Chemical Physics Letters 387 (2004) 238–242

www.elsevier.com/locate/cplett

A QSPR study on optical limiting of organic compounds

Per Lind a, Cesar Lopes b, Kjell €Oberg c, Bertil Eliasson c,*

a Swedish Defence Research Agency, Division of NBC-Defence, SE-901 82 Ume�a, Swedenb Swedish Defence Research Agency, Division of Sensor Technology, SE-581 11 Link€oping, Sweden

c Organic Chemistry, Department of Chemistry, Ume�a University, SE-901 87 Ume�a, Sweden

Received 1 December 2003; in final form 28 January 2004

Published online: 6 March 2004

Abstract

The optical limiting performance of 23 structurally different organic compounds has been measured at the wavelength of 532 nm.

Molecular orbital ab initio calculations were performed to generate molecular electronic variables that were applied in a quantitative

structure–property relationship (QSPR) study. A model that predicts the optical limiting response was constructed by using a partial

least square (PLS) analysis. Six variables that play a major role for the optical limiting ability of organic materials were identified.

� 2004 Elsevier B.V. All rights reserved.

1. Introduction

The interest in organic materials for optical limiting

(OL) devices has increased dramatically over the lastdecade, and a large number of different organic sub-

strates have been investigated for OL applications [1–5].

The possibility to synthetically tailor organic molecules

in order to enhance a required effect is virtually unlim-

ited. This has resulted in the search for computational

methods and reliable structure–property models to

provide useful guidance for synthetic chemists [6–9].

However, many of such studies focus on the third-order hyperpolarizability tensor c, but the relation be-

tween c and optical limiting properties of organic

materials is not straightforward. Two-photon absorp-

tion (TPA) [10] is a major contributing effect to OL and

is thus of special interest in structure–property relation

studies. Several investigations on TPA have been re-

ported over the last couple of years [11–14]. These

studies have given some insight in how organic mole-cules should be designed in order to display an enhanced

TPA cross-section. For example, the presence of p-do-nor groups at both ends of a conjugated molecular

bridge and the effective conjugation length of that bridge

* Corresponding author. Fax: +46-90-136310.

E-mail address: Bertil.Eliasson@chem.umu.se (B. Eliasson).

0009-2614/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2004.02.023

as well as the polarizability and the planarity of the

molecule have all proven to be important parameters to

consider for the design of TPA-chromophores [15].

Reverse saturable absorption (RSA) [16,17] is an-other major contributor to OL effects, but structure–

property relationships for RSA appears to be much less

studied although some examples can be found in liter-

ature [18–20]. It has been shown that the presence of a

heavy atom in a molecule can facilitate intersystem

crossing from an excited singlet state to a triplet state

and that this heavy-atom effect [21] is an important

structural feature for a substance to display significantRSA [22].

To our knowledge there are no examples in literature

of structure–property relationship studies on OL per-

formance in organic compounds using a partial least

square (PLS) [23] method. A PLS study utilizes a mul-

tivariate approach where molecular properties (vari-

ables) can be used to comprise an X-matrix, which is

then related to a response, Y.Subsequently the dataset is analyzed to build a model

to be used for prediction of the OL response of new

compounds. Important variables that describe the re-

sponse can also be identified from the model.

The purpose of this PLS study is to identify such

variables regardless of which electronic process that is

accountable for the effect. In future extensions of the

P. Lind et al. / Chemical Physics Letters 387 (2004) 238–242 239

work, we anticipate that it also should be possibly to

acquire more knowledge on the causes for OL.

Both the choice of variables and the selection of

compounds, with respect to relevance for describing the

specific OL parameters of interest, will determine thequality and the usefulness of the model. It can be ex-

pected that for instance a dataset of similar compounds

will provide a good model for new compounds in such a

series, but the model may not be useful for new com-

pounds with a different type of molecular structure.

We have used readily accessible variables from den-

sity functional calculations in this analysis that describe

molecular structure and properties of the electronicground state (GS). Although it may appear more ra-

tional to use variables related to excited states instead of

the GS to obtain information on nonlinear optical

Table 1

Structure, optical limiting performance and linear transmission of the 23 co

Object no. Structure Iouta(lJ) Tb (%) O

1 35.7 99.8

2 40.0 100

3 33.3 100

4 44.0 86.0

5 23.4 94.3

6 36.1 100

7 21.9 96.6

8 21.3 91.9

9 23.4 100

10 20.5 99.1

11 23.0 100

12 20.0 100

aOutput energy read at an input energy of 150 lJ, compensated for linearbLinear transmission at 532 nm.

processes, we have limited this work to the more readily

available GS data. A reason for this is that we do not

want to exclude the possibility that (i) GS and excited-

state properties are interrelated to such an extent that

the more simple calculations of GS properties are suffi-cient, and (ii) OL to some extent is caused by unknown

processes, less related to excited state properties.

A relatively small number of organic compounds

were chosen for the study, see structural formulas in

Table 1. The compounds were not selected to represent a

particular class of molecules, but rather to include sev-

eral common but different types of structures, such as

compounds with strong electron donor or acceptorsubstituents, heteroaromatics and non-polar aromatic

hydrocarbons. The OL of the compounds was measured

at 532 nm, which is the wavelength most frequently used

mpounds used in the PLS study

bject no. Structure Iouta (lJ) Tb(%)

13 19.8 100

14 18.5 100

15 7.9 98.4

16 15.8 97.9

17 13.8 94.1

18 11.8 93.3

19 39.9 93.8

20 30.5 100

21 20.7 95.2

22 17.7 82.4

23 29.6 98.0

absorption.

240 P. Lind et al. / Chemical Physics Letters 387 (2004) 238–242

for OL studies and also a wavelength well inside the

visible region.

This study should be viewed as the first step of a more

extensive investigation, where coming phases concern

additional compounds and the OL response measured atseveral wavelengths. Another aspect that also needs at-

tention in future studies is that the OL is a function of

laser characteristics such as pulse length and pulse rep-

etition rate.

Table 2

Results from the PLS analysis

Model Na Kb Ac R2Xd R2Ye Q2f

M1 23 41 1 0.548 0.558 0.476

M2 23 17 2 0.812 0.610 0.436

M3 23 9 2 0.774 0.696 0.477

M4 23 6 1 0.836 0.557 0.454

aNumber of compounds in the model.bNumber of variables.cNumber of PLS components.

2. Methodology

All MO calculations were performed using GAUSSIANAUSSIAN

98W software [24]. The geometries of the molecules were

optimized with the B3LYP density functional method

[25], using the 6–31G* basis set, and were followed by

frequency calculations to verify true energy minima.

The compounds (Table 1) were obtained commer-

cially and used as such, except for compounds 5 [26], 7

[27] and 11–14, which were synthesized in our labora-tory [28]. All compounds were dissolved in THF to give

a concentration of 10 mM in 2 mm quartz cuvets.

The OL spectra were recorded with a f/5 focusing

system using a frequency doubled Nd:YAG laser

delivering 5 ns pulses at 532 nm with a repetition rate of

10 Hz [29]. The model response was based on the output

energy (Iout) read at an input energy (Iin) from the laser

of 150 lJ, but in order to ease the interpretation of thePLS model, the inverse of Iout was used since otherwise a

large response value would correspond to a weak optical

limiting. Further 1/Iout was multiplied by the linear

transmission (T ) value at 532 nm, to give the response,

Y. To some extent, this should compensate for an ex-

pected enhanced nonlinear absorption for compounds

with greater linear absorption at 532 nm compared with

other compounds having smaller linear absorption atthat wavelength.

d By the model explained variance in descriptor matrix, X.e By the model explained variance in Y.f Cross-validated variance in Y.

Fig. 1. Score plot of M1, showing the grouping of compounds.

3. Model building

As variables for the X-matrix, the following molec-

ular properties were used in the first PLS model (M1);

the energy of the first five levels of highest occupied andlowest unoccupied MOs (HOMO)4 to HOMO and

LUMO to LUMO+4 in a.u.), the energy difference be-

tween all five HOMOs and five LUMOs, the number of

electrons (e�), the molecular weight (Mw), the number

of occupied MOs over )10 eV (OMO>)10), the total

dipole moment (tot.dipolm. in Debye), the mean polar-

izability (mean polz. in a.u.) and the mean quadrupole

moment (mean qua. in a.u.).To validate the results and to decide the number of

components in each PLS model, we used cross-valida-

tion [30], a statistical method where one part of the data

is used to construct a model and the other part is used to

test the predictability of the model.

4. Results and discussion

The first PLS model, M1, based on the 23 compounds

and using all the variables, gave one PLS component

explaining 54.8% of the variation of the response, Y, with

a corresponding cross-validated value (Q2) of 47.6%,

Table 2. The score plot, Fig. 1, based on two PLS com-

ponents for visualization, displays the grouping of the

molecules. It is noteworthy that compounds 1–5, whichall group together (left in Fig. 1) and give poor responses,

are relatively small unsymmetrical molecules with several

heteroatoms that form donor–acceptor groups, for in-

stance amino and nitro groups, respectively. The mole-

cules also have a large ground state dipole moment.

Compounds with large OL responses, such as 16–18,

group at the other end of the plot. The loading column

plot, Fig. 2, displays the relative importance of thevariables for modelling the response. As seen in Fig. 2,

the most important variables used for modelling the

response in M1 are the mean quadrupole moment,

the mean polarizability and the number of OMOs above

)10 eV, which are all positively correlated to the re-

sponse. A high value of these variables denotes a large

Fig. 4. Calculated vs observed values for M4.

Fig. 2. Loading column plot of M1, displaying the relative importance of the variables for modelling the response.

P. Lind et al. / Chemical Physics Letters 387 (2004) 238–242 241

response. A negative value of a variable shows a negative

correlation to the response, that is, a small figure is as-

sociated with a greater response than is a large negative

figure. It is interesting to note that ground state total

dipole moment is negatively correlated to the response.

An analysis of the HOMO–LUMO coefficients shows

that all HOMO–LUMO differences display a strongnegative correlation to the response, indicating that

small band gaps are required for a good response. The

strong positive correlation of HOMO-levels is also worth

observing.

A new PLS model was calculated where all the dif-

ferences between HOMOs and LUMOs were combined

into one variable, total LUMO) total HOMO. This

resulted in a simpler model, M2, with similar charac-teristics as M1, see Table 2.

In an attempt to further simplify the model, all five

HOMO variables were added together to one variable

(total HOMO) and the same operation was done to the

LUMO variables (total LUMO). This resulted in a third

model, M3, which does not differ much in description

from M1 and M2, Table 2, but actually gives a higher

Q2-value. The loading column plot for M3, displayed inFig. 3, shows that the variables tot.LUMO–tot.HOMO

and total dipole moment are negatively correlated to the

response, while total LUMO has only a small influence

and the remaining variables exhibit a strong positive

correlation.

A last PLS model, M4, were constructed using the six

most important variables suggested by M3, thus leaving

out the molecular weight, the total dipole moment andthe total LUMO variables.

Fig. 3. Loading column plot displaying the relative importance of each

variable modelling the response in M3.

This model is comparable in characteristics to the

previous models, see Table 2, and has a cross-validated

variance in Y of 45.4% which is an acceptable number.

This indicates that six variables are sufficient for mod-

elling the response, as is visualized in the plot of ob-

served versus calculated values, see Fig. 4.

The six remaining variables are of roughly equalimportance as seen in the loading column plot for M4 in

Fig. 5.

The positive response of variables OMOs >)10 eV

and total HOMO indicates that a good OL compound

should have many occupied MOs at high energy levels.

The obvious interpretation of this is that the outer elec-

trons, which are less tightly bound to the molecular core,

are more easily affected by an external electric field. In p-systems, this can well be accompanied by high polariz-

ability and/or hyperpolarizability. In line with this, it can

Fig. 5. Loading column plot displaying the relative importance of each

variable modelling the response in M4.

242 P. Lind et al. / Chemical Physics Letters 387 (2004) 238–242

be rationalized that compounds with many heteroatoms

and donor–acceptor groups (such as 1–5) perform less

well since such structural features tend to lower the en-

ergy level of the occupied MOs in the molecule.

The importance of the quadrupole moment for TPAhas previously been reported by Albota et al. [31]. This

study also demonstrates that the magnitude of the

ground state quadrupole moment should be taken into

account in the design of optical limiting materials. In

addition, the mean polarizability appears to be of im-

portance for modelling the OL performance of an or-

ganic material.

5. Summary and conclusions

In this study the optical power limiting of 23 differentorganic structures has been investigated at 532 nm

without attempts to differentiate between various

mechanisms that produce the optical limiting. By using a

PLS approach we have identified six different molecular

properties that are important for modelling the optical

limiting ability of an organic substance; the number of

electrons, the number of OMOs above )10 eV, the mean

polarizability, the mean quadrupole moment, the totalenergy of the five highest OMOs and the difference in

energy between the five lowest UMOs and five highest

OMOs. Our results imply that these molecular proper-

ties, all easily acquired from ab initio calculations, are to

be considered in the search for, and modelling of, new

OL chromophores. By the use of these variables it may

also be possible to predict what type of modification on

an already existing OL chromophore that is most likelyto have a positive impact on the OL performance.

This work represents the first phase of a more ex-

tensive investigation, where future steps are planned to

include additional and possibly more homogeneous

classes of compounds as well as the OL response at

several different wavelengths. In coming studies, also the

initial choice of variables may be varied; especially in-

teresting would be inclusion of variables more directlyrelated to electronic excited states (transition dipole

moments, lifetime and absorption of excited states, rates

of intersystem crossing).

Acknowledgements

This work was supported by a Photonics in DefenseApplications program run jointly by the Swedish De-

fence Research Agency (FOI) and Defence Material

Administration (FMV).

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