Research Article Static and Dynamic Electronic (Hyper ...downloads.hindawi.com/journals/tswj/2013/832682.pdf · e Scientic World Journal 0.4 0.3 0.2 0.1 0.0 12 14 16 18 20 22 26 28

Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 832682 9 pageshttpdxdoiorg1011552013832682

Research ArticleStatic and Dynamic Electronic (Hyper)polarizabilities ofDimethylnaphthalene Isomers Characterization of SpatialContributions by Density Analysis

Andrea Alparone

Department of Chemistry University of Catania Viale A Doria 6 95125 Catania Italy

Correspondence should be addressed to Andrea Alparone agalparonegmailcom

Received 12 August 2013 Accepted 4 September 2013

Academic Editors N Lisitza and P Pietrzyk

Copyright copy 2013 Andrea Alparone This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Static and frequency-dependent electronic (hyper)polarizabilities of the dimethylnaphthalene (DMN) isomers were computed invacuum using the Coulomb-attenuating Density Functional Theory method The nonlinear optical Second Harmonic Generation(SHG) and Electro-Optical Pockels Effect (EOPE) were investigated at the characteristic NdYAG laser wavelength of 1064 nmTheresponse electric properties especially the longitudinal polarizability polarizability anisotropy and first-order hyperpolarizabilityare significantly affected by the position of the methyl groups The SHG and EOPE techniques can be potentially useful todiscriminate the 120572120572-DMN isomers (26-DMN lt 27-DMN lt 23-DMN) as well as the 120573120573-DMN isomers (15-DMN lt 14-DMN lt 18-DMN) The (hyper)polarizability differences among the investigated DMNs were elucidated through density analysiscalculations The predicted polarizabilities exhibit good linear relationships with the experimental first-order biomass-normalizedrate coefficient a physicochemical property connected to the rates of biodegradation processes of polycyclic aromatic hydrocarbons

1 Introduction

Polycyclic aromatic hydrocarbons (PAHs) are very stableorganic lipophilic pollutants principally produced duringincomplete combustion processes often exhibiting high lev-els of toxicity mutagenicity and carcinogenicity to humansandor other living creatures [1ndash5] Since PAHs are ubiq-uitous contaminants there is much interest in searchingpractical strategies for their identification and removal fromenvironments Generally alkylated derivatives are found inprevalence in the environmental samples of PAHs [6ndash8]Dimethylnaphthalenes (DMNs) are substituted PAHs of greatenvironmental interest [9ndash15] DMNs can exist as ten iso-meric forms (Figure 1) 12-DMN 13-DMN 14-DMN 15-DMN 16-DMN 17-DMN 18-DMN 23-DMN 26-DMNand 27-DMN It has been previously recognized that theenzymatic biodegradation of DMNs in aqueous media isstrongly affected by the specific position of the methylsubstituents [12] Indeed the first-order biomass-normalizedrate coefficient (119896119887) of DMNs varies within one order of mag-nitude the 120573120573-disubstituted isomers showing the maximum

119896119887 values along the series [12] Therefore the detection of theDMN isomers in the environmental mixtures is of funda-mental importance from environmental and biochemicalviewpoints On the basis of experimental and theoreticalinvestigations the active site of the enzyme which controlsthe biodegradative mechanism is mainly characterized byhydrophobic residues [12 13] involving contributions fromdispersive andor inductive forces in enzyme-substrate com-plex formation This result has been corroborated by recentcomputational studies on the electronic polarizabilities (120572)[14 16] and Raman spectra [15] of alkylated-naphthalenesthe average polarizabilities [14] and summation of theRamanactivities [15] of DMNs being found to be linearly related tothe experimental 119896119887 values However although the averagepolarizabilities (⟨120572⟩) of DMNs regularly increase in the order⟨120572⟩(120572120572-DMNs) lt ⟨120572⟩(120572120573-DMNs) lt ⟨120572⟩(120573120573-DMNs) theyslightly vary among the ten isomers (up to 35) Thus theaverage polarizability is little useful to discriminate unam-biguously the DMN isomers A physicochemical propertymuchmore affected by the structural features is the electronicfirst-order hyperpolarizability (120573) and the related nonlinear

2 The Scientific World Journal

1

2

3

45

6

7

8

9

10

y

x

Figure 1 Coordinate system and atom numbering of dimethylnaphthalene (DMN) isomers

optical (NLO) properties Second Harmonic Generation(SHG) and Electro-Optical Pockels Effect (EOPE) [17ndash32]SHGmeasurements are currently employed for the structuralidentification of biomolecules such as peptides and proteins[28ndash32]

Themain focus of this study is to determine the static andfrequency-dependent electronic 120572 and 120573 values of the seriesof the DMN isomers aiming to explore the effects of the posi-tion of the CH3 groups on these electric properties poten-tially helpful for the isomeric discrimination The electronic(hyper)polarizabilities are commonly predicted by means ofab initio andor Density Functional Theory (DFT) computa-tionsHowever aswell-known in the literature for an accuratedetermination of the electronic (hyper)polarizabilities thechoice of the functional is critical especially in the case of120587-conjugated compounds [33] In fact on the whole theconventional DFT methods tend to systematically overesti-mate the electronic (hyper)polarizabilities obtained by high-level correlated ab initio levels On the other hand the long-range corrected DFTmethods incorporating nonlocal effects[34 35] describe adequately the diffuse regions of the chargedistributions giving much more satisfactory performancesfor the prediction of the response electric properties Inthe present study we used the Coulomb-attenuating hybridexchange-correlation functional (CAM-B3LYP) [36] whichhas been recently employed with success for computingelectronic (hyper)polarizabilities of organic compounds [37ndash48]

2 Computational Details

All calculations were performed with the Gaussian 09program [49] We used the molecular geometries pre-viously optimized at the DFT-B3LYP level with the 6-31Glowast basis set [14] Static and frequency-dependent elec-tronic (hyper)polarizability tensor components 120572119894119895 and120573119894119895119895 (119894 119895 = 119909 119910 119911) were obtained through the Coupled-Perturbed Hartree-Fock procedure [50 51] using the DFT-CAM-B3LYPmethodwith the polarized and diffuse 6-31+Glowastbasis set The CAM-B3LYP functional and the 6-31+Glowast basis

set can be considered suitable choices especially for theprediction of the electronic (hyper)polarizabilities of organicmolecules [37ndash48 52ndash54] However we checked the perfor-mances of the basis set (6-31+Glowast versus POL Sadlejrsquos basis set[55]) and level of calculation (CAM-B3LYP versus second-order Moslashller-Plesset perturbation theory (MP2)) on therelated compound toluene Dynamic (hyper)polarizabilitieswere evaluated at the experimental NdYAG laser wavelengthof 1064 nm (ℏ120596 = 004282 au) for the SHG [120573(minus2120596 120596 120596)]and EOPE [120573(minus120596 120596 0)] NLO processes

We report the dipole moments (120583) the isotropicallyaveraged polarizabilities (⟨120572⟩) the polarizability anisotropies(Δ120572) and the isotropically first-order hyperpolarizabilities(120573vec) which are defined respectively as [56]

120583 = radic1205832119909

+ 1205832119910

+ 1205832119911

⟨120572⟩ =

1

3

(120572119909119909 + 120572119910119910 + 120572119911119911)

Δ120572 =

1

2

[ (120572119909119909 minus 120572119910119910)

2

+ (120572119909119909 minus 120572119911119911)2

+ (120572119910119910 minus 120572119911119911)

2

+ 6 (1205722

119909119910+ 1205722

119909119911+ 1205722

119910119911) ]

12

120573vec = radic1205732119909

+ 1205732119910

+ 1205732119911

(1)

where 120573119894 (119894 = 119909 119910 119911) is given by 120573119894 = (13) sum119895=119909119910119911

(120573119894119895119895 +

120573119895119894119895 + 120573119895119895119894)

3 Results and Discussion

31 Basis Set and Level of Calculation Effects Response ElectricProperties of Toluene For an accurate prediction of theelectronic (hyper)polarizabilities the choice of the basis setand level of computation is of crucial importance [57ndash67] Inthe present study we explored the effects of the basis set andtheoretical level on toluene as a test case Table 1 reports the

The Scientific World Journal 3

Table 1 Static electronic ⟨120572⟩ (A3) Δ120572 (A3) and 120573vec (10minus53 C3m3Jminus2)

of toluenea

⟨120572⟩ Δ120572 120573vec

CAM-B3LYPPOL 1225 668 2793CAM-B3LYP6-31+Glowast 1150 643 3166MP26-31+Glowast 1143 624 3124aAll calculations are carried out on the B3LYP6-31Glowast geometry

⟨120572⟩Δ120572 and120573vec values of toluene calculated using the CAM-B3LYP and MP2 levels with the 6-31+Glowast and Sadlejrsquos POLbasis set The latter basis set was specifically constructed forpolarizability computations and has been recently employedwith success to predict the electronic polarizabilities ofnaphthalene (N) [68] However it is well-demonstrated thatfor 120587-conjugated compounds the smaller 6-31+Glowast basis setfurnishes an adequate alternative to the POL as well asmore extended basis sets for predicting response electricproperties but at significantly minor computational costs[39 45ndash48 52ndash54]

The present results show that when passing from the6-31+Glowast to the POL basis set only marginal effects areobserved In fact the ⟨120572⟩ and Δ120572 values increase by 075 A3

(+65) and 025 A3 (+39) respectively whereas the 120573vecdecreases by 373 times 10minus53 C3m3Jminus2 (minus133) Note that the(hyper)polarizability calculations carried out using the 6-31+Glowast basis set require noticeablyminor CPU resources thanthose with the POL basis set (by about a factor of twenty)In addition we investigated the effects of the computa-tional method by comparing the CAM-B3LYP and MP2(hyper)polarizability data In line with the recent literature[37ndash39 45ndash48 69] the differences between the two levels arefurther smaller than those found for the basis sets the ⟨120572⟩Δ120572 and 120573vec values being calculated within 007 A3 (06)019 A3 (30) and 42 times 10minus53 C3m3Jminus2 (13) respectivelyThus considering the above results the CAM-B3LYP6-31+Glowast level can be judged as an acceptable compromisebetween accuracy and computational cost and has beenentirely employed for the subsequent calculations on thestatic and frequency-dependent (hyper)polarizabilities of theDMN isomers

32 Static and Dynamic Polarizabilities of the DMN IsomersTable 2 lists the static and frequency-dependent polarizabil-ities of the DMNs calculated in the gas phase at the CAM-B3LYP6-31+Glowast level For all the isomers 120572119909119909 is the largestcomponent giving 43ndash49 of the total polarizabilities (120572119909119909 +

120572119910119910 + 120572119911119911) The dispersion effects here evaluated at the ℏ120596 =004282 au are rather modest increasing the static 120572119909119909 ⟨120572⟩

and Δ120572 values by 054ndash070 A3 + (2) 034ndash036 A3 (+2)and 040ndash055 A3 (+3) respectively Table 2 also reports thedata of the unsubstituted compoundN forwhich some exper-imental and high-level correlated ab initio values are availablein the literature [68 70] The static CAM-B3LYP6-31+Glowast120572119909119909 ⟨120572⟩ and Δ120572 values of N agree satisfactorily with boththe observed (within minus08 minus28 and +23 resp) [70] andCCSDPOL data (within minus20 minus40 and +24 resp) [68]

Not surprisingly the static CAM-B3LYP6-31+Glowast⟨120572⟩ valuesof the DMN isomers underestimate the previously calculatedB3LYP6-31+Glowast figures [14] by 042ndash051 A3 (20ndash24) prin-cipally owing to the introduction of nonlocal effects

The order of the static and dynamic CAM-B3LYP6-31+Glowast120572119909119909 values is the following

14-DMN sim 15-DMN lt 18-DMN lt 12-DMN lt 13-DMN sim 16-DMN lt 17-DMN lt 23-DMN lt 26-DMN sim 27-DMN

For the ⟨120572⟩ values the above order is slightly modified withthe 18-DMN and 26-DMN isomers being respectively theless and more polarizable along the series

18-DMN lt 14-DMN sim 15-DMN lt 12-DMN lt 17-DMNsim 13-DMNsim 16-DMNlt 23-DMNlt 27-DMNsim 26-DMN

The order of the Δ120572 values is rather similar to that found forthe 120572119909119909 data except for the inversions between 16-DMN and17-DMN and between 26-DMN and 27-DMN

14-DMN lt 15-DMN lt 18-DMN lt 12-DMN sim 13-DMNsim 17-DMNlt 16-DMNlt 23-DMNlt 27-DMNlt 26-DMN

All the predicted polarizabilities concordantly increase onpassing from the120572120572-DMNs to the120572120573-DMNs and then to the120573120573-DMNs in agreement with the previous ⟨120572⟩ data obtainedat the B3LYP6-31+Glowast level in gaseous and aqueous phases[14] Specifically when we compare the 14-DMN and 26-DMN isomers the static CAM-B3LYP6-31+Glowast 120572119909119909 ⟨120572⟩ andΔ120572 values enhance by 451 A3 (+170) 053 A3 (+26) and332 A3 (+241) respectively However whereas the static⟨120572⟩ data slightly change along the series of isomers (within065 A3 32) the Δ120572 and 120572119909119909 values are distributed overlarger ranges beingwithin 332 A3 (241) and 454 A3 (171)respectively On the whole these results suggest that incomparison to the average polarizabilities the 120572119909119909 and Δ120572

properties are much more affected by the position of themethyl substituent being potentially useful to identify theDMN isomers Additionally in agreement with a previousstudy on the average polarizabilities [14] the present 120572119909119909

and Δ120572 data of DMNs are found to be linearly related tothe biodegradation experimental biomass-normalized first-order rate coefficients 119896119887 [12] confirming the crucial roleof the polarizabilities in the biodegradation process of thisgroup of organic pollutants The 120572119909119909119896119887 ⟨120572⟩119896119887 and Δ120572119896119887

linear relationships are displayed in Figure 2 showing goodstatistics since the 119903 value is predicted between 097 and100 (following the discussion reported in [14] the 27-DMNisomer was excluded from the relationships)

In order to explain the polarizability differences amongthe DMN isomers we analyzed the spatial contributions ofelectrons to the polarizabilities by using the concept of den-sity of polarizability 120588

(1)

119895(119903) [71 72] The 120588

(1)

119895(119903) is defined as

derivative of the charge density function 120588(119903 119865) with respect


04

03

02

01

0012 14 16 18 20 22 26 28 30 32

Δ120572

27-DMN

26-DMN

18-DMN

120572xx

(a) (b) (c)kb

((m

g of

pro

tein

L)(

hminus1))minus1

Polarizability (A3)

120572⟩

⟩

Figure 2 Relationships between the experimental biomass-normalized first-order rate coefficient 119896119887 [12] and the gas phase CAM-B3LYP6-31+Glowast polarizabilities of the DMN isomers (a) 119896119887 = minus0591 + 0046 times Δ120572 (119903 = 097) (b) 119896119887 = minus5245 + 0258 times ⟨120572⟩ (119903 = 100) (c)119896119887

= minus0826 + 0033 times 120572119909119909

(119903 = 097)

Table 2 Static and dynamic (ℏ120596 = 004282 au) electronic 120572119909119909 (A3) ⟨120572⟩ (A3) and Δ120572 (A3) of the dimethylnaphthalene isomers and

naphthalenea

ℏ120596

120572119909119909(minus120596 120596) ⟨120572⟩(minus120596 120596) Δ120572(minus120596 120596)

119896119887

b

0 004282 0 004282 0 00428212-DMN 2853 2914 2065 2100 1500 1546 0100 plusmn 003

13-DMN 2874 2936 2077 2112 1503 1550 0120 plusmn 004

14-DMN 2655 2709 2054 2089 1380 1420 0055 plusmn 002

15-DMN 2658 2712 2055 2090 1389 1430 0065 plusmn 001

16-DMN 2876 2938 2078 2113 1519 15650120 plusmn 004

17-DMN 2884 2946 2076 2111 1508 155518-DMN 2677 2732 2042 2076 1397 1438

0033 plusmn 002

23-DMN 3058 3127 2090 2125 1655 170826-DMN 3106 3176 2107 2143 1712 1767 0200 plusmn 005

27-DMN 3109 3179 2106 2142 1690 1745 0360 plusmn 007

N 2420(2439)c 1691(1740)c 1321(1291)caAll calculations were carried out at the CAM-B3LYP6-31+Glowast level on the B3LYP6-31Glowast geometry taken from [14]bExperimental first-order biomass-normalized rate coefficient 119896119887 ((mg of proteinL)minus1(h)minus1) in aqueous systems [12]c[70]

to the applied fields 119865 (119903 is the position vector) The 120588(119903 119865) iscommonly expanded in powers of 119865 as

120588 (119903 119865) = 120588(0)

(119903) + sum

119895

120588(1)

119895(119903) 119865119895 +

1

2

sum

119895

120588(2)

119895119896(119903) 119865119895119865119896

+

1

2

sum

119895

120588(3)

119895119896119897(119903) 119865119895119865119896119865119897 + sdot sdot sdot

120588(1)

119895(119903) =

120597120588 (119903 119865)

120597119865119895

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0

120572119894119895 = minus int 119903119894 120588(1)

119895(119903) 119889119903

(2)

For a certain positive-negative 120588(1)

119895(119903) pair the sign is positive

when the direction of the positive to negative densitiescoincides with the positive direction of the chosen coordinatesystemwhereas themagnitude is proportional to the distancebetween the two densities In the present study we deter-mined the 120588

(1)

119895(119903) densities at the CAM-B3LYP6-31+Glowast level

for the longitudinal component (119895 = 119909) As representativecases of the 120572120572-DMN and 120573120573-DMN isomers we investi-gated the 120588

(1)

119909(119903) densities for 14-DMN and 23-DMN The

120588(1)

119909(119903) distributions are displayed in Figure 3 From the

CAM-B3LYP6-31+Glowast computations the 120572119909119909(23-DMN)value is higher than the corresponding datumof the 14-DMNisomer by about 4 A3 (Table 2) For both the isomers thelargest positive to negative 120588

(1)

119909(119903) contributions are mainly

placed over the N moiety However as can be appreciated


120572xx = 2655 A3

120572xx = 3058A3

X

Figure 3 Calculated 120588(1)

119909(119903) density distributions for the 14-DMN

(top) and 23-DMN (bottom) isomers Positive and negative arerepresented by yellow and blue isosurfaces (0001 au) respectivelyCAM-B3LYP6-31+Glowast results

from the plots in Figure 3 the 23-DMN isomer exhibitsadditional relevant120588

(1)

119909(119903) densities localized on both theCH3

groups These methylic 120588(1)

119909(119903) amplitudes are much more

conspicuous than those found for the 14-DMN isomercontributing to the increase of the 120572119909119909 component by ca 17

33 Static and Dynamic First-Order Hyperpolarizabilitiesof the DMN Isomers The calculated static 120573119909119909119909 and 120573vecvalues of the DMN isomers obtained in vacuum at theCAM-B3LYP6-31+Glowast level are collected in Table 3 As forthe computed dipole moments [14] due to the mutual dis-position of the methyl substituents the 15-DMN and 26-DMN isomers are nonpolar compounds In the presentstudy besides to the static first-order hyperpolarizabilities wealso determined the frequency-dependent properties for theSHG and EOPE NLO phenomena since observed data arenearly always obtained at incident optical fields In order tominimize resonance enhancements the dynamic hyperpo-larizabilities were evaluated at the 120582 value of 1064 nm (ℏ120596 =004282 au) which is sufficiently apart from the observedlowest-energy absorption of DMNs (the experimental 120582maxvalues are in the range 274ndash289 nm) [73] The dynamic120573vec(minus120596120590 1205961 1205962) data are included in Table 3 As should beexpected 120573vec(minus2120596 120596 120596) gt 120573vec(minus120596 120596 0) for all the isomers

120573xxx = 641 times 10minus53 C3m3Jminus2


X




The dispersion effects enhance the static 120573vec(000) values by6ndash18 and 17ndash57 for the EOPE and SHG processesrespectively the largest increases being found for 14-DMNin agreement with its highest 120582max value among the DMNisomers

The static and dynamic 120573vec values concordantly predictthe following order

14-DMN lt 16-DMN lt 27-DMN lt 13-DMN lt 17-DMN lt 18-DMN lt 12-DMN lt 23-DMN

Note that the above order is rather different from thoseobtained for the polarizabilities a 120573vec versus 119896119887 relationshipcannot be established In particular the static and dynamicCAM-B3LYP6-31+Glowast 120573vec(23-DMN) values are calculatedto be 5-6 times higher than the corresponding data obtainedfor the 14-DMN isomer More importantly we notice thatthe first-order hyperpolarizabilities of the 120573120573-DMNs aresomewhat different from each other for the 26-DMN isomerthe 120573vec is zero since it belongs to the 1198622ℎ symmetry pointgroup whereas the 120573vec(23-DMN)120573vec(27-DMN) ratios arepredicted to be 25ndash27 by the present static and dynamiccomputations Similarly the 120573vec values of the 120572120572-DMN


Table 3 Calculated 120583(119863) static and dynamic (ℏ120596 = 004282 au) electronic 120573119909119909119909(0 0 0) and 120573vec(minus120596120590 1205961 1205962) (10minus53 C3m3Jminus2) of thedimethylnaphthalene isomersa

120583 120573119909119909119909(0 0 0) 120573vec(0 0 0) 120573vec(minus120596 120596 0) 120573vec(minus2120596 120596 120596)

12-DMN 069 4303 7439 8080 923413-DMN 054 minus4120 5996 6605 782314-DMN 006 625 1796 2116 282215-DMN 000 00 00 00 0016-DMN 049 minus3488 4489 4745 529017-DMN 062 3703 6284 6701 737518-DMN 066 00 6733 7342 859323-DMN 090 8798 11575 12569 1474926-DMN 000 00 00 00 0027-DMN 020 00 4617 4970 5419aAll calculations were carried out at the CAM-B3LYP6-31+Glowast level on the B3LYP6-31Glowast geometry

isomers are rather different from each other In fact on pass-ing from 14-DMN to 18-DMN the 120573vec(minus120596120590 1205961 1205962) dataincrease by a factor of threefour whereas the 120573vec(15-DMN) value is zero (1198622ℎ symmetry point group) Note thata somewhat different situation occurs for the 120572120573-DMNisomers which exhibit hyperpolarizabilities much closer toeach other

Interestingly as for the computed 120573vec data 120583(14-DMN)

and 120583(23-DMN) (Table 3) are respectively the smallest andgreatest 120583 values along the series of the DMNs The orderof the 120583 values is roughly similar to that of the first-orderhyperpolarizabilities a linear relationship between the 120573vecand 120583 values being established (120573vec = 11832 + 9486 times 120583119903 = 092) This result indicates that as for the 120583 data the120573vec values of the DMNs are mainly affected by the mutualdisposition of the CH3 groups mesomeric effect enhance-ments of the hyperpolarizabilities being expected to bemarginal

As for the polarizabilities we explored the hyperpolar-izability differences between the 14-DMN and 23-DMNisomers through hyperpolarizability density analyses The 120573

density 120588(2)

(119903) is expressed as follows [71 74]

120588(2)

119895119896(119903) =

1205972120588 (119903 119865)

120597119865119895120597119865119896

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0119865119896=0

120573119894119895119896 = minus

1

2

int 119903120588(2)

119895119896(119903) 119889119903

(3)

By analyzing the main contributing components for the14-DMN isomer the largest hyperpolarizability componentlies along the 119909-axis At the CAM-B3LYP6-31+Glowast level thestatic 120573119909119909119909(14-DMN) value is calculated to be 625 times

10minus53 C3m3Jminus2 recovering ca 35 of the 120573vec(0 0 0) valueSimilarly the 120573119909119909119909 component dominates the first-orderhyperpolarizability of 23-DMN the 120573119909119909119909(0 0 0)120573vec(0 0 0)

ratio being calculated to be 076 Thus we computed the120588(2)

119895119896(119903) distributions for the 119909119909 component at the CAM-

B3LYP6-31+Glowast level using a numerical procedure describedin detail in [74] Figure 4 displays the 120588

(2)

119909119909(119903) densities for

the 14-DMN and 23-DMN isomers As can be seen fromthe graphical representations for both the isomers themost significant 120588

(2)

119909119909(119903) amplitude is furnished by the N

skeleton although it is much more expanded in the caseof the 23-DMN isomer In addition different from the 14-DMN isomer for 23-DMN a conspicuous positive 120588

(2)

119909119909(119903)

contribution is also provided by both the CH3 groups On thewhole the above 120588

(2)

119909119909(119903) results are in qualitative agreement

with the calculated static hyperpolarizabilities the 120573119909119909119909(23-DMN)120573119909119909119909(14-DMN) and 120573vec(23-DMN)120573vec(14-DMN)ratios being predicted to be 14 and 6 respectively

4 Conclusions

In this study we investigated the electronic polarizabilitiesand first-order hyperpolarizabilities of the series of DMNisomersThe computations were performed in vacuum usingthe CAM-B3LYP functional and the 6-31+Glowast basis set Theresponse electric properties were obtained in the static anddynamic regimes for the SHG and EOPE NLO phenomenaat the 120582 value of 1064 nm The average polarizability varies alittle along the series of isomers whereas both the longitu-dinal polarizability and anisotropy of polarizability are muchmore affected by the position of the methyl substituents Inagreement with recent theoretical studies on the polarizabil-ities [14] and Raman spectra [15] linear relationships areestablished between the calculated polarizabilities and theexperimental biodegradation rates of DMNs confirming theimportant role of dispersive andor inductive interactions forthe biodegradative mechanisms of this group of substitutedPAH isomers

The static and frequency-dependent first-order hyperpo-larizabilities are strongly dependent on the relative position ofthe CH3 groups This is especially evident for the 120572120572-DMNand 120573120573-DMN isomers 26-DMN lt 27-DMN lt 23-DMNand 15-DMN lt 14-DMN lt 18-DMN The present resultssuggest that some DMN isomers might be distinguishedthrough SHG and EOPE NLO measurements Density anal-ysis computations are useful for qualitative interpretations ofthe (hyper)polarizabilities of the DMN isomers


References

[1] J C Arcos and M F Argus ldquoMolecular geometry and car-cinogenic activity of aromatic compounds New perspectivesrdquoAdvances in Cancer Research vol 11 pp 305ndash471 1969

[2] D Hoffmann and E L Wynder ldquoOrganic particulate pollu-tantsmdashchemical analysis and bioassays for carcinogenicityrdquo inAir Pollution A C Stern Ed vol 2 pp 361ndash455 AcademicPress New York NY USA 1977

[3] H V Gelboin and P O P Tsrsquoo Polycyclic Hydrocarbons andCancer Academic Press New York NY USA 1978

[4] R G Harvey Polycyclic Aromatic Hydrocarbons Chemistry andCarcinogenicity Cambridge University Press Cambridge UK1991

[5] B J Finlayson-Pitts and J N Pitts Chemistry of the Upperand Lower Atmosphere Academic Press San Diego Calif USA2000

[6] C A Peters ldquoCoal tar dissolution in water-misclble solventsexperimental evaluationrdquo Environment Science Technology vol27 no 13 pp 2831ndash2843 1993

[7] K L Garcia J J Delfino and D H Powell ldquoNon-regulatedorganic compounds in Florida sedimentsrdquoWater Research vol27 no 11 pp 1601ndash1613 1993

[8] L P Burkhard and B R Sheedy ldquoEvaluation of screeningprocedures for bioconcentratable organic chemicals in effluentsand sedimentsrdquo Environmental Toxicology and Chemistry vol14 no 4 pp 697ndash711 1995

[9] R Atkinson and S M Aschmann ldquoKinetics of the reactionsof naphthalene 2-methylnaphthalene and 23-dimethylnaph-thalenewithOHradicals andwithO3 at 295plusmn 1 Krdquo InternationalJournal of Chemical Kinetics vol 18 pp 569ndash573 1986

[10] C E Banceu CMihele D A Lane and N J Bunce ldquoReactionsof methylated naphthalenes with hydroxyl radicals under simu-lated atmospheric conditionsrdquo Polycyclic Aromatic Compoundsvol 18 no 4 pp 415ndash425 2001

[11] P T Phousongphouang and J Arey ldquoRate constants for the gas-phase reactions of a series of alkylnaphthalenes with the OHradicalrdquo Environmental Science and Technology vol 36 no 9pp 1947ndash1952 2002

[12] K H Wammer and C A Peters ldquoPolycyclic aromatic hydro-carbon biodegradation rates A Structure-based Studyrdquo Envi-ronmental Science and Technology vol 39 no 8 pp 2571ndash25782005

[13] K H Wammer and C A Peters ldquoA molecular modelinganalysis of polycyclic aromatic hydrocarbon biodegradationby naphthalene dioxygenaserdquo Environmental Toxicology andChemistry vol 25 no 4 pp 912ndash920 2006

[14] V Librando and A Alparone ldquoElectronic polarizability as apredictor of biodegradation rates of dimethylnaphthalenes Anab initio and density functional theory studyrdquo EnvironmentalScience and Technology vol 41 no 5 pp 1646ndash1652 2007

[15] A Alparone and V Librando ldquoRaman DFT study of dimethyl-naphthalenes isomer identification and prediction of biodegra-dation rate coefficientsrdquo Structural Chemistry vol 23 pp 1467ndash1474 2012

[16] V Librando and A Alparone ldquoStructure vibrational propertiesand polarizabilities of methylnaphthalene isomers A quantum-mechanical approachrdquo Polycyclic Aromatic Compounds vol 27no 1 pp 65ndash94 2007

[17] J S Salafsky ldquoSecond-harmonic generation as a probe ofconformational change in moleculesrdquo Chemical Physics Lettersvol 381 no 5-6 pp 705ndash709 2003

[18] M Sliwa K Nakatani T Asahi P G Lacroix R B Pansu andH Masuhara ldquoPolarization and wavelength dependent non-linear optical properties of a photo-switchable organic crystalrdquoChemical Physics Letters vol 437 no 4ndash6 pp 212ndash217 2007

[19] M Sliwa S Letard I Malfant et al ldquoDesign synthesisstructural and nonlinear optical properties of photochromiccrystals toward reversible molecular switchesrdquo Chemistry ofMaterials vol 17 no 18 pp 4727ndash4735 2005

[20] A Alparone ldquoDipole (hyper)polarizabilities of fluorinated ben-zenes an ab initio investigationrdquo Journal of Fluorine Chemistryvol 144 pp 94ndash101 2012

[21] G J M Velders J-M Gillet P J Becker and D Feil ldquoElectrondensity analysis of nonlinear optical materials An ab initiostudy of different conformations of benzene derivativesrdquo Jour-nal of Physical Chemistry vol 95 no 22 pp 8601ndash8608 1991

[22] E Hendrickx K Clays A Persoons C Dehu and J L BredasldquoThe bacteriorhodopsin chromophore retinal and derivativesan experimental and theoretical investigation of the second-order optical propertiesrdquo Journal of the American ChemicalSociety vol 117 no 12 pp 3547ndash3555 1995

[23] A Alparone A Millefiori and S Millefiori ldquoElectronic dipolepolarizability and hyperpolarizability of formic acidrdquo ChemicalPhysics Letters vol 409 no 4-6 pp 288ndash294 2005

[24] W Niewodniczanski and W Bartkowiak ldquoTheoretical study ofgeometrical and nonlinear optical properties of pyridinum N-phenolate betaine dyesrdquo Journal of Molecular Modeling vol 13no 6-7 pp 793ndash800 2007

[25] Z-M Su H-L Xu Z-R Li S Muhammad F L Gu and KHarigaya ldquoKnot-isomers of mobius cyclacene How does thenumber of knots influence the structure and first hyperpolar-izabilityrdquo Journal of Physical Chemistry C vol 113 no 34 pp15380ndash15383 2009

[26] A Plaquet B Champagne F Castet et al ldquoTheoretical inves-tigation of the dynamic first hyperpolarizability of DHA-VHFmolecular switchesrdquo New Journal of Chemistry vol 33 no 6pp 1349ndash1356 2009

[27] J Lipinski and W Bartkowiak ldquoConformation and solventdependence of the first and second molecular hyperpolariz-abilities of charge-transfer chromophores Quantum-chemicalcalculationsrdquo Chemical Physics vol 245 no 1-3 pp 263ndash2761999

[28] J Perrenoud-Rinuy P-F Brevet and H H Girault ldquoSecondharmonic generation study of myoglobin and hemoglobinand their protoporphyrin IX chromophore at the water12-dichloroethane interfacerdquo Physical Chemistry Chemical Physicsvol 4 no 19 pp 4774ndash4781 2002

[29] S A Mitchell and R A McAloney ldquoSecond harmonic opticalactivity of tryptophan derivatives adsorbed at the airwaterinterfacerdquo Journal of Physical Chemistry B vol 108 no 3 pp1020ndash1029 2004

[30] J S Salafsky ldquoSecond-harmonic generation for studying struc-tural motion of biological molecules in real time and spacerdquoPhysical Chemistry Chemical Physics vol 9 no 42 pp 5704ndash5711 2007

[31] R M Williams W R Zipfel and W W Webb ldquoInterpretingsecond-harmonic generation images of collagen I fibrilsrdquo Bio-physical Journal vol 88 no 2 pp 1377ndash1386 2005

[32] W-L Chen T-H Li P-J Su et al ldquoSecond harmonic gener-ation 120594 tensor microscopy for tissue imagingrdquo Applied PhysicsLetters vol 94 no 18 Article ID 183902 3 pages 2009

[33] B Champagne E A Perpete S J A Van Gisbergen et alldquoAssessment of conventional density functional schemes for


computing the polarizabilities and hyperpolarizabilities of con-jugated oligomers an ab initio investigation of polyacetylenechainsrdquo Journal of Chemical Physics vol 109 no 23 pp 10489ndash10498 1998

[34] M Kamiya H Sekino T Tsuneda and K Hirao ldquoNonlin-ear optical property calculations by the long-range-correctedcoupled-perturbed Kohn-Sham methodrdquo Journal of ChemicalPhysics vol 122 no 23 Article ID 234111 10 pages 2005

[35] H Sekino Y Maeda M Kamiya and K Hirao ldquoPolarizabilityand second hyperpolarizability evaluation of long moleculesby the density functional theory with long-range correctionrdquoJournal of Chemical Physics vol 126 no 1 Article ID 0141072007

[36] T Yanai D P Tew and N C Handy ldquoA new hybrid exchange-correlation functional using the Coulomb-attenuating method(CAM-B3LYP)rdquo Chemical Physics Letters vol 393 no 1ndash3 pp51ndash57 2004

[37] A Alparone ldquoLinear and nonlinear optical properties of nucleicacid basesrdquo Chemical Physics vol 410 pp 90ndash98 2013

[38] D Jacquemin E A Perpete G Scalmani M J Frisch RKobayashi and C Adamo ldquoAssessment of the efficiency oflong-range corrected functionals for some properties of largecompoundsrdquo Journal of Chemical Physics vol 126 no 14 ArticleID 144105 12 pages 2007

[39] P A Limacher K V Mikkelsen and H P Luthi ldquoOn theaccurate calculation of polarizabilities and second hyperpolar-izabilities of polyacetylene oligomer chains using the CAM-B3LYP density functionalrdquo Journal of Chemical Physics vol 130no 19 Article ID 194114 7 pages 2009

[40] M Nakano T Minami H Fukui et al ldquoApproximate spin-projected spin-unrestricted density functional theory methodapplication to the diradical character dependences of the(hyper)polarizabilities in p-quinodimethanemodelsrdquoChemicalPhysics Letters vol 501 no 1-3 pp 140ndash145 2010

[41] A Alparone ldquoComparative study of CCSD(T) and DFT meth-ods electronic (hyper)polarizabilities of glycinerdquo ChemicalPhysics Letters vol 514 no 1ndash3 pp 21ndash25 2011

[42] C-C Zhang H-L Xu Y-Y Hu S-L Sun and Z-M SuldquoQuantum chemical research on structures linear and nonlin-ear optical properties of the Lin-acenes salt (119899= 1 2 3 and 4)rdquoJournal of Physical Chemistry A vol 115 no 10 pp 2035ndash20402011

[43] T Pluta M Kolaski M Medvedrsquo and S Budzak ldquoDipolemoment and polarizability of the low-lying excited states ofuracilrdquo Chemical Physics Letters vol 546 pp 24ndash29 2012

[44] M Medved S Budzak and T Pluta ldquoStatic NLO responsesof fluorinated polyacetylene chains evaluated with long-rangecorrected density functionalsrdquoChemical Physics Letters vol 515no 1ndash3 pp 78ndash84 2011

[45] A Alparone ldquoEvolution of electric dipole (hyper)polariza-bilities of b-strand polyglycine single chains an ab initio andDFT theoretical studyrdquo Journal of Physical Chemistry A vol 117pp 5184ndash5194 2013

[46] A Alparone ldquoThe effect of secondary structures on the NLOproperties of single chain oligopeptides a comparison between120573-strand and 120572-helix polyglycinesrdquo Physical Chemistry Chemi-cal Physics vol 15 pp 12958ndash12962 2013

[47] A Alparone ldquoElectron correlation effects and density analysisof the first-order hyperpolarizability of neutral guanine tau-tomersrdquo Journal of Molecular Modeling vol 19 pp 3095ndash31022013

[48] A Alparone ldquoResponse electric properties of 120572-helix polyg-lycines a CAM-B3LYP DFT investigationrdquo Chemical PhysicsLetters vol 563 pp 88ndash92 2013

[49] M J Frisch G W Trucks H B Schlegel et al ldquoGaussian 09Revision A02rdquo Gaussian Wallingford Conn USA 2009

[50] H Sekino and R J Bartlett ldquoFrequency dependent nonlin-ear optical properties of moleculesrdquo The Journal of ChemicalPhysics vol 85 no 2 pp 976ndash989 1986

[51] J E Rice and N C Handy ldquoThe calculation of frequency-dependent hyperpolarizabilities including electron correlation-effectsrdquo International Journal of QuantumChemistry vol 43 pp91ndash118 1992

[52] V LibrandoAAlparone andZMinniti ldquoComputational studyon dipole moment polarizability and second hyperpolarizabil-ity of nitronaphthalenesrdquo Journal of Molecular Structure vol856 no 1ndash3 pp 105ndash111 2008

[53] M Torrent-Sucarrat M Sola M Duran J M Luis and BKirtman ldquoBasis set and electron correlation effects on abinitio electronic and vibrational nonlinear optical properties ofconjugated organic moleculesrdquo Journal of Chemical Physics vol118 no 2 pp 711ndash718 2003

[54] A Alparone and V Librando ldquoPhysicochemical characteriza-tion of environmental mutagens 3-nitro-6-azabenzo[a]pyreneand its N-oxide derivativerdquoMonatshefte fur Chemie vol 143 pp1123ndash1132 2012

[55] I Cernusak V Kello and A J Sadlej ldquoStandardized medium-size basis sets for calculations of molecular electric propertiesgroup IIIArdquo Collection of Czechoslovak Chemical Communica-tions vol 68 no 2 pp 211ndash239 2003

[56] V Keshari W M K P Wijekoon P N Prasad and S PKarna ldquoHyperpolarizabilities of organic molecules Ab initiotime-dependent coupled perturbed HartreemdashFockmdashRoothaanstudies of basic heterocyclic structuresrdquo Journal of PhysicalChemistry vol 99 no 22 pp 9045ndash9050 1995

[57] J E Rice R D Amos S M Colwell N C Handy and J SanzldquoFrequency dependent hyperpolarizabilities with application toformaldehyde and methyl fluoriderdquo The Journal of ChemicalPhysics vol 93 no 12 pp 8828ndash8839 1990

[58] H Sekino and R J Bartlett ldquoMolecular hyperpolarizabilitiesrdquoJournal of Chemical Physics vol 98 no 4 pp 3022ndash3037 1993

[59] F Sim S Chin M Dupuis and J E Rice ldquoElectron correlationeffects in hyperpolarizabilities of p-nitroanilinerdquo Journal ofPhysical Chemistry vol 97 no 6 pp 1158ndash1163 1993

[60] G Maroulis and A JThakkar ldquoPolarizabillties and hyperpolar-izabilities of F2rdquoThe Journal of Chemical Physics vol 90 no 1pp 366ndash370 1989

[61] E F Archibong and A J Thakkar ldquoHyperpolarizabilities andpolarizabilities of Li-1 and B+ finite-field coupled-cluster calcu-lationsrdquo Chemical Physics Letters vol 173 no 5-6 pp 579ndash5841990

[62] E F Archibong and A J Thakkar ldquoStatic polarizabilities andhyperpolarizabilities and multipole moments for Cl2 and Br2Electron correlation and molecular vibration effectsrdquo ChemicalPhysics Letters vol 201 no 5-6 pp 485ndash492 1993

[63] G Maroulis ldquoHyperpolarizability of H2O revisited accurateestimate of the basis set limit and the size of electron correlationeffectsrdquo Chemical Physics Letters vol 289 no 3-4 pp 403ndash4111998

[64] D Xenides and G Maroulis ldquoBasis set and electron correlationeffects on the first and second static hyperpolarizability of SO2rdquoChemical Physics Letters vol 319 no 5-6 pp 618ndash624 2000


[65] H A Kurtz J J P Stewart and K M Dieter ldquoCalculationof the nonlinear optical properties of moleculesrdquo Journal ofComputational Chemistry vol 11 pp 82ndash87 1990

[66] D M Bishop and G Maroulis ldquoAccurate prediction of stat-ic polarizabilities and hyperpolarizabilities A study on FH(X1Σ+)rdquoThe Journal of Chemical Physics vol 82 no 5 pp 2380ndash

2391 1985[67] J E Rice and N C Handy ldquoThe calculation of frequency-

dependent polarizabilities as pseudo-energy derivativesrdquo TheJournal of Chemical Physics vol 94 no 7 pp 4959ndash4971 1991

[68] J R Hammond K Kowalski and W A Dejong ldquoDynamicpolarizabilities of polyaromatic hydrocarbons using coupled-cluster linear response theoryrdquo Journal of Chemical Physics vol127 no 14 Article ID 144105 9 pages 2007

[69] A Alparone ldquoStructural energetic and response electric prop-erties of cyclic selenium clusters an ab initio and density fun-ctional theory studyrdquo Theoretical Chemistry Accounts vol 131article 1239 pp 1ndash14 2012

[70] M F Vuks ldquoDetermination of optical anisotropy of aromaticmolecules from double refraction in crystalsrdquo Optics Spec-troscopy vol 20 pp 361ndash368 1966

[71] M Nakano I Shigemoto S Yamada and K Yamaguchi ldquoSize-consistent approach and density analysis of hyperpolarizabilitysecond hyperpolarizabilities of polymeric systems with andwithout defectsrdquo The Journal of Chemical Physics vol 103 no10 pp 4175ndash4191 1995

[72] M Nakano S Ohta K Tokushima et al ldquoFirst and secondhyperpolarizabilities of donor-acceptor disubstituted diphen-alenyl radical systemsrdquo Chemical Physics Letters vol 443 no1ndash3 pp 95ndash101 2007

[73] N Mora-Diez R J Boyd and G L Heard ldquoEffects of alkylsubstituents on the excited states of naphthalene SemiempiricalStudyrdquo Journal of Physical Chemistry A vol 104 no 5 pp 1020ndash1029 2000

[74] S Yamada M Nakano I Shigemoto S Kiribayashi and KYamaguchi ldquoIntense electron correlation dependence of thefirst hyperpolarizabilities 120573 of a nitroxide radical and formalde-hyderdquo Chemical Physics Letters vol 267 no 5-6 pp 445ndash4511997

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


1

2

3

45

6

7

8

9

10

y

x

Figure 1 Coordinate system and atom numbering of dimethylnaphthalene (DMN) isomers

optical (NLO) properties Second Harmonic Generation(SHG) and Electro-Optical Pockels Effect (EOPE) [17ndash32]SHGmeasurements are currently employed for the structuralidentification of biomolecules such as peptides and proteins[28ndash32]

Themain focus of this study is to determine the static andfrequency-dependent electronic 120572 and 120573 values of the seriesof the DMN isomers aiming to explore the effects of the posi-tion of the CH3 groups on these electric properties poten-tially helpful for the isomeric discrimination The electronic(hyper)polarizabilities are commonly predicted by means ofab initio andor Density Functional Theory (DFT) computa-tionsHowever aswell-known in the literature for an accuratedetermination of the electronic (hyper)polarizabilities thechoice of the functional is critical especially in the case of120587-conjugated compounds [33] In fact on the whole theconventional DFT methods tend to systematically overesti-mate the electronic (hyper)polarizabilities obtained by high-level correlated ab initio levels On the other hand the long-range corrected DFTmethods incorporating nonlocal effects[34 35] describe adequately the diffuse regions of the chargedistributions giving much more satisfactory performancesfor the prediction of the response electric properties Inthe present study we used the Coulomb-attenuating hybridexchange-correlation functional (CAM-B3LYP) [36] whichhas been recently employed with success for computingelectronic (hyper)polarizabilities of organic compounds [37ndash48]

2 Computational Details

All calculations were performed with the Gaussian 09program [49] We used the molecular geometries pre-viously optimized at the DFT-B3LYP level with the 6-31Glowast basis set [14] Static and frequency-dependent elec-tronic (hyper)polarizability tensor components 120572119894119895 and120573119894119895119895 (119894 119895 = 119909 119910 119911) were obtained through the Coupled-Perturbed Hartree-Fock procedure [50 51] using the DFT-CAM-B3LYPmethodwith the polarized and diffuse 6-31+Glowastbasis set The CAM-B3LYP functional and the 6-31+Glowast basis

set can be considered suitable choices especially for theprediction of the electronic (hyper)polarizabilities of organicmolecules [37ndash48 52ndash54] However we checked the perfor-mances of the basis set (6-31+Glowast versus POL Sadlejrsquos basis set[55]) and level of calculation (CAM-B3LYP versus second-order Moslashller-Plesset perturbation theory (MP2)) on therelated compound toluene Dynamic (hyper)polarizabilitieswere evaluated at the experimental NdYAG laser wavelengthof 1064 nm (ℏ120596 = 004282 au) for the SHG [120573(minus2120596 120596 120596)]and EOPE [120573(minus120596 120596 0)] NLO processes

We report the dipole moments (120583) the isotropicallyaveraged polarizabilities (⟨120572⟩) the polarizability anisotropies(Δ120572) and the isotropically first-order hyperpolarizabilities(120573vec) which are defined respectively as [56]

120583 = radic1205832119909

+ 1205832119910

+ 1205832119911

⟨120572⟩ =

1

3

(120572119909119909 + 120572119910119910 + 120572119911119911)

Δ120572 =

1

2

[ (120572119909119909 minus 120572119910119910)

2

+ (120572119909119909 minus 120572119911119911)2

+ (120572119910119910 minus 120572119911119911)

2

+ 6 (1205722

119909119910+ 1205722

119909119911+ 1205722

119910119911) ]

12

120573vec = radic1205732119909

+ 1205732119910

+ 1205732119911

(1)

where 120573119894 (119894 = 119909 119910 119911) is given by 120573119894 = (13) sum119895=119909119910119911

(120573119894119895119895 +

120573119895119894119895 + 120573119895119895119894)

3 Results and Discussion

31 Basis Set and Level of Calculation Effects Response ElectricProperties of Toluene For an accurate prediction of theelectronic (hyper)polarizabilities the choice of the basis setand level of computation is of crucial importance [57ndash67] Inthe present study we explored the effects of the basis set andtheoretical level on toluene as a test case Table 1 reports the



of toluenea

⟨120572⟩ Δ120572 120573vec




















(1)

119895(119903) [71 72] The 120588

(1)

119895(119903) is defined as



04

03

02

01

0012 14 16 18 20 22 26 28 30 32

Δ120572

27-DMN

26-DMN

18-DMN

120572xx

(a) (b) (c)kb

((m

g of

pro

tein

L)(

hminus1))minus1

Polarizability (A3)

120572⟩

⟩


= minus0826 + 0033 times 120572119909119909

(119903 = 097)


naphthalenea

ℏ120596


119896119887

b

0 004282 0 004282 0 00428212-DMN 2853 2914 2065 2100 1500 1546 0100 plusmn 003

13-DMN 2874 2936 2077 2112 1503 1550 0120 plusmn 004

14-DMN 2655 2709 2054 2089 1380 1420 0055 plusmn 002

15-DMN 2658 2712 2055 2090 1389 1430 0065 plusmn 001

16-DMN 2876 2938 2078 2113 1519 15650120 plusmn 004

17-DMN 2884 2946 2076 2111 1508 155518-DMN 2677 2732 2042 2076 1397 1438

0033 plusmn 002

23-DMN 3058 3127 2090 2125 1655 170826-DMN 3106 3176 2107 2143 1712 1767 0200 plusmn 005

27-DMN 3109 3179 2106 2142 1690 1745 0360 plusmn 007



120588 (119903 119865) = 120588(0)

(119903) + sum

119895

120588(1)

119895(119903) 119865119895 +

1

2

sum

119895

120588(2)

119895119896(119903) 119865119895119865119896

+

1

2

sum

119895

120588(3)

119895119896119897(119903) 119865119895119865119896119865119897 + sdot sdot sdot

120588(1)

119895(119903) =

120597120588 (119903 119865)

120597119865119895

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0

120572119894119895 = minus int 119903119894 120588(1)

119895(119903) 119889119903

(2)




(1)



(1)


120588(1)



(1)




120572xx = 2655 A3

120572xx = 3058A3

X





(1)








X
















density 120588(2)


120588(2)

119895119896(119903) =

1205972120588 (119903 119865)

120597119865119895120597119865119896

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0119865119896=0

120573119894119895119896 = minus

1

2

int 119903120588(2)

119895119896(119903) 119889119903

(3)






(2)

119909119909(119903) densities for


(2)



(2)

119909119909(119903)


(2)



4 Conclusions




References
























































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



of toluenea

⟨120572⟩ Δ120572 120573vec




















(1)

119895(119903) [71 72] The 120588

(1)

119895(119903) is defined as



04

03

02

01

0012 14 16 18 20 22 26 28 30 32

Δ120572

27-DMN

26-DMN

18-DMN

120572xx

(a) (b) (c)kb

((m

g of

pro

tein

L)(

hminus1))minus1

Polarizability (A3)

120572⟩

⟩


= minus0826 + 0033 times 120572119909119909

(119903 = 097)


naphthalenea

ℏ120596


119896119887

b

0 004282 0 004282 0 00428212-DMN 2853 2914 2065 2100 1500 1546 0100 plusmn 003

13-DMN 2874 2936 2077 2112 1503 1550 0120 plusmn 004

14-DMN 2655 2709 2054 2089 1380 1420 0055 plusmn 002

15-DMN 2658 2712 2055 2090 1389 1430 0065 plusmn 001

16-DMN 2876 2938 2078 2113 1519 15650120 plusmn 004

17-DMN 2884 2946 2076 2111 1508 155518-DMN 2677 2732 2042 2076 1397 1438

0033 plusmn 002

23-DMN 3058 3127 2090 2125 1655 170826-DMN 3106 3176 2107 2143 1712 1767 0200 plusmn 005

27-DMN 3109 3179 2106 2142 1690 1745 0360 plusmn 007



120588 (119903 119865) = 120588(0)

(119903) + sum

119895

120588(1)

119895(119903) 119865119895 +

1

2

sum

119895

120588(2)

119895119896(119903) 119865119895119865119896

+

1

2

sum

119895

120588(3)

119895119896119897(119903) 119865119895119865119896119865119897 + sdot sdot sdot

120588(1)

119895(119903) =

120597120588 (119903 119865)

120597119865119895

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0

120572119894119895 = minus int 119903119894 120588(1)

119895(119903) 119889119903

(2)




(1)



(1)


120588(1)



(1)




120572xx = 2655 A3

120572xx = 3058A3

X





(1)








X
















density 120588(2)


120588(2)

119895119896(119903) =

1205972120588 (119903 119865)

120597119865119895120597119865119896

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0119865119896=0

120573119894119895119896 = minus

1

2

int 119903120588(2)

119895119896(119903) 119889119903

(3)






(2)

119909119909(119903) densities for


(2)



(2)

119909119909(119903)


(2)



4 Conclusions




References
























































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


04

03

02

01

0012 14 16 18 20 22 26 28 30 32

Δ120572

27-DMN

26-DMN

18-DMN

120572xx

(a) (b) (c)kb

((m

g of

pro

tein

L)(

hminus1))minus1

Polarizability (A3)

120572⟩

⟩


= minus0826 + 0033 times 120572119909119909

(119903 = 097)


naphthalenea

ℏ120596


119896119887

b

0 004282 0 004282 0 00428212-DMN 2853 2914 2065 2100 1500 1546 0100 plusmn 003

13-DMN 2874 2936 2077 2112 1503 1550 0120 plusmn 004

14-DMN 2655 2709 2054 2089 1380 1420 0055 plusmn 002

15-DMN 2658 2712 2055 2090 1389 1430 0065 plusmn 001

16-DMN 2876 2938 2078 2113 1519 15650120 plusmn 004

17-DMN 2884 2946 2076 2111 1508 155518-DMN 2677 2732 2042 2076 1397 1438

0033 plusmn 002

23-DMN 3058 3127 2090 2125 1655 170826-DMN 3106 3176 2107 2143 1712 1767 0200 plusmn 005

27-DMN 3109 3179 2106 2142 1690 1745 0360 plusmn 007



120588 (119903 119865) = 120588(0)

(119903) + sum

119895

120588(1)

119895(119903) 119865119895 +

1

2

sum

119895

120588(2)

119895119896(119903) 119865119895119865119896

+

1

2

sum

119895

120588(3)

119895119896119897(119903) 119865119895119865119896119865119897 + sdot sdot sdot

120588(1)

119895(119903) =

120597120588 (119903 119865)

120597119865119895

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0

120572119894119895 = minus int 119903119894 120588(1)

119895(119903) 119889119903

(2)




(1)



(1)


120588(1)



(1)




120572xx = 2655 A3

120572xx = 3058A3

X





(1)








X
















density 120588(2)


120588(2)

119895119896(119903) =

1205972120588 (119903 119865)

120597119865119895120597119865119896

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0119865119896=0

120573119894119895119896 = minus

1

2

int 119903120588(2)

119895119896(119903) 119889119903

(3)






(2)

119909119909(119903) densities for


(2)



(2)

119909119909(119903)


(2)



4 Conclusions




References
























































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


120572xx = 2655 A3

120572xx = 3058A3

X





(1)








X
















density 120588(2)


120588(2)

119895119896(119903) =

1205972120588 (119903 119865)

120597119865119895120597119865119896

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0119865119896=0

120573119894119895119896 = minus

1

2

int 119903120588(2)

119895119896(119903) 119889119903

(3)






(2)

119909119909(119903) densities for


(2)



(2)

119909119909(119903)


(2)



4 Conclusions




References
























































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of









density 120588(2)


120588(2)

119895119896(119903) =

1205972120588 (119903 119865)

120597119865119895120597119865119896

1003816100381610038161003816100381610038161003816100381610038161003816119865119895=0119865119896=0

120573119894119895119896 = minus

1

2

int 119903120588(2)

119895119896(119903) 119889119903

(3)






(2)

119909119909(119903) densities for


(2)



(2)

119909119909(119903)


(2)



4 Conclusions




References
























































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


References
























































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






















Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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