Me1.1841.195

5.2985.364

4.7584.770

43574798

0.4950.533

0.9911.12

189 (0.15)45.1 (0.07)111 (0.11)

0.31

F1.1921.205

5.3225.384

4.7314.743

47685171

0.4830.529

0.9711.10

235 (0.19)59.3 (0.09)140 (0.14)

0.07

H1.1821.194

5.4275.488

4.8844.895

43794776

0.4240.463

0.8170.877

1270 (1.00)661 (1.00)1023 (1.00)

0

Cl1.2111.218

5.3605.421

4.6934.705

53775777

0.5540.600

1.201.29

19.4 (0.02)6.93 (0.01)13.1 (0.01)

0.11

CN1.2341.245

5.6015.662

4.7854.796

65806986

0.6290.680

1.481.61

0.93 (310-3)0.21 (310-4)0.58 (610-4)

0.66

23

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 4-

MeOPhOH 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 short-

wavelength 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(S1S0) 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

References

30

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