Linear and nonlinear optical properties of some organoxenon derivatives

Aggelos Avramopoulos

Institute of Organic and Pharmaceutical Chemistry, National Hellenic Research Foundation, 48 Vas. Constantinou Ave., Athens 11635, Greece

Luis Serrano-Andrés

Institute of Molecular Science, Universitat de Valencia, Apartado 22085, ES-46071 Valencia, Spain

Jiabo Li

SciNet Technologies, San Diego, California 92127, USA Heribert Reis and Manthos G. Papadopoulosa)

Institute of Organic and Pharmaceutical Chemistry, National Hellenic Research Foundation, 48 Vas. Constantinou Ave., Athens 11635, Greece

(Received 29 June 2007; accepted 25 September 2007; published online 4 December 2007)

We employ a series of state-of-the-art computational techniques to study the effect of inserting one or more Xe atoms in HC2H and HC4H, on the linear and nonlinear optical (L&NLO) properties of the resulting compounds. It has been found that the inserted Xe has a great effect on the L&NLO properties of the organoxenon derivatives. We analyze the bonding in HXeC2H, and the change of the electronic structure, which is induced by inserting Xe, in order to rationalize the observed extraordinary L&NLO properties. The derivatives, which are of interest in this work, have been synthesized in a Xe matrix. Thus the effect of the local field (LF), due to the Xe environment, on the properties of HXeC2H, has also been computed. It has been found that the LF effect on some properties is significant. The calculations have been performed by employing a hierarchy of basis sets and the techniques MP2 and CCSD(T) for taking into account correlation. For the interpretation of the results we have employed the complete active space valence bond and CASSCF/CASPT2 methods. © 2007 American Institute of Physics. [DOI: 10.1063/1.2800023]

I. INTRODUCTION

Pauling predicted that heavier noble gas atoms could participate in bond formation.1 He explained this by invoking the reduced stability of their outer electrons, due to the strong screening of the inner electrons. Although predictions for stable noble gas derivatives can be found, since at least 1902, the first Xe derivative, XePtF6, was not reported until 1962 by Bartlett, proving thus wrong the widely held opinion that the noble gases are inert. Bartlett's discovery was only the beginning for a large number of Xe derivatives, which have been reported since then. Christe4 considers that the recent burst of startling discoveries may signal the beginning of a renaissance in the noble gas chemistry.

Among the many important recent developments in the Xe chemistry, we note the fluorinated Xe derivatives [e.g., XeF2 XeF4 (Ref. 5)], their cations (e.g., [XeF]+), the organ-oxenonium salts4,6 as well as the preparation and characterization of hydrides HXeY, where Y denotes an electronegative group.7

The first stable derivative, with a Xe-C bond, has been reported by Frohn and Jakobs in

1989. Since then

compounds involving the bond Xe-C have been synthesized.9 We note that Fankowski et at.10 prepared XeC2, the structure of which is bent and it is characterized by substantial charge separation.

a'Author to whom correspondence should be addressed. Electronic mail: mpapad@eie.gr.

The first prediction for a fluorine-free alkynylxenon compound was reported by Lundell et at.,6 who discussed the stability and reported the spectroscopic properties of HXeC2H, HXeC2XeH, and some other organoxenon derivatives. Khriachtchev et at.9 synthesized and identified HXeC2H and HXeC2XeH, while experimental evidence for the formation of HXeC2H has also been reported simultaneously by Feldman et at.11 These derivatives do not contain fluorine, which distinguishes them from previous organoxenon compounds. It is noted that since the electron affinity of the C2nH radicals increases with n, then the stability of HXeC2nH should enhance with increasing n.11 The strong electronegative character of C2 has been pointed out by Maier and Lautz.12

Insertion compounds of Xe into HCnH are prepared by dissociation of the appropriate precursor in solid Xe by UV light or fast electrons. This process is followed by annealing.9,11 For example, Tanskanen et at.13 reported the synthesis of HXeC4H, which involves UV photolysis of C4H2 in a Xe matrix and annealing. Global diffusion of H atoms in solid Xe at ~40 K leads to the reaction H+Xe + C4H and the production of HXeC4H. The considered rare gas molecules easily decompose upon irradiation by light.

In the present work we report the linear and nonlinear optical (L&NLO) properties of HXeC2H, HXeC2XeH, and three of the Xe derivatives of HC4H. We consider the following questions: (i) how the inserted Xe affects the L&NLO properties of HXeC2H and (ii) how the position of

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© 2007 American Institute of Physics

Xe in HC4H as well as the number of Xe atoms affect the L&NLO properties of the organoxenon derivative. Electronic, and to a smaller extent vibrational, contributions to the L&NLO properties are computed. As the Xe derivatives have been synthesized in a Xe matrix, we also calculated the effect of the environment, which consists of Xe atoms, on the studied L&NLO properties.

Insertion of Xe in HC2H or HC4H induces a considerable change in the electronic structure. We have thus discussed the bonding in HXeC2H and how the changes in the electronic structure affect the L&NLO properties.

The L&NLO properties are of great current interest, because they allow to advance our understanding of the electronic and vibrational structure of the molecules. In addition, they are key parameters for the design of materials with many applications (e.g., fiber optic communication, all optical switching).

This work is organized as follows. In the second section, we present the computational methods, which have been employed for the calculation of the L&NLO properties of the considered derivatives; in the third section, the L&NLO properties are presented as well as their interpretation, and finally the fourth section involves the concluding remarks.

II. COMPUTATIONAL METHODS

The geometries, harmonic frequencies, and (hyper)polar-izabilities of a series of organoxenon derivatives are presented. A hierarchy of computational techniques has been employed including HF, MP2, and CCSD(T). The coupled cluster approach, which involves the iterative calculation of single and double excitation amplitudes as well as a pertur-bative treatment of triple excitations, has been selected, because it provides a satisfactory estimate of the correlation contribution,14 while MP2 is one of the most frequently used techniques for the calculation of the above contribution. We have performed CASSCF calculations for the ground state of the studied molecules, at the same level as those later described for C2H2 and HXeC2H, and in all cases one single electronic configuration dominated the wave function, at

least by 87%. The computations have been performed by

employing the aug-cc-pVnZ, where n=2-5. This systematically built series of basis sets allows the extrapolation to the "complete" basis set limit. By such a procedure one may estimate the error associated with a given approximate wave function.16 We have also employed the HyPol basis set, de-

veloped by Sadlej et al., which is known to give reasonably accurate (hyper)polarizabilities.

For Xe, a small core (28 electrons), energy consistent, relativistic pseudopotential (PP) has been used.18 The 4spd outer-core shell is treated explicitly together with the 5sp valence orbitals. The usefulness and reliability of the pseudopotentials and, in particular, the large-core ones for the calculation of (hyper)plarizabilities have been discussed by various authors.19-21 The relativistic correction to the L&NLO properties has been estimated by employing the Douglas-Kroll approximation,22 in connection with the HyPol basis,17 which has been specifically developed for rela-tivistic calculations.

The properties of the considered derivatives have been computed by employing geometries optimized at the HF or MP2 levels. In addition, for two derivatives geometry data have been taken from the literature. The method which has been used for each molecule is specified. The geometry optimizations, which have been performed in this work, employed the aug-cc-pVDZ basis sets for H, C, and Xe. For the latter the basis set has been developed in connection with the employed pseudopotential.18

The vibrational contributions to the polarizability and first hyperpolarizability of H-XeC2H have been also computed. At static fields (w=0) the pure vibrational (pv) term may have a significant contribution. Bishop and Kirtman23-26 developed a perturbation theory approach for the calculation of apV and ffzVz. In the present work we use a double harmonic approximation for the evaluation of these properties:

2n(0,0).

C = = 3 2

(drfl dQa){(day ¿>Qa)o

where i=x,y,z and wa are the harmonic frequencies. The required dipole moment and polarizability derivatives have been computed at the HF and MP2 levels of theory by employing the aug-cc-pVDZ basis set.

Local field expression in dipolar approximation. The Xe derivatives, which are studied in this work, are produced in a Xe matrix. The L&NLO properties computed and reported here refer to isolated molecules. Thus it would be useful and interesting to find out the effect of the environment of the surrounding Xe atoms on the L&NLO properties of HXeC2H, which will be considered as a model compound.

We shall first determine the local field by employing Eq. (3):

Fk'a = (e0^cell) 1 2 Lkk'a$[^k'$ + ak',$yFk'y\, (3)

where N is the number of the molecules in the cell, a,$, y are Cartesian components, Fka denotes the permanent local field on molecule k' due to the surrounding molecules at sites k, Vcell is the volume of the cell, e0 the permittivity of vacuum, fik, $ and aka$ are the dipole moment and polariz-ability components of the free molecule k' , respectively, and L(11) is the Lorentz-factor tensor computed in conducting boundary conditions. The local field (LF) is found by an iterative procedure. The approximated LF, given by Eq. (3), is due to a specified number of Xe atoms. These define the environment of HXeC2H. Then in the presence of the determined LF, we shall compute the L&NLO properties of HXeC2H. In that way, we shall be able to estimate the effect of the local field.

The bonding of the considered derivatives has been studied by employing the complete active space valence bond (CASVB) theory28 and the VB2000 software.29 The CASSCF/ CASPT2 (Ref. 30) method has also been used in order to comment on the changes in the electronic structure of HC2H,

TABLE I. The equilibrium structure of H-Xe-C=C-H (in A) and the harmonic frequencies (in cm ') of H-Xe-C=C—H.

Method R(C = C) R(C-H) R(Xe-C) R(H-Xe) «(C-H) «(C=C) «(Xe-H) Benda Benda ^(Xe-C) «(H-Xe-C)a

MP2/aug-cc-pVDZb 1.249 1.078 2.350 1.750 3444.3 1931.1 1681.3 676.8 612.6 313.4 153.1

MP2/aug-cc-pVTZc 1.230 1.064 2.329 1.734

MP2 / LJ18/6-311 ++G(2d ,2p)d 1.225 1.062 2.322 1.750 3462.3 1970.4 1735.9 687.8 640.6 327.2 131.4

CCSD(T) / LJ18/6-311+ + G(2d ,2p)e 1.223 1.065 2.351 1.767 3419.9 2000.4 1620.8 657.6 614.2 313.2 131.6

B3LYP/LANL2DZf 1.237 1.069 2.405 2.320

Experiment8 3273 1748 1486 626

The basis sets for H and C have been taken from Ref. 15 and for Xe from Ref. 18. Xe is treated with a small core relativistic pseudopotential. cThe employed basis sets, as well as the pseudopotential used for Xe are described in footnote b. dReference 6. A pseudopotential has been employed for Xe with core (Q) involving 36 electrons. [Ref. 70(a)]. eReference 6. Information for the employed pseudopotential for Xe is given in footnote d. fReference 35. Q(Xe)=46 electrons [Ref. 70(b)]. gReferences 9 and 11.

which are induced by the insertion of Xe, and which are essential for the analysis of the L&NLO properties of the Xe derivatives. For the computations the following programs

31 32 33

have been used: GAUSSIAN 98, DALTON, MOLCAS, and

VB2000. The reported L&NLO properties are given in a.u. Conversion factors to Système International (SI) are given in Ref. 34.

III. RESULTS AND DISCUSSION

In this section we present (i) the equilibrium structure and the harmonic frequencies of HXeC2H; (ii) the chemical bonding in HXeC2H; (iii) the charge transfer, which takes place in the considered Xe derivatives, as well as between HXeC2H and the Xe environment; (iv) the L&NLO properties (electronic contributions) of the organoxenon compounds together with the factors which affect them (e.g., basis set, correlation, relativistic correction, etc.); (v) the vibrational contributions to L&NLO properties; and (vi) the effect of the local field, which is due to the Xe environment, on the properties of interest. Particular care has been taken for the analysis and interpretation of the presented results.

A. Structure and harmonic frequencies

The structure of the molecules of interest has been either optimized in the present work or taken from the literature (Table I). All the considered molecules are linear except of HXeC2XeC2XeH, which has a slightly nonlinear structure. We have found that the C-C-Xe angle is bent by 2°, while Lundell et al.6 found an angle of ~4°. The slightly bent structure of this molecule explains the small computed fiz and Pzzz.

The effect of the basis set on the bond lengths of HXeC2H has also been studied, by employing MP2/aug-cc-pVnZ, where n=2,3. It is observed that both basis sets give

similar results, which are in satisfactory agreement with those reported by Lundell et al.6 and Brown et al.35 Thus for the geometry optimization of the larger molecules we shall employ the aug-cc-pVDZ method. In Fig. 1 we present the optimized structure of HXeC2XeH (MP2) and HXeC2XeC2XeH (HF). The methods of optimization are shown in parentheses.

The harmonic frequencies of HXeC2H have also been reported (Table I). We computed them at the MP2/aug-cc-pVDZ level. Our values differ from the experimental ones by 5.0%-11.6%. This discrepancy is due to (a) neglect of anhar-monicity effects and (b) the experimental frequencies refer to HXeC2H, trapped in solid Xe. The Xe matrix effects are not taken into account by our values. Runeberg et al.36((a) employing HArF as a model have shown that when the anhar-monicities and the matrix effects are taken into account the computed values (LMP2/AVDZ) approach satisfactorily the experimental data. The harmonic frequencies are essential for the computation of the vibrational properties, which we shall discuss.

B. Chemical bonding

We selected HXeC2H, as an example of the considered derivatives, in order to discuss the nature of chemical bonding in the considered systems. For this compound, CASVB

calculations were performed, using VB2000, an ab initio valence bond program based on an algebrant algorithm and

group function theory.

The CASVB method is equivalent to CASSCF, with the following advantage. Since the VB orbitals can be nonorthogonal and the CASVB wave function is invariant under an arbitrary linear transformation of the basis of the CAS space, the maximum localization of VB orbitals can be performed without losing any accuracy. By default, the VB2000 program maximizes orbital localization for the CASVB wave

TABLE II. The resonance structures of HXeC2H and the corresponding weights, energies (a.u.), dipole moments (a.u.), and atomic charges.

Atomic chargesb

Structures Weight (%)a Energy Dipole moment H Xe C C H

H-Xe+C-CH (I) 44 -7276.9008 -2.989 0.08 0.73 -0.66 -0.29 0.13

H-Xe-CCH (II) 26 -7276.8174 0.301 0.03 0.00 0.07 -0.24 0.14

H-Xe+-CCH (III) 14 -7276.6906 3.194 -0.74 0.71 0.12 -0.23 0.14

H-Xe2+C-CH (IV) 11 -7276.6305 -0.088 -0.70 1.47 -0.61 -0.28 0.13

H+XeC-CH (V) 5 -7276.5544 -6.055 0.85 0.04 -0.73 -0.29 0.13

CASVB (6,4) -7277.0212 -1.149 -0.07 0.54 -0.34 -0.26 0.14

aThe weights of resonance structures are computed according to Coulson-Chirgwin formula. (Ref. 36). bThe Lowdin population analysis was used for computing atomic charges.

function. The localization of the VB orbitals makes the interpretation of the CASVB wave function, in terms of resonance structures, particularly attractive.

The CASVB (6,4) space (that is, six electrons distributed in four orbitals) was used for the description of the charge-shifting bonding in HXeC2H. The 3-21G* basis set was employed, which is considered adequate for our analysis. We recall that although in our computations Xe is treated by employing a PP, this has not yet been implemented in VB2000; thus all electron computations have been performed with this software. The above defined four orbitals are one s and one p orbital for Xe, one s orbital for H, and one sp (hybrid) orbital for carbon next to Xe. Hydrogen and carbon provide one electron each and Xe provides four. The p orbital for Xe is pointing to its two neighbors. The relativistic correction has not been taken into account in the CASVB computations. However, the relativistic effect on the bonding of HXeC2H is expected to be quite small, since only the valence s and p orbitals of Xe are involved in the bonding.

There are ten VB structures in the CASVB (6,4) wave function. However, only five resonance structures have significant contribution to the CASVB wave function (Table II). The other five resonance structures, which have been neglected in the present analysis, have extremely small contribution; the sum of their weights is less than 1%. The weights have been computed according to the Coulson-Chirgwin formula (or sometimes called Mulliken-type weights) .36(b)

Table II shows that structure (I) has the largest weight and the positive charge is mainly localized on Xe, as it is in structures (III) and (IV). However, in structure (V) it is mainly localized on H (bonded with Xe). In all five significant resonance structures of HXeC2H, the 5s orbital of Xe is not actively involved in the bonding (this orbital is always doubly occupied), but the 5pz (Xe) orbital is involved in bonding.

It has been found that HXeC2H has a very large covalent-ionic resonance energy (Table II) .The energy difference between that of structure (I) and the CASVB wave function is 75 kcal / mol. The bonds between Xe and its neighbor atoms (H and C) are not ordinary covalent or ionic bonds. The bonding energy comes from the very strong resonance energy between the charge-shift (ionic) structures and neutral structure (II). This is typical for lone-pair rich molecules (e.g., F2), as Hiberty et al.31 recently have reported.

The structure weights show why the molecule has a di-

pole moment pointing from right to left (HXeC2H). The major resonance structure (I) has a positive charge on Xe, and a negative charge on carbon with which it is bonded; therefore the dipole moment is pointing from C to Xe.

C. Charge transfer

Two processes of charge transfer will be considered for the analysis of the reported results. The first is related with the charge transferred from Xe to the rest of the molecule (e.g., in HXeC2H). As we have shown in the previous work

on the NLO properties of HArF, the involved charge transfer is instrumental for the analysis of the properties of interest. The natural bond orbital (NBO) charge distribution of the considered Xe derivatives is reported in Table III. The discussion, which relies on the NBO charges, is complementary to the analysis of the VB resonance structures, which was given in the previous paragraphs. The NBO charges have been computed by employing the HF and MP2 techniques. There is no substantial difference between the results computed with the above methods.

We observe that Xe of HXeC2H, and to a less extent H, bonded to C2, carry a positive charge. The rest of the molecule has a negative charge. Similar charges have been computed for HXeC4H. It is interesting to note that the NBO analysis for HXeC2H, given in Table III, and the Lowdin population analysis presented in Table II, are in qualitative agreement. The two Xe atoms of HXeC2XeH represent the positively charged part of the molecule. All the other atoms have a negative charge. The Xe atom of HC2XeC2H has a remarkably larger positive charge than that of HXeC4H (Table III).

The Xe atom in the middle of HXeC2XeC2XeH has a larger positive charge than the Xe atoms, which approach the ends of the molecule (Table III). This observation is in agreement with the result found in the pair HXeC4H /HC2XeC2H. It has been found that the H atoms in HC2XeC2H have a positive charge, while in HXeC2XeC2XeH, the H atoms have a small negative charge.

Comparison of the charge of Xe in the pair HXeC2H / HXeC4H shows the negligible effect of the chain length on the charge of Xe (Table III). The pair HXeC2H / HXeC2XeH allows to comment on the effect of the increasing number of Xe atoms on their charge. In the considered example the above effect is small.

TABLE III. Natural bond orbital charge distribution of some Xe derivatives.

HXeC2H HXeC2XeH HXeC4H HC2XeC2H HXeC2XeC2XeH

Atom HFa MP2b Lundell et al? Brown et al.A Atom HF MP2

H -0.10 -0.11 -0.17 -0.10 H -0.15 -0.14

Xe 0.79 0.70 0.77 0.54 Xe 0.78 0.68

C -0.57 -0.51 -0.49 -0.32 C -0.63 -0.54

C -0.34 -0.30 -0.31 -0.38 C -0.63 -0.54

H 0.23 0.22 0.20 0.26 Xe 0.78 0.68

H -0.15 -0.14

Atom HF MP2 Atom HF MP2 Atom HF

H -0.09 -0.10 H 0.23 0.22 H -0.09

Xe 0.79 0.71 C -0.25 -0.25 Xe 0.78

C -0.46 -0.41 C -0.49 -0.43 C -0.59

C -0.20 -0.16 Xe 1.02 0.91 C -0.59

C -0.07 -0.08 C -0.49 -0.43 Xe 0.98

C -0.20 -0.18 C -0.25 -0.25 C -0.59

H 0.24 0.23 H 0.23 0.23 C -0.59

Xe 0.78

H -0.09

aMethod: HF/aug-cc-pvDZ. Xe: SC pseudopotential; Q=28 (Ref. 18).

bMethod: MP2/aug-cc-pvDZ; Xe: small core (SC) pseudopotential; Q=28 (Ref. 18). Footnote c of Table I. cMethod: MP2/LJ18/6-311 + + G(2rf,2p) (footnote d, Table I). dMethod: B3LYP/LANL2DZ (footnote f, Table I).

It is understood that the considered Xe derivatives are produced in a Xe matrix. Thus it would be useful to find out if some significant charge transfer takes place in the system {Xe matrix}/{Xe derivative}. Two models have been adopted for the discussion of this question. The first involves six Xe atoms octahedrally placed around HXeC2H (Fig. 2). The distances A1A2 (7.56 a.u.) and A2A3 (9.45 a.u.) were optimized

FIG. 2. Six Xe atoms octahedrally placed and eight Xe atoms cubically arranged around a HXeC2H molecule.

at the MP2/aug-cc-pVDZ (=B1) level and the obtained lengths are given in parentheses. The second model involves eight Xe atoms arranged in a cube (Fig. 2; A1A2 = 15.12 a.u.). Employing NBO analysis, at the MP2/B1 level, we have found that an insignificant charge transfer takes place, that is, 0.02 and 0.002 electrons are transferred from the Xe environment to HXeC2H, in the first and second models, respectively.

D. C2H2 and C4H2

There is an extensive literature on C2H2, for example, Medved et al?3 employing the CCSD(T)/aug-cc-pVTZ method found azz=30.43 a.u. and yzzzz=3285 a.u., while Keir et al. experimentally determined azz =31.60 a.u. at 632.8 nm.40 Karamanis and Maroulis41 reported for azz of C4H2 the following property values, 88.37 (22 839), 85.42 (33 089), and 85.40 (30 274) a.u., at the HF, MP2, and CCSD(T) levels, respectively (basis set: [5s3p3d1//3s3p1d]). The corresponding yzzzz values are given in parentheses. It is observed that our values, given in Table IV, are in satisfactory agreement with the above property values. Other (hyper)polarizabilty values are given in Refs. 42-48.

E. Literature values for a and y of Xe

Hohm and Trumper,49 employing refractivity data determined «=27.12 a.u. Several high quality results have been reported for the polarizability of Xe.50,51 Shelton52 employing electric field induced second harmonic generation reported y= 6888 a.u. Several theoretical estimates for y of Xe have been published.50,51,53 From the results of y for Xe (Table IV), it is observed that MP2 recovers most of the correlation contribution, which can be computed at the CCSD(T) level. The quality of the basis set has a very significant effect, considering the great improvement, which is achieved by using aug-cc-pV5Z, in comparison with the aug-cc-pVDZ result.

TABLE IV. The dipole moment and the (hyper)polarizabilites of HCwCH, HCwC-CwC-H and Xe. All values are in a.u.

Derivative Cor.a azz. Y zzzz Method

H-Cw C-Hb 32.87 2664 HF/B1c

4 31.64 3277 MP2/B1

4 31.84 3330 CCSD(T)/B1

H-Cw C-Cw C-Hd 86.42 22488 HF/B1

4 83.66 31224 MP2/B1

Xe 25.07 1973 HF/B1

26 25.29 2320 MP2/B1

26 27.04 5789 MP2/B4

26 25.53 2388 CCSD(T)/B1

27.16e 6888f

27.08g

27.82h

aTotal number of correlated electrons.

bThe geometry of the derivatives has been optimized by employing the MP2/aug-cc-pvDZ method. For Xe a small core (core: 28 electrons) has been employed (footnote b, Table I). The technique used for the computation of the properties is given in the table. A finite perturbation approach has been employed for the computation of the properties (F =0.0, ±0.001, ±0.002 a.u.). cB1:aug-cc-pVDZ.

dThe geometry of Ref. 39 has been used for the computation of the properties. A numerical fitting approach has

been used employing the following fields: 0.0±0.001, ±0.002, ±0.005, ±0.01 a.u.

eExperimental value [Ref. 51(b)].

Experimental value [Ref. 52].

gExperimental value [Ref. 51(c)].

hExperimental value [Ref. 51 (d)].

F. The L&NLO properties

The results of Table V mainly demonstrate how the L&NLO properties of HC2H and HC4H are affected by inserting one or more Xe atoms and by extending the chain (Cn) length. The present analysis will focus on the properties along the z axis, along which the molecule is placed. The other components are much smaller. For example, at the HF/ HyPol level we have found for HXeC2H: axx = ayy =42.98 a.u. and azz =123.72 a.u.; f3zxx= fizyy = -49.3 a.u. and Pzzz =1009.3 a.u.; yxxxx =Tyyyy = 13 039 a.u., yxxzz=6703 a.u. and yzzzz=46 661 a.u.

The basis set effect. We have employed the basis sets aug-cc-pVnZ, where n = 2-4 at the HF level. The effect of the basis on fiz and a.z is very small. The effect on (3zzz and yzzzz, as one would expect, is larger. For example, the difference of yzzzz, employing DZ and QZ sets, is 11.7% (Table V). HyPol is also giving results in reasonable agreement with the properties produced with the augmented correlation-consistent basis sets.

Complete basis set limit. In Table V we present the property values at the "complete" basis set (CBS) limit. Data derived with the basis sets aug-cc-pVnZ, where n = 2-5, have been employed at the HF and the MP2 levels. For the extrapolation to the CBS limit we have employed the

function54

A(X) = A(») + Be-C(X-2),

where A(X) is the property of interest, A(^) is the property value at the CBS limit, and X is the cardinal number of each set. It is observed (Table V) that as X increases the properties

smoothly converge, in particular, at the MP2 level, to the CBS limit. Woon and Dunning16 noted that reliable estimates of the CBS limit for molecular polarizabilities can be obtained with the augmented basis sets.

It would be useful to compare the aug-cc-pVDZ(=B1) results with the corresponding estimated CBS limits, since B1 will be used for the computation of the properties of the larger molecules. There is satisfactory agreement between the B1 data and the estimates of the CBS limit for fiz and azz and a reasonable agreement for (3zzz and yzzzz. The discrepancy observed for yzzzz between the two approaches is likely to be due to the less satisfactory description of y for Xe with B1 (Tables IV).

Effect of core electrons of Xe. We have considered two cases; in the first case 18 electrons and in the second case 26 electrons have been treated explicitly and correlated for Xe. It is observed that both cases give practically the same fiz, azz, fizzz, and yzzzz [theory: MP2/B1 and CCSD(T)/B1].

The relativistic effect. The employed PP for Xe takes into account the effect of the relativistic correction, since the PP has been adjusted by employing reference atomic valence energies computed from all electron four-component multi-

configuration Dirac-Hartree-Fock calculations for a multi-

tude of valence and outer-core excited states. However, it would be useful and interesting to find out the magnitude of the relativistic effect on the considered L&NLO properties. Thus, the relativistic correction has been estimated by comparing the HF/B4 and HF/B4/DK results (Table V). The latter data have been computed by employing for Xe a basis set (HyPol), specifically derived for relativistic computa-

TABLE V. The dipole moment and the (hyper)polarizabilites of some Xe derivatives. All values are in a.u.

Derivative a / b [¿z azz fizzz yzzzz Method

H-Xe-Cw C- -Hb,c -1.430 123.52 995.5 42294 HF/B1d

-1.966 119.47 832.1 36432 HF/B1e

-1.427 123.87 1048.2 46780 HF/B2f

-1.423 123.90 1056.3 47900 HF/B3g

-1.422 123.88 1072.8 49200 HF/B4h

-1.422 123.89 1072.3 49300 hf'

-1.396 123.72 1009.3 46660 HF/B5j

-1.440 124.06 1066.4 48260 HF/DK/B5k

4 / 26 -1.083 125.64 778.9 41262 MP2/B1

4 /18 -1.085 125.69 781.9 41318 MP2/B1

4 / 26 -1.630 122.54 621.7 36024 MP2/B1e

4 /16 -1.082 125,52 774.5 41046 MP2/B1

4 / 26 -1.098 126.19 862.7 45700 MP2/B2

4 / 26 -1.105 126.45 890.2 47670 MP2/B3

4 / 26 -1.111 126.54 918.4 49650 MP2/B4

4 / 26 -1.117 126.63 925.6 50387 MP2'

4 / 26 -1.077 125.38 679.4 38740 CCSD(T)/B1

4 /18 -1.078 125.44 679.7 38649 CCSD(T)/B1

4 /16 -1.077 125.31 677.6 38709 CCSD(T)/B1

H-Xe-Cw C- -Xe-Hw 0.0 281.60 0.0 222000 HF/B1

4 / 26 0.0 289.30 0.0 378000 MP2/B1

H-Xe-Cw C- ■C=C-HmJ -1.745 198.86 1272.5 93500 HF/B1

4 / 26 -1.315 200.54 983.4 111190 MP2/B1

H-CwC-Xe- ■Cw C-Hnl 0.0 171.97 0.0 2544 HF/B1

4 / 26 0.0 162.00 0.0 28488 MP2/B1

H-Xe-CwC- Xe-CwC-Xe-Ho,l 0.003 471.6 3.9 321600 HF/B1

aTotal number of correlated electrons for C (a) and Xe (b).

bThe geometry of the derivatives has been optimized by employing the MP2/aug-cc-pvDZ method. For Xe a small core (core: 28 electrons) has been employed (Ref. 18). The technique used for the computation of the properties is given in the table.

cA finite perturbation approach has been employed for the computation of the properties (F=0.0, ±0.001,

±0.002 a.u.), except of the case described by footnote h.

dB1:aug-cc-pVDZ (footnote b, Table I).

eEffective properties. Local field: -4.4 X 10-3 a.u.

fB2:aug-cc-pVTZ (footnote b, Table I).

gB3:aug-cc-pVQZ (footnote b, Table I).

hB4:aug-cc-pV5Z (footnote b, Table I). A numerical fitting approach of the following fields has been used: 0.0±0.001, ±0.002, ±0.005, ±0.01 a.u. iEstimated basis set limit by employing Eq. (4). jB5:HyPol (Ref. 17).

kDK denotes the Douglas-Kroll approximation employed for taking into account the relativistic correction (Ref. 22).

'A numerical fitting approach has been used, employing the following fields. 0.0±0.001, ±0.002, ±0.003, ±0.004, ±0.005, ±0.008, ±0.01 a.u.

mThe geometry of Ref. 13 was used for the computation of the properties. nThe geometry of Ref. 57 was used for the computation of the properties.

oThe geometry of the compound has been optimized by employing the HF/aug-cc-pVDZ method.

tions. The relativistic correction has been taken into account by using the Douglas-Kroll (DK) approximation. It is observed that the relativistic effects are 5.4% and 3.3%, for (3zzz and yzzzz, respectively, while for fiz and azz are 3.1% and 0.3%, respectively.

The correlation effect. Correlation at the MP2 level has the following effects:

(i) It increases azz of HXeC2H, HXeC2XeH, and HXeC4H.

(ii) It decreases azz of HC2XeC2H.

(iii) It decreases fiz (in absolute value) and (3zzz of HXeC2H and HXeC4H.

(iv) It leads to a small decrease of yzzzz of HXeC2H.

The CCSD(T) method decreases fiz (in absolute value), azz, (3zzz, and yzzzz of HXeC2H in comparison with the MP2 values.

Effect of Xe on the (hyper)polarizabilities. Comparing the results of HXeC2H with those of C2H2 and Xe, we observe that at the HF/ B1 level of theory, the effect of Xe is very significant (Tables IV and V). For example, it is found

that azz(HXeC2H) -azz(C2H2) -a(Xe) = 65.58 a.u. This G. Stability

value is 113.2% of azz(C2H2) and a(Xe). The same trend is shown at the MP2 and CCSD(T) levels.

Due to symmetry the 3zzz value of C2H2, C4H2, and Xe is zero. The value of 3zzz for HXeC2H is very large. This may be appreciated by comparing the first hyperpolarizabil-ity of the Xe derivative with para-nitroaniline, which is 797.5 (Ref. 38) at the HF/Pol level.55,56 The effect of Xe on the formation of yzzzz is very large. This may be seen by noting that ?zzzz(HXeC2H) - y^^^) -y(Xe) = 37 657 a.u. (HF/B1). yzzzz(HXeC2H) is 8.1 times larger than that of yzzzz(C2H2) and y(Xe). This effect is confirmed at the MP2 and CCSd(t) levels of theory (Table V).

Insertion of a second Xe atom leads to a significant increase of the (hyper)polarizability, for example, the ratio P(HXeC2XeH)/P(HXeC2H) takes the values of 2.3 and 5.2 for P =azz and P = yzzzz, respectively (HF/B1). azz and yzzzz of HXeC2XeC2XeH are considerably larger than

Tanskanen et al. comparing the properties of HXeC2H and HXeC4H noted that the latter is more strongly bound (by 1.06 eV). Evidence for this is provided by the blueshift of the H-Xe stretching frequency for HXeC4H, which has been estimated to be 23 cm-1. The shortening of H-Xe in

HXeC4H (by 0.01 A) also indicates a greater stability.

Brown et al. predicted that the linear polymer made of -(XeC2)- is characterized by high stability due to the significant energy barrier for the removal of Xe atom. Analysis of the decomposition channels shows that HXeC2H is 34 kcal mol-1 more stable than H+Xe+C2H, but 104 kcal mol-1 less stable than Xe+HC2H.57

HXeC2H

HXeC2XeH

example, rzzzz(HXeC2XeC2XeH) = 1.2[yzzzz(HXeC2H)

+ yzzzz(HXeC2XeH)] (method:HF/B1). The significant effect of inserting one, and even more of three, Xe atoms on yzzzz, is shown by observing the ratios (HF/B1): yzzzz(HXeC4H)/yzzzz(HC4H)=4.9 and yzzzz(HXeC2XeC2XeH)/yzzzz(HC4H) = 14.3. The results of HXeC4H and HC2XeC2H show that the position of Xe has a great effect on both azz and yzzzz (Table V). For example, yzzzz of HXeC4H is 3.9 times larger than that of HC2XeC2H (MP2/B1).

Vibratonal contributions. The pv contributions apz and fOpx have also been computed by employing the methods HF/aug-cc-pVDZ and MP2/aug-cc-pVDZ at the double harmonic approximation level. This approximation allows us to identify the modes with more significant contribution to the properties of interest. apz (=[^2](0,0)) are 96.21 and 60.13 a.u. at the HF and MP2 levels of theory, respectively. The electronic contributions computed by employing the optimized geometry at the corresponding level of theory are 115.81 (HF) and 125.98 (MP2) a.u.

Employing Eqs. (1) and (2) we can comment on the modes with the dominant contributions to apz'. It is thus found that the vibrational modes H-Xe and Xe-C with frequencies 1681 (2021) cm-1 and 313 (277) cm-1 at the MP2 level contribute 13.1 (7.6) and 46.8(88.5) to [^2](°,0). The corresponding values computed at the HF level are given in parentheses. It is inferred that the MP2 value of [^2](0,0) is remarkably smaller than the corresponding value at the HF level.

Similar observations have been made for ¡3pvzz (=[^a](°,0)), for which the values 431 and -835 a.u. have been computed at the HF and MP2 levels, respectively. The corresponding values for the electronic contribution to 3zzz are 1040.6 and 785.6 a.u. The difference in sign between the HF and MP2 values for [^a](°,0) is noted. At the MP2 level the H-Xe and Xe-C modes are associated with 1212 (1074) and -2079 (-669) a.u. contributions to [^a](°,0). The values computed at the HF level are given in parentheses. The significant effect of correlation at the MP2 level on the contribution of the Xe-C mode is noted.

H. Local field effect

The discrete LF approximation has been applied in order to find the effect of the environment, which consists of the surrounding Xe atoms, on the computed (hyper)polarizabili-ties, of HXeC2H. Only the dipole and induced dipole interactions between HXeC2H and the Xe environment were considered. The dipole moment and dipole polarizability of the isolated HXeC2H have been computed at the CCSD(T) level of theory with the aug-cc-pvDZ basis set (Table V), while for Xe atom the experimental polarizability 27.10 a.u. was used (Table IV). The crystal structure of Xe is a cubic closed packed, with cell parameters a=b = c = 6.2023 A and angles a=3= y=90.0°.58

We have developed two crystal models, A and B, in order to compute the LF due to the surrounding Xe atoms on HXeC2H. Model A is cubic closed packed, with dimensions a = b = c = 24.8092 A. It includes 255 Xe atoms surrounding HXeC2H (Fig. 3). Model B is a parallelogram with dimensions a=b = 6.2023 A and c = 24.8092 A. It includes 63 Xe atoms (Fig. 4). This model (B) was created by the one dimensional expansion of the crystal structure of Xe along the dipole axis (z axis) of HXeC2H. These models were designed in order to show how the number of Xe atoms, which surround HXeC2H, affect the LF. The structure of models A and B is presented in Figs. 3 and 4. The values we computed for LF (Fz) are -4.4 X 10-3 and -4.0 X 10-3 a.u., for models A and B, respectively.

The L&NLO properties of HXeC2H, in the presence of the LF (model A), have been computed by employing the HF/B1 and MP2/B1 methods (Table V). We observe that there is a significant difference in some of the considered properties. For example, at the MP2 level the LF imposes the following changes, in comparison with the properties which correspond to the isolated molecule: fiz (50.5%), azz (2.5%), 3zzz (20.2%), and yzzzz (12.7%). A similar trend has been found at the HF level. It is observed that the greatest effect has been found for fiz and 3zzz.

The effect of the local field on the stability of HXeC2H. It is noted that the effect of the LF, which is exercised by the Xe atoms (model A), surrounding HXeC2H, is stabilizing, considering that the Xe environment lowers the energy of the above molecule by 0.0214 a.u. at the MP2 level.

I. Interpretation of the results

In this section we will interpret the reported L&NLO properties. In particular, we would like to connect the changes in the electronic structure of HC2H, imposed by the insertion of Xe, with the observed change in the L&NLO properties. This discussion relies on a sum-over-states (SOS) perturbative approach. The high-level ab initio multiconfigu-rational CASSCF/CASPT2 method,30 which has been successfully applied in spectroscopy and photochemistry,59,60 was employed to compute the excited states of acetylene and HXeC2H, at the optimized MP2/aug-cc-pVTZ ground-state geometries. Relativistic ANO-RCC type one-electron basis sets61,62 contracted to Xe[7s6p4d2f1g]/C[4s3p2d1f]/ H[3s2p1d] were employed.

Different active spaces were tested to assure the reliability of the obtained results. The final calculations comprise 10 electrons distributed in 14 orbitals, CASSCF(10,14), and include 3 a, 2n, 3o- , and 2n valence orbitals plus four Ryd-berg orbitals, one s and three p. The standard zeroth-order CASPT2 Hamiltonian was employed, whereas an imaginary level shift of 0.2 a.u. was used in order to avoid intruder state problems.63 Transition dipole moments (TDMs) are then obtained at the CASSCF level, whereas excitation energies are computed at the CASPT2 level. The calculations were per-

formed with the quantum chemistry package MOLCAS.6.0.

Table VI compiles computed excitation energies and os-

cillator strengths for HC2H and HXeC2H, together with the values obtained using the SOS expressions for ground-state polarizabilities, and first and second (three-state SOS) hyperpolarizabilities. - Excitation energies of acetylene are favorably compared with other values, experimental or theoretical.68,69 Focusing on the excited states structure of both molecules, two striking features can be observed.

First, insertion of the Xe atom leads to much larger a bonds and therefore lower energy excited states with involvement of a, a orbitals in HXeC2H, as compared to the HC2H spectrum. Unlike acetylene, where the low-lying na state (a is mainly the antibonding CC orbital) is expected above 9.0 eV, in HXeCCH the lowest singlet excited state (of na type), at the ground-state geometry, is computed at 5.32 eV and involves the aXe-H* antibonding orbital, with diffuse Rydberg-like s character, whereas the second singlet excited state, computed at 6.45 eV, is of aa character. It is observed that the low-lying valence nn states are not strongly perturbed by the insertion of the Xe atom, and therefore they cannot be considered responsible for the change of the NLO property values (Table VI).

The second important difference is the reduction of the symmetry in HXeC2H, which yields much larger oscillator strength values for many of the transitions. As a consequence, in HXeC2H, we have an electronic spectrum lower

TABLE VI. Experimental and CASPT2 computed excitation energies (AE/ eV) as well as related oscillator strengths (f for the low-lying excited singlet states of HC2H and HXeC2H. The L&NLO properties estimated by means of the SOS approach are also included.

State HC2H HXeC2H

AE f Exp.a State AE f

X X 1E+

1 X (W) 6.67 7.1 11n (W) 5.32 0.0015

1 1A„ (W) 7.05 7.2 21E+ (0-0-*) 6.45 0.3805

1 1n„ (n3s) 8.08 0.0933 8.16 1(W) 6.51

1 1ng (v3pa) 8.39 8.55 1 1A (W) 6.72

1 (v3p„) 9.08 2 1n (^3s) 7.00 0.0315

1 1Ag ( v3p„) 9.12 9.02 3 1E+ (00*) 7.50 0.1932

2 (n3pj 9.13 9.21 3 1n (v3pa) 7.53 0.0123

2 (™*) 10.27 0.9757 4 1n (oV) 7.57 0.6146

= 3473 a.u.

SOS-computed NLO properties

/¿z=-0.71 a.u. azz=26.51 a.u. Pzzz =557.5 a.u.

yzzzz=

For values and assignments see discussion in Refs. 68 and 71.

a = 11.07 a.u.

in energy, more dense (in the number of low-lying states), and with many nonzero contributions in the transition dipole moment matrix.

The NLO properties, according to the SOS expression, are proportional to products of TDM elements and inversely proportional to products of energy differences, and, therefore, in this case an enhancement of the NLO values of HXeC2H can be expected with respect to acetylene. Indeed, as reported in Table VI, SOS-computed and yzzz of HXeC2H increase with respect to HC2H, by two- and threefold factors. Although the proportionality is far from the near four- and tenfold factors obtained by the CCSD(T)/B1 (Table V), it clearly reflects the expected trends. It is necessary to remember that for a better performance of the SOS method, a much larger number of excited states must be taken into account.67

IV. CONCLUDING REMARKS

We presented the L&NLO properties of HXeC2H, HXeC2XeH, and three of the Xe derivatives of HC4H. We have computed the NBO charge distribution of the considered derivatives and discussed how the intramolecular environment affects the charge of Xe and the other involved atoms.

The weights of the five resonance structures of HXeC2H have been calculated and the bonding, which is instrumental in the understanding of the extraordinary L&NLO properties of the derivatives of interest, has been analyzed. Since the considered organoxenon derivatives have been synthesized in a xenon matrix, we have computed the effect of the local field, which is produced by the Xe environment on the L&NLO properties of HXeC2H. By employing two models (an octahedral and a cubic one) we have found that an insignificant charge transfer takes place between the Xe environment and HXeC2H. In addition, we have computed the effect of the LF on the properties of interest and it has been found

that in some cases it is significant ,^zz). We have performed a detailed analysis of the factors which affect the quality of the results (e.g., basis set, correlation, relativistic correction, core electrons of Xe). The main result of this work is the great effect of the inserted Xe on the L&NLO properties of the resulting derivatives. This significant result has been rationalized by employing the changes in the electronic spectrum, which are induced by the inserted Xe. The proposed interpretation scheme has been verified by SOS calculations.

ACKNOWLEDGMENTS

L.S.A. acknowledges financial support obtained by Project Nos. CTQ2004-01739 and CTQ2007-61260 of the Spanish MEC/FEDER and GV06-192 of the Generalitat Valenciana. The authors would like to thank Professor A. J. Sadlej for his useful comments.

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