Filename: b312115a

Back | Show only these items: | The S1 neutral and D0 cationic states of fluorobenzene and fluorobenzene–argon probed by ZEKE spectroscopy with partial rotational resolution

1
The S₁ neutral and D₀ cationic states of fluorobenzene and fluorobenzene–argon probed by ZEKE spectroscopy with partial rotational resolution

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

Rotationally resolved zero electron kinetic energy (ZEKE) spectra of fluorobenzene and fluorobenzene–argon have been investigated using a spectator orbital model to interpret the rotational structure.

Type: Object | Advantage: None | Novelty: None | ConceptID: Obj1

Unlike a frozen core model this model relates to the electronic structure in both final and initial states.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

A new ZEKE electron detection scheme was employed to record ZEKE excitation spectra as a function of the S₁ ← S₀ excitation laser photon energy, with fixed photon energy of the ionization laser.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met1

These ZEKE excitation spectra are a sensitive probe of the rotational constants of all three states involved, the S₀ and S₁ of the neutral and the D₀ of the cation.

Type: Object | Advantage: None | Novelty: None | ConceptID: Obj1

The rotational constants of the fluorobenzene cation were found to be A⁺ = 5406.8 ± 5.3 MHz, B⁺ = 2689.7 ± 3.5 MHz, and C⁺ = 1812.1 ± 1.8 MHz.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

The rotational constants for the argon complex were found to be A′ = 1773.3 ± 1.7 MHz, B′ = 1148.9 ± 1.4 MHz, and C′ = 996.83 ± 0.98 MHz in the intermediate S₁ state, and A⁺ = 1848.8 ± 1.8 MHz, B⁺ = 1076.6 ± 1.4 MHz, and C⁺ = 908.37 ± 0.89 MHz in the cationic D₀ state.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

Two structural parameters of the complex were derived from these rotational constants, the distance between the argon atom and the aromatic ring, r_z and the distance in the plane of the aromatic ring between the centre of mass and the argon atom r_x.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

These two parameters were determined as r_x = 0.78 Å and r_z = 3.33 Å in the S₁ state and r_x = 0.36 Å and r_z = 3.76 Å in the D₀ state.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

Introduction

In many studies of the rotational structure of electronic excitations, it has not been possible to resolve individual rotational transitions.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

Despite this, the band profile for these transitions has often proved sufficient to obtain reliable rotational constants.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

A prime example comes from early rotational analyses of the S₁ ← S₀ spectrum of benzene¹ that were successfully carried out using rotational band contour analysis.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

This study was able to demonstrate some of the effects of the high symmetry of benzene on the observed spectra.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

Presently, the use of rotational band contour analysis to obtain rotational constants from S₁ ← S₀ spectra has become a more or less standard spectroscopic technique.^2–4

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met2

However, for transitions from a neutral molecule to an ion core, such as observed in rotationally resolved ZEKE spectroscopy, the situation is much less clear.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

For ionizing transitions or transitions to Rydberg states the selection rules for the change in angular momentum between the neutral and ionic states do not arise simply from the interaction with the photon.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

Instead, angular momentum is transferred to the continuum or Rydberg electron in the final state.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

Hence, in order to apply rotational band contour analysis to ZEKE spectra a model must be employed to account for the ionisation dynamics.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

In rotationally resolved ZEKE spectroscopy, the selection rules for changes in total angular momentum between the neutral (J) and ionic rotational states (J⁺) are not just given by ΔJ = J⁺–J = 0, ±1 since angular momentum can be transferred to the final state Rydberg electron.^5–9

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

The conservation of angular momentum requires that the vector sum of the angular momenta involved, i.e. of the initial (neutral) rotational state (J), the photon (1), the final (ionic) rotational state (J⁺) and the Rydberg electron (l) is equal to zero.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

The ammonia molecule was the first polyatomic molecule studied by ZEKE spectroscopy for which full rotational resolution in the cation was achieved.^10,11

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

This was followed by a study on the rotational structure of benzene.¹²

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

In both cases, the selection rules that exist for these highly symmetric molecules were illustrated.¹³

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

To do this, a compound state was introduced as an intermediate between the initial and final states in the ZEKE transition, using this model, selection rules for allowed transitions could be deduced.^11,13

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

The recorded spectra were found to be in good agreement with the symmetry selection rules that arise from the compound state model.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

A number of other models have been used previously to analyze the rotational structure in ZEKE spectra: Multichannel quantum defect theory (MQDT)¹⁴ has been employed to predict the line intensities for the spectra arising from small molecules such as hydrogen¹⁵ and water,¹⁶ where it was demonstrated to be a valuable tool, particularly with respect to final state interactions (i.e. rotational autoionization), which can have an additional effect on the intensities of ZEKE transitions.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

The role of autoionization in these smaller molecules is important.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

However, for larger molecules, the final state interactions are expected to even out,¹⁷ and furthermore the parameters necessary for applying MQDT become harder to obtain as the molecular core becomes less atomic-like as in ammonia.¹⁸

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

A model by Wang and McKoy has been developed to analyse rotationally resolved ZEKE spectra.¹⁹

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

The method relies on ab initio calculations, which treat the final state wavefunction as the product between the ionic core and scattering wavefunctions found in the field of the ionic core.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

The model has been applied to many, mainly diatomic, molecules and, most recently, the complex formed between sodium and water.²⁰

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

This approach has given very good agreement for rotationally resolved ZEKE spectra and also for photoelectron spectra including their angular distributions.²¹

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

Also, the photoionization dynamics have been very successfully described in terms of bound-free one-electron radial matrix elements and phase shifts for the interpretation of angular photoelectron distributions.^5–9

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

All this work has so far not been extended to larger molecular systems, in particular asymmetric rotor molecules and molecular clusters.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot1

The spectator model, which is the method presented in this paper, has successfully been shown to reproduce the transition intensities in the fully rotationally resolved ZEKE spectra of benzene,²² despite the fact that no account has been taken of the final state interactions.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The model used here is also used to highlight interesting ionisation dynamics in the ZEKE spectroscopy of butylbenzene.²³

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

In this paper, we present a novel approach to describe the ionization dynamics, based on a Rydberg-like spectator orbital description.²⁴

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

This spectator model is simple enough that it can be reliably applied to larger, asymmetric top molecules where final state interactions do not have a significant effect on the relative intensities of ZEKE transitions, and thus facilitate rotational band contour analysis of ZEKE spectra.^2,22–25

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The fluorobenzene molecule is an ideal prototype molecule for spectroscopic studies in a supersonic jet expansion.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

The molecule has a relatively high vapour pressure, and hence it can be seeded into the jet without difficulty.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

Furthermore, the monosubstituted aromatic ring gives rise to strong electronic transitions to the S₁ state, which are symmetry allowed.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

Fluorobenzene has been well characterised by spectroscopy in the S₀, S₁ and the D₀ (cation) states.^26–29

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

The ground state rotational constants are available from microwave spectroscopy,²⁶ whilst S₁ state rotational constants have been obtained using high-resolution laser induced fluorescence (LIF)²⁷ spectroscopy.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

The fluorobenzene cation has been studied using mass-analysed threshold ionisation (MATI) spectroscopy,²⁹ but until now no rotational constants have been obtained for the cation.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

Systems with simple structures such as fluorobenzene, stand as a useful test for the application of the spectator model to asymmetric tops; the equilibrium structure (and even the harmonic frequencies) of such molecules can generally be obtained with sufficient accuracy to reproduce experimentally determined rotational constants using electronic structure methods.^30,31

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

However, weaker interactions with shallow potential minima can be poorly reproduced by electronic structure methods as these interactions arise mainly from electron correlation, hence the rotational constants of weakly bound clusters are much more informative.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

It is therefore useful to show that the spectator model can be successfully applied in the study of weakly bound clusters; hence this study is also applied to fluorobenzene argon.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

Many studies using complexes of argon with aromatic compounds have shown unambiguously from the band profile that, in a supersonic jet expansion, argon will preferentially bind above the aromatic ring.^2,32,33

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

These studies are also useful probes of how the argon binding changes on excitation.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

Typically, the argon is more closely bound in the excited state, which is reflected in a red shift from the monomer excitation to that in the complex (i.e. the vibrationless band origin appears to lower energy for the complex as opposed to the monomer).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

This is indeed the case for fluorobenzene–argon,³⁴ whose structure is depicted in Fig. 1.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

The two structural parameters, r_z and r_x, required to define the position of the argon atom are indicated in this figure.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

The ground state of the complex has been studied using Fourier transform microwave spectroscopy by Stahl and Grabow.³⁴

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

Precise rotational constants were obtained, with the argon structural parameters evaluated as r_z = 355 pm and r_x = –46 pm.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

These results are further supported by the ab initio work of Hobza et al.,³⁵ which involved the use of an extended basis set for the argon atom ([7s4p2d]) to recover the correlation energy using the MP2 method.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

Three intermolecular modes have been observed for fluorobenzene argon in the S₁ state using REMPI spectroscopy by Bieske et al.³⁶

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac14

The cation has been studied on three occasions.^29,37,38

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac14

A vibrational progression in the b_x mode (see Fig. 1) was observed in the ZEKE spectra recorded by Shinohara et al.;³⁸ a Franck–Condon analysis of this progression led to the conclusion that the argon atom was shifted by 7° along the bending coordinate on ionisation from the S₁ state; a calculation based on ab initio atomic charges in the neutral and the cation led to the conclusion that the argon moves toward the fluorine atom.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac15

A similar situation is observed with argon complexes with other electron withdrawing groups such as aniline³⁹ and benzonitrile.⁴⁰

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac15

Given that the rotational constants of the monomer are known, it is possible to obtain zero-point vibrationally averaged values for the structural parameters r_x and r_z.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac16

Assuming the geometric structure of the monomer is not significantly perturbed by the presence of the argon atom,³² the two structural parameters can be obtained by combining the two sets of rotational constants.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac16

The rotational band contour in ZEKE spectroscopy additionally reflects the electronic structure of the molecule; hence it is expected to give an indication of the perturbation of the electronic structure by the argon atom.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac16

Theoretical details

The main premise behind the spectator model, used to reproduce the ZEKE band contour, is to treat the initial state in the ZEKE transition (using a two photon ionisation scheme, this is the intermediate state) with an N electron wavefunction, Ψ′, as a Rydberg-like state, having a separate spectator electron coupled to the ionic core with N – 1 electron wavefunction, Ψ⁺.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

This arises as the first term in an expansion of the intermediate state wavefunction in terms of all the possible states of the ion, Ψ_n⁺, and a single electron wavefunction, that arises from the projection of a given state of the ion on the intermediate state wavefunction eqn. (1).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

Only the first term in this expansion is important, as higher terms will not contribute to the intensity of the ZEKE transition, as they would have no overlap with the ionic wavefunction.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The Rydberg-like orbital in this initial state is therefore termed the spectator orbital, Ψ′_s, which is obtained as the projection of the N–1 electron ionic core wavefunction, Ψ⁺, on to Ψ′.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

This expansion gives rise to a set of orbitals that are non-orthogonal, the spectator orbital is therefore quite different to the orbitals obtained in a Hartree–Fock calculation.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

As the ionising photon interacts only with the spectator orbital (the ion core, Ψ⁺, is already fully electronically relaxed) the ionisation process is effectively reduced from a complex multi-electron process to a single electron process.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

Rotational angular momentum in the initial state can be decoupled into the angular momentum of the spectator electron and rotational angular momentum of the ionic core.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The various angular momenta are referred to according to the symbols listed in Table 1, corresponding to the symmetric top basis functions used to describe the asymmetric top wavefunctions.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The symmetry of the spectator electron is restricted to the product of the symmetry of the ionic core state and the initial state in the ZEKE transition (eqn. (2)) Γ_{Ψ′_s} = Γ_Ψ′ ⊗ Γ_Ψ⁺

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

This can be used to restrict the number of coefficients required to describe the spectator electron.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The values of the l′ and λ′ that are allowed are determined using symmetry correlation tables projecting the cylindrical group D_∞h onto the molecular symmetry group of the molecule in question.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

However, the values depend upon the choice of z-axis, which can logically lie along any of the three principal inertial axes.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The selection rules,¹¹ which arise from the triangle conditions of angular momentum coupling,⁴¹ are given by eqn. (3).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

J′ + l′ ≥ N⁺ ⩾ |J′ – l′|,K⁺ = K′ – λ′

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

An advantage of the spectator model over the compound state model arises, because the symmetry selection rules are not dependent on the interaction of the photon to form the compound state.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

Hence, only the symmetry of the spectator orbital needs to be considered.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

However, it should be noted that this is a limiting case, and in the spectator model, there is no allowance for the fact that the photon angular momentum can be transferred to the core.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The spectator model is an appropriate description; in a dynamic picture, the excited electron will not spend long in the core region after the interaction with the photon.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

The expression for the two photon ZEKE transition intensity for an asymmetric top from this model can be shown to be given by eqn. (4).²⁴

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

The background for the derivation of eqn. (4) can be found in ^{refs. 11, 42 and 43}.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

Any of the three inertial axes can be taken as the z-axis; for fluorobenzene, the c-axis is chosen in order to reflect the symmetry axis in the analogous benzene system.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

The model treats ionization as having occurred from an orbital produced by the projection of the cationic state electronic wavefunction onto that of the intermediate state.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

The expression for the transition intensities is dependent on the radial matrix elements, which relate to the angular distribution of the spectator orbital.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

The radial matrix elements resolve effectively to a series of parameters, γ, which are dependent on only the angular momentum of the spectator electron, l′, and its projection λ′.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

In the expression for the intensity the term γ_l′λ′ appears, which carries information about the angular distribution of the spectator orbital from which ionisation occurs.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

These are the expansion coefficients, γ_l′λ′ = 〈l′λ′|Ψ′_s〉 = 〈l′λ′Ψ⁺|Ψ′〉.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

The expression for the transition intensities, in terms of the ground state (S₀) angular momentum, J″, the intermediate state (S₁) angular momentum J′, the cationic angular momentum excluding electron spin, N⁺, the population in the intermediate state, ρ, and the polarizations of the first and second photon, p′ and p″, is given by eqn. (4).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

In eqn. (4) the sums over K⁺ and K′ come from the expansion of the asymmetric rotor wavefunctions of the ion and the neutral in their respective symmetric rotor basis functions with expansion coefficients α_K⁺ and α_K′ and [l] ≡ [2l + 1].

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

Expression (4) contains terms arising from k = 0, 1 and 2.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

The non-zero values of k originate from the effect of polarization in the two-photon ionization process.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

The k = 1 term is non-zero only for circular polarizations (p″ = ±1 and p′ = ± 1) or crossed linear polarizations and is zero for linear parallel photon polarizations as used in the present experiments.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

The k = 2 term appears complicated, however, our calculations have shown that the k = 2 term is only about 5% of the k = 0 term and hence only makes a minor contribution when parallel linear photon polarizations are used in the experiment.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

However, the k = 2 term cannot be neglected when circular polarizations or crossed linear polarizations are used.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

Discarding the k = 2 term (and the k = 1 term) the transition probability becomes just the one-photon transition probability eqn. (5), which is a simple equation giving intensities that depend only on the values of γ_l′λ′.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

The simplicity of eqn. (5) becomes apparent when considering the radial matrix elements R_ll′.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

Since the sum over λ′, K⁺,K′ does not contain l (the Rydberg or continuum angular momentum) the sum over l can effectively be carried out, thus defining the parameters describing the ionization dynamics as solely the spectator orbital coefficients γ_l′λ′ and a constant radial part R_l′.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

In this way, the Rydberg or continuum part of the problem has thus effectively been removed from the problem.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

100

Since fluorobenzene (FB) is an asymmetric top, the choice of z-axis for the spectator orbital angular momentum can be assigned to any of the three principal axes.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

101

As with butylbenzene,²³ the c-axis, which is approximately perpendicular to the aromatic plane in FB, is chosen.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

102

(the a and b- axes both lie in the aromatic plane, respectively along and across the direction of the side chain).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

103

Although a number of parameters are necessary to describe the spectator orbital, the values of l′ and λ′ determine the selection rules, hence each parameter will have a specific effect on the branch structure of the spectra, and can therefore be independently determined.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

104

If the first term in eqn. (1) were sufficient to describe the electronic structure of the intermediate state, the charge density difference between the cation and the intermediate state (i.e. |〈Ψ′|Ψ′〉|²–|〈Ψ⁺|Ψ⁺〉|²) would be an exact representation of the spectator orbital (i.e. |〈Ψ⁺|Ψ′〉|²).

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

105

As the first term of the expansion would not fully describe the electronic structure, the difference in charge density is an approximate representation of the spectator orbital that can be readily obtained using standard ab initio methods.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

106

As an example the charge density difference between the S₁ state in fluorobenzene and the ground state fluorobenzene cation, calculated using the complete active space self-consistent field (CASSCF) method using eight electrons in the seven orbitals of aromatic character, is depicted in Fig. 2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

107

Scrutiny of the charge density difference reveals it to take both positive and negative values, indicating there are some regions where the electron density is in fact higher in the cation.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

108

The presence of the negative regions is highlighted in the plot of the charge density difference given in Fig. 3, which has been radially averaged about the centre of charge.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

109

This is an indication of the approximate nature of this method for obtaining the spectator electron, as the negative parts can only arise as a consequence of the higher terms in the expansion.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

110

The shift in electron density, which for fluorobenzene accounts for less than 1% of the charge density difference, is reflected in a reduction in the overall intensity of ZEKE transitions independently of the rotational sublevels involved, as seen for two butylbenzene isomers.^44,23

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

111

Estimates for the parameters, γ_l′λ′, were first obtained from an expansion about the centre of mass of the radially averaged electron density presented in Fig. 3 in angular momentum functions.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

112

From these starting parameters the rotational structure in the ZEKE spectra was fitted to optimized parameters γ_l′λ′ by a least squares procedure using eqn. (5).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

113

Then, eqn. (4) was employed for the final fit of the rotational structure.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

114

It was found that when using the full two-photon transition formula the rotational band profile was still insensitive to the radial matrix elements R_ll′, hence in the fit only γ_l′λ′ was optimised.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

115

This is due to the minor contribution of the k = 2 term in eqn.(4).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

116

This k = 2 term contribution is so insignificant that the weighting of the two radial matrix elements R_l–1l′ and R_l+1l′ cannot be obtained from the fit.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

117

It should be noted, however, that this should be possible for measurements with crossed or circular polarizations for which the k = 2 (and, of course, the k = 1) term in eqn. (4) will be enhanced relatively to the k = 0 term.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

118

Also, it should be noted that there is always an uncertainty in the absolute sign of γ_l′λ′ obtained from either the electron density, or fitting to the spectra.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

119

The only way to obtain the absolute sign of the parameters is to calculate the expansion coefficients directly, from the spectator orbital⁴⁵.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

Experimental

120

The experimental spectra presented were recorded using the apparatus described in .^{ref. 46}

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

121

Both the S₁ ← S₀ transition and the ionising transition, in the monomer and the complex, were promoted using the frequency doubled output from two (Radiant Narrowscan) dye lasers, using Coumarin-153 dissolved in isopropyl alcohol, pumped by the third harmonic of the Nd:YAG (Continuum Surelite III) laser.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

122

In order to accurately calibrate the lasers, each spectrum was recorded simultaneously with an iodine absorption spectrum.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

123

The fluorobenzene was introduced into the supersonic jet expansion by passing argon, at a stagnation pressure of 500 mbar, over a sample holder (containing fluorobenzene) situated outside the vacuum chamber.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

124

The fluorobenzene monomer was produced in the molecular beam with a rotational temperature of approximately 6 K. In order to produce fluorobenzene argon clusters in the source, the stagnation pressure of the argon was increased to 2 bar.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

125

REMPI spectra were recorded using a 1 kV extraction pulse to accelerate the ions into the reflectron.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

126

ZEKE spectra were recorded synchronously with high resolution MATI spectra using the pulse sequence given in .^{ref. 46}

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

127

The discrimination field was set at 0.67 V cm^–1, whereas the ionisation field was 0.33 V cm^–1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

128

The resolution obtained for the ZEKE spectra was found to be 0.27 ± 0.01 cm^–1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

129

The ions were accelerated with a 1 kV extraction pulse, and the reflectron voltage was reduced to remove the kinetic energy compensation.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

130

A resonant two-photon ZEKE spectrum is in effect a two-dimensional spectrum; the signal depends both upon the energy from the excitation laser and the ionisation laser.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

131

The excitation laser determines which subset of the rotational levels is populated prior to the ZEKE transition, and the ionisation laser determines the transition energy between the rotational levels.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

132

Thus, the rotational band structure forms a contour.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

133

An impression of the two-dimensional contour associated with fluorobenzene is given in Fig. 4; the width of the peaks is taken to be that expected under experimental conditions (excitation laser FWHM = 0.08 cm^–1, ZEKE line width FWHM = 0.2 cm^–1).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

134

To record such a contour experimentally would be impractical due to the number of data points required.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

135

However, by obtaining a series of well calibrated spectra, scanning either the excitation laser to give a ZEKE excitation spectrum (corresponding to a horizontal slice from Fig. 4), or the ionising laser to give a conventional ZEKE spectrum (corresponding to a vertical slice from Fig. 4), the contour can be effectively sampled giving a greater amount of data with which to obtain fitting parameters than can be obtained simply by recording conventional ZEKE spectra.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

Results and analysis

136

The REMPI spectrum recorded for the origin band of the S₁ ← S₀ transition in fluorobenzene, with a simulation based on the rotational constants from ^{ref. 27} is shown in Fig. 5; the rotational temperature of the band was found to be 6.8 K, this was used as the temperature in all subsequent simulations for the monomer.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

137

The origin band of the D₀ ← S₁ transition was probed giving both ZEKE (Fig. 6) and ZEKE excitation (Fig. 7) spectra.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

138

Although all the band profiles presented were found to be reproducible, daily optimisation of the experimental conditions was found to subtly change the effective magnitude of the extraction field, which is seen as a small shift in the band origin of the MATI spectra, thus to remove the necessity of a separate parameter for the origin of each ZEKE spectrum, all the data presented had to be recorded in one sitting.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

139

The four ZEKE spectra presented in Fig. 6 and the nine ZEKE excitation spectra presented in Fig. 7 were all able to be reproduced, in each case the ionising and excitation laser energies for all these spectra are indicated in the figure captions.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

140

The trend for the ZEKE band to get broader as the excitation laser is moved away from the band centre results from the fact that the higher J states probed have more widely spaced energy levels.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

141

The apparently similar trend for the ZEKE excitation spectra is misleading, as the width of the band does not change.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

142

The stronger signals from the centre of the band disappear, increasing the relative height of the high J wings of the P and R branches.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

143

The rotational constants and the spectator orbital coefficients, γ_l′λ′, were simultaneously fit to all the experimental spectra using a least squares fitting procedure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

144

The initial guess for γ_l′λ′ were obtained from the single centre expansion of the electron density difference, whereas ab initio values were used for the rotational constants.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

145

The symmetry restrictions on the values of l′ and λ′ depend on the symmetry of the spectator orbital and the choice of z-axis for the expansion of the spectator orbital.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

146

The symmetry of the S₁ state is A₂, which corresponds to an S₁ ← S₀ transition moment polarised along the b-axis (the short axis in the plane of the molecule) the symmetry of the D₀ state is B₁, hence according to eqn. (2), the spectator orbital must have b₂ symmetry.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

147

Taking the c-axis in fluorobenzene, which is perpendicular to the plane of the molecule, to be the z-axis means that b₂ symmetry correlates to values of l′ and λ′ such that odd values of l′ correspond to symmetric (+) combinations of even |λ′| (i.e. |λ′〉 + |–λ′〉) whereas, even values of l′ correspond to antisymmetric (–) combinations of odd |λ′| (i.e. |λ′〉 – |–λ′〉) these are denoted as λ^±.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs9

148

The angular distribution of the radially averaged electron density difference was expanded to give the approximate values of the spectator orbital coefficients as listed in Table 2.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

149

The fitted values of γ_l′λ′ are listed alongside the calculated values in Table 2; the rotational constants obtained are listed in Table 3.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

150

The adiabatic ionisation potential of fluorobenzene was found to be 74227.09 ± 0.18 cm^–1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

151

The rotational constants for the S₁ state of fluorobenzene argon were not available from previous literature.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

152

However, values for the ground state rotational constants could be taken from the work of Stahl et al.,³⁴ using which, a fit could be made to the experimental REMPI spectra yielding the S₁ state rotational constants.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

153

The experimental and simulated spectra are presented in Fig. 8; the simulation could not be relied upon to yield useful information as a wide range of parameters could be used to reproduce the spectrum equally well.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

154

The ZEKE spectra presented in Fig. 9 were each recorded via the intermediate resonances as indicated in the figure caption.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

155

Each of the ZEKE excitation spectra given in Fig. 10 were recorded with the ionisation laser fixed at the energies indicated in the figure caption.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

156

The simulations in Fig. 9 and Fig. 10 correspond to the optimised values of the γ_l′λ′ parameters listed in Table 4, which are listed against the values associated with the spectator orbital of the monomer, which differ from those listed in Table 2 as they had to be transformed, using rotation matrices, into the correct inertial frame.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

157

This is necessary due to the fact that the argon atom does not necessarily bind above the centre of mass of the monomer causing the a-axis in the complex to deviate from the direction of the c-axis in the monomer.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

158

In the inertial frame of the fluorobenzene argon complex, there are more contributions to the spectator orbital because the symmetry is reduced from B₂ (C_2v) in the monomer to A″ (C_s) in the complex.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs10

159

Taking the rotational constants obtained for the S₁ state of the complex from the REMPI spectrum it was found that the inertial frame is rotated by 25° about the b-axis of the monomer relative to the aromatic plane.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs11

160

For the simulations in Fig. 9 the spectator orbital coefficients were optimised, allowing for the perturbation caused by the argon atom on the spectator orbital.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

161

Values for the rotational constants in the S₀, S₁ and D₀ states are presented in Table 5.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

162

Two values are given for the S₁ state; those obtained by fitting the REMPI spectra, and those obtained by fitting to the ZEKE excitation spectra.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

163

The band origin for the S₀ ← S₁ transition was found to be 37790.50 ± 0.04 cm^–1, giving a field corrected⁴⁷ adiabatic ionisation potential of 74003.99 ± 0.18 cm^–1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

164

On the basis of the ZEKE excitation spectra, the rotational temperature in the molecular beam was 2.1 K.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

165

Zero-point vibrationally averaged values for the structural parameters r_x and r_z are obtained by combining the experimentally obtained moments of inertia from the monomer with those from the complex.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

166

Thus r_x and r_z can be obtained.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

167

Furthermore, for any given position of the argon atom there is an angle, θ, which represents the rotation of the principal axis system about the (monomer) b axis relative to the aromatic plane, this should not be confused with the b_x coordinate, which describes the asymmetric intermolecular bend.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs12

168

The values obtained for the S₁and D₀ states are given in Table 6, along with those calculated for the ground state in ^{ref. 34}

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

Discussion

169

For the spectroscopy of the fluorobenzene cation, it may seem inappropriate to use the ZEKE excitation spectra as a basis for measuring the cationic rotational constants.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac17

170

However, many advantages can be gained as a result of using these spectra.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac17

171

The dependence of the simulations on the rotational constants in the ion is illustrated in Fig. 11 and Fig. 12.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs13

172

A series of ZEKE spectra recorded by scanning the excitation and ionisation lasers respectively are shown as a function of the A rotational constant, which is varied by 5% from the ab initio values obtained in the CASSCF calculation.

Type: Object | Advantage: None | Novelty: None | ConceptID: Obj1

173

It is apparent from Fig. 12 how the profiles of the spectra recorded by scanning the excitation laser have a much stronger dependence on the rotational constants.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs13

174

This can be a significant advantage for experimental reasons.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

175

It takes a shorter time to record these spectra as the signal to noise ratio is better.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

176

Furthermore, the range of these spectra are shorter as signals correspond to the transitions in the S₁ ← S₀ transition, which is governed by the ΔJ = 0, ±1 selection rule.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs14

177

(The D₀ ← S₁ transition energy, which is fixed in these scans, covers a much broader range due to the possibility of higher angular momentum transfer) The fact that these spectra show a greater dependence on the rotational constants does not mean the ZEKE spectra recorded in the conventional manner (scanning the ionisation laser) are unnecessary.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

178

The energy of the fixed laser is not calibrated introducing an uncertainty, which is addressed by having a combination of both ZEKE and ZEKE excitation spectra.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

179

Furthermore, the branch structure of the conventional ZEKE spectra correlates directly with the spectator orbital parameters, which are needed to simulate the ZEKE excitation spectra.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

180

The reproduction of the ZEKE intensities for fluorobenzene using the spectator model does not appear to suffer from rotational state dependent autoionisation, as was observed for benzene.²²

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs15

181

This may be due to the fact that there are too many bands overlapping in a given spectrum to notice the effect.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

182

However, the number of pathways for rotational autoionisation should be much higher from any given state in an asymmetric rotor as opposed to a symmetric rotor.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

183

Therefore, the cross-section for rotational autoionisation will not be so strongly state dependent.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

184

However, it may still be expected that ZEKE signals arising from cations with a higher rotational angular momentum will be depleted to a greater extent by rotational autoionisation, or conversely, transitions into lower angular momentum states are enhanced more by pseudo autoionisation.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp2

185

This effect can be seen as the simulated ZEKE spectra exhibit stronger signals in the blue end of the spectrum than are seen in the experimental spectra.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs16

186

In the analysis of the rotationally resolved ZEKE spectra of nitric oxide,⁴⁸ this was proposed as being a dominant effect on the ZEKE intensity.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac18

187

The effect does not appear to be very significant, perhaps as consequence of the experimental conditions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

188

The values obtained for the rotational constants are close enough to those from the ab initio calculation to assume that the calculated geometry is an accurate representation of the molecule.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

189

This is unsurprising, as ab initio methods should work very well for smaller molecular systems such as fluorobenzene, which do not have any weak intramolecular interactions that can have an effect on the structure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

190

The values of γ_l′λ′ calculated from the electron density difference bear some relation to those obtained by fitting to the experiment.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

191

The experimental uncertainty in the parameters is not as great as may be expected given the number of parameters present, as each value of γ_l′λ′ corresponds to a markedly different part of the profile: different values of l′ give rise to different ΔJ selection rules, and different values of λ′ give rise to different ΔK propensities (that is preferred values ΔK_a and ΔK_c, or in the ZEKE spectroscopy of symmetric tops the ΔK selection rules).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res25

192

Furthermore the presence of these parameters does not really affect the uncertainty in the rotational constants.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs18

193

The former are a function of the energy of the transitions and the latter are a function of the intensity of the transitions.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs18

194

The mechanism through which the value of l affects the line intensity is down to the number of differently polarised final states that can be accessed with a given l.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac19

195

Hence, in order to reliably probe the values of the radial matrix elements, the rotational band profile can be studied as a function of the polarisation of the ionising and excitation lasers.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac19

196

For the fluorobenzene argon complex S₁ ← S₀ spectrum we encountered great difficulty in fitting the band contour.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs19

197

A major reason for this is due to the congestion of the spectra limiting the number of resolved bands.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res26

198

However, the relatively large shift in the equilibrium position of the argon causes a rotation of the inertial axes by 17° between the S₀ and S₁ states (corresponding to a change in the b_x coordinate by 6.3°).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs20

199

This gives rise to perturbations in the transition intensities by an effect referred to as axis tilting,^49,50 which has not been taken into account in the simulation of the S₁ ← S₀ transition.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs20

200

As axis tilting only perturbs the intensities of transitions, the rotational transition energies are not affected; hence, the rotational constants obtained for the intermediate state using the much less congested ZEKE excitation spectra should be reliable.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

201

The effect of axis tilting on ZEKE intensities may be reflected in a perturbation of the spectator orbital, whereupon it will be compensated for by small changes in the spectator orbital coefficients.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

202

The structural parameters derived from the rotational constants listed in Table 6 are consistent with structural changes that may be expected to occur.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res27

203

The change in the b_x bending coordinate of 7° between the S₁ state and the cation predicted in ref. ³⁸ from a Franck–Condon analysis is supported by the structures determined from the rotational coordinates, which indicate a change in the coordinate of 7.7°.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res27

204

The movement of the argon atom away from the fluorine atom on excitation can be attributed to an increased charge separation in the excited state, bringing about both an attraction to the positive charge in the aromatic ring region, and a repulsive interaction with the increased electron density in the region of the fluorine atom.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res28

205

Upon ionisation, the opposite effect is seen as the reduced negative charge causes the fluorine atom to exert a lesser repulsive force on the argon atom than in the S₀ and S₁ states.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res28

206

This is consistent with the charge-induced dipole calculations carried out by Shinohara et al.³⁸

Type: Result | Advantage: None | Novelty: None | ConceptID: Res28

207

The changes in the spectator orbital coefficients between the monomer and the complex are significant for four coefficients.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

208

There is a reduction in the magnitude of the γ_31⁺ and γ_33⁺ coefficients, whereas there a significant increase is seen in the γ_55⁺ and γ_53⁺ coefficients.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

209

All these contributions have a symmetry which would correspond to an imbalance between the electron density above and below the aromatic ring.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

210

The combination of these changes indicates an increased probability of ionisation away from the centre of positive charge.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

211

From this it is inferred that the presence of the argon atom causes an increase in the probability of ionisation from the region between the argon atom and the centre of positive charge in the cation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Concluding remarks

212

ZEKE spectroscopy of fluorobenzene and its complex with argon, via the S₁ intermediate states, yield rotational band contours that were successfully simulated using a Rydberg-like spectator orbital model.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

213

By recording band profiles as a function of both the ionising and excitation lasers, reliable values for the cationic rotational constants can be obtained—even for a reasonably large molecular cluster.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

214

The estimated angular momentum contributions were found to be a useful approximation to those found by obtaining fits to the experimental spectra.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

215

The method used to estimate these parameters could be improved upon by resorting to higher level configuration interaction ab initio methods.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

216

In the case of the complex, the difficulties in finding rotational constants in the S₁ state with REMPI spectroscopy are overcome by additional information on the S₁ ← S₀ transition available from ZEKE excitation spectra.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

217

The movement of the argon atom in transitions between the three states studied is consistent with previous studies and empirical calculations that have been carried out for the system.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

218

The effect of the argon atom on the spectator orbital is small but significant; the changes between the monomer spectator orbital projected into the inertial frame of the complex and those found for the complex can be reasonably accounted for as being a consequence of the perturbation of the electronic structure by the argon atom.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

219

However, some of the observed changes in the spectator orbital coefficients may be reflecting the presence of axis-tilting transitions.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6