DFT Calculation of Static First Hyperpolarizabilities and Linear Optical

Article pubs.acs.org/Organometallics

DFT Calculation of Static First Hyperpolarizabilities and Linear Optical Properties of Metal Alkynyl Complexes Erandi Kulasekera, Simon Petrie, Robert Stranger,* and Mark G. Humphrey Research School of Chemistry, Australian National University, Canberra, Australian Capital Territory 0200, Australia S Supporting Information *

ABSTRACT: Density functional theory (DFT) and timedependent density functional theory (TD-DFT) calculations are reported for a set of organometallic compounds for which the first hyperpolarizability values, β, have previously been determined in the laboratory. These calculations, which utilized a variety of density functionals and basis sets, address such aspects as the implications of molecular conformation and the extent of bond delocalization on the calculated β values. We also explore here the simplification of ligands for computational expedience and the influence of incorporation or exclusion of solvent corrections on β. The results of our study are likely to be of value in guiding subsequent efforts toward the reliable predictive calculation of the first hyperpolarizabilities and linear optical properties for organometallic compounds of interest to experimentalists.

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DFT)14−19 have become an increasingly powerful and versatile tool. DFT, in particular, appears very well suited to the modeling and exploration of large TM-containing systems, while electronic excitation spectra and response properties can be assessed using time-dependent DFT (TD-DFT). Studies on the NLO properties of small to medium-sized (predominantly organic) molecules have indicated that TD-DFT calculations on these properties are generally accurate and show good agreement with experimental values. Though TD-DFT shows great promise in the exploration of NLO properties, allowing researchers to vary the structures of candidate organometallics in ways which might be excessively time-consuming or impractical in a laboratory complex, the calculations required to assess NLO properties, particularly for organometallic compounds, are not yet routine. The accurate prediction of NLO properties requires large basis sets and an appropriate treatment of electron correlation, and such considerations often incur substantial computational expense (particularly if highly accurate values are sought rather than merely an indication of the trends in NLO properties as a function of some structural parameter). Studies conducted to date have included the calculation of mononuclear electron-rich organoiron complexes,20,21 alkynylbis(diphosphine)ruthenium complexes,8 ferrocenyl systems coupled with metal carbonyls,22 and various other organometallic systems.14−16,23−27 However, there are few studies that have explored the performance of TD-DFT for larger organometallics, and some such studies have indicated problems in the application of TD-DFT to long π-conjugated molecules and extended organometallic com-

INTRODUCTION There is considerable interest in nonlinear optical (NLO) materials because of the potential such materials hold for applications in optical switching and signal processing, optical computing, dynamic holography, electro-optical, and photonic technologies.1−5 Advances in the field of NLO materials depend, to a significant extent, on the characterization and synthesis of novel chromophores with large static first (or higher) hyperpolarizabilities, and many laboratory and spectroscopic studies have been undertaken to this end. Considerable interest has been shown in transition-metal (TM) organometallics and coordination complexes as potential building blocks for possible reversible modulation of quadratic and cubic NLO properties.6−9 Attractive features of TM complexes as candidate NLO materials include the capability to vary the identity of the metal center(s), the oxidation state(s), the stereochemistry, and the identity of the coordinated ligands. Complexation also affords a mechanism by which organic elements with high NLO activity and organic ligands with unusual structural aspects (or intrinsically poor stability in isolation) can be combined. Particular attention has been focused on TM-containing systems with substantial π conjugation, combining one or more unsaturated ligands anchored through a linear MCC fragment. An advantage of such a structural feature is that it provides a pathway for delocalization of electron density along the metal−ligand axis, resulting in an enhancement of the quadratic and cubic hyperpolarizabilities10−12 predominantly along this axis. Alongside the laboratory and spectroscopic techniques now accepted as suitable for the characterization of novel NLO materials, computational methods (including semiempirical methods13 and ab initio and density functional theory, © 2014 American Chemical Society

Received: July 4, 2013 Published: May 13, 2014 2434

dx.doi.org/10.1021/om500124c | Organometallics 2014, 33, 2434−2447

Organometallics

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Table 1. Molecular Quadratic NLO Measurements for the Complexes of Interest complex 1 2 3 4 5 6 7 8 9 10 11

formula 5

[Fe(CCC6H4-4-NO2)(dppe)(η -C5H5)] [Ru(CCC6H4-4-NO2)(dppe)(η5-C5H5)] [Os(CCC6H4-4-NO2)(dppe)(η5-C5H5)] [Au(CCC6H4-4-NO2)(PPh3)] [Au(CCC6H4-4-NO2)(PMe3)] trans-[Ru(CCPh)Cl(dppm)2] trans-[Ru(CCPh)Cl(dppe)2] trans-[Ru(CCC6H4-4-NO2)Cl(dppm)2] trans-[Ru(CCC6H4-4-C6H4-4-NO2)Cl(dppm)2] trans-[Ru(CCC6H4-4-CCC6H4-4-NO2)Cl(dppm)2] trans-[Ru(CCC6H4-(4-CCC6H4)2-4-NO2)Cl(dppm)2]

λmax (nm)a

β (10‑30 esu)b

β0 (10−30 esu)

solvent

ref

symmetryc

498 447 461 338 339 308 319 473 465 464 439

665 664 929 22 50 20 6 767 933 833 1379

64 161 188 12 27 12 3 129 178 161 365

THF THF THF THF THF THF THF THF THF THF THF

25 25 25 56 57 58 59 58 58 59 59

C1 C1 C1 Cs Cs C2v C2 C2v C2v C2v C2v

Optical absorption maximum. bDetermined by the hyper-Rayleigh scattering (HRS) technique. Values are typically ±15%. See text for details. Symmetry imposed in DFT and TD-DFT calculations on the target structures.

a c

derivation of some laboratory measurements of hyperpolarizability is modeled on the UV/vis spectroscopy of compounds of interest, we explore the influence of the aforementioned factors on the computed optical spectra for these compounds.

plexes, with the computation of substantially overestimated values for the hyperpolarizability. These problems with hyperpolarizability calculations for larger organometallics are attributed to the lack of an appropriate general exchangecorrelation (XC) functional, leading to the underestimation of long-range electronic excitations.28−31 Environmental effects also merit consideration when comparing experimental and computed polarizabilities or hyperpolarizabilities. Most laboratory measurements of such properties are undertaken in solvent, while quantum chemical calculations are often performed in vacuo. Several studies have indicated the influence of solvent polarity on both electronic excitations and hyperpolarizability. Correction for solvent effects in quantum chemical calculations can be attempted through the use of such methodologies as the polarizable continuum model (PCM),32 solvation models (SM),33 and the conductor-like screening model (COSMO);34 these models all seek to mimic solvation through construction of a soluteaccommodating cavity within a surrounding dielectric medium. Several studies have now addressed solvent effects in the calculation of polarizabilities and hyperpolarizabilities.14−16,35−38 A study by Wu and co-workers39 on the W(CO)5DAS chromophore ((4-dimethylamino-4′-stilbazole)tungsten pentacarbonyl) has shown β to be remarkably dependent on the dielectric constant (ε), a result consistent with studies demonstrating that different solvents can yield markedly different hyperpolarizability responses for a given solute species.40 There are also significant structural considerations appropriate to the computational treatment of larger organometallics. Computational expense scales with increasing molecular size; additionally, the potential energy surface for a large organometallic will often include many more stationary points (corresponding to different conformers of the compound) than is the case for a smaller homologue, thereby exacerbating the computational expense, and a degree of symmetry which might reasonably be imposed upon a smaller homologue (thus simplifying the task of computation) will often not be appropriate in calculations on a large organometallic. With these considerations in mind, we have turned our attention to the assessment of DFT and TD-DFT calculations on larger organometallics, so as to establish a set of guidelines for the expedient, efficient, and accurate treatment of these species. The choice of basis set, density functional, ligand simplification, stereochemistry, and solvent effects have all been assessed as to their influence on the computed results. In addition, since the

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COMPUTATIONAL METHODS

Unless otherwise indicated, the DFT/TDDFT calculations reported here were performed using the ADF2009.01 and ADF2010.01 versions of the Amsterdam Density Functional (ADF) program.41,42 Aside from one set of calculations detailed in the Supporting Information, all ADF calculations reported here employed all-electron valence triple-ζ plus polarization (TZP) Slater orbital basis sets for all atoms. All calculations included correction for scalar relativistic effects through the zeroth-order regular approximation (ZORA) treatment. 43 Geometry optimization was performed using the Becke−Perdew (BP) exchange-correlation (XC) functional;44,45 additional density functionals were used in subsequent single-point calculations on these optimized geometries, as reported in subsequent sections. Comprehensive efforts were made to assess all relevant conformations of the appropriate molecular point group symmetry for each complex (variously C1, Cs, C2, or C2v), to obtain the lowest-energy minimum for each compound. Solvent corrections, where applied, used the conductor-like screening model (COSMO) implemented within ADF.34,46 For evaluation of the influence of range separation on calculated hyperpolarizability values, calculations were performed using the Gaussian09 program suite.47 These calculations used the SDD basis set and associated pseudopotential48 for transition-metal atoms and the split-valence triple-ζ 6-311G** basis set49 for all other atoms. Functionals employed in these calculations were BP86, 44,45 B3LYP, 50,51 and the related range-separated functionals LCBP8644,45,53 and CAM-B3LYP.50,51,53 The total second-order polarizability (βtot) is expressed by

βtot = (βx 2 + βy 2 + βz 2)1/2

(1)

where βx, βy, and βz are the components of the second-order polarizability tensor along the x, y, and z axes, respectively, and where βi is defined as

βi = βiii +

1 3

∑ (βijj + βjij + βjji) i≠j

(2)

The 27 components of the indicated 3 × 3 × 3 matrix can be reduced to 10 components through the application of Kleinman symmetry, where βxyy = βyxy = βyyx, βyyz = βyzy = βzyy, etc..54 The complete equation to calculate the magnitude of the total first hyperpolarizability tensor is then 2435


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β0 = β(1 − (λmax /λ)2 )(1 − (2λmax /λ)2 )

βtot = [(βxxx + βxyy + βxzz )2 + (βyyy + βyzz + βyxx )2 1/2

+ (βzzz + βzxx + βzyy)2 ]

where λmax is the optical absorption maximum and λ is the fundamental wavelength of the laser;10 while the model has proven useful with organometallic and coordination complexes, its shortcomings are known and have been discussed elsewhere.60,61

(3)

β was calculated using the RESPONSE module implemented in ADF.55 The ALLCOMPONENTS subkey was specified to obtain the entire polarizability tensor, instead of just the z component, while the subkeys DYNAHYP and HYPERPOL were also selected. The output of these calculations included all nonzero components of the tensors governing the static β. The numerical integration parameter, used to determine the precision of numerical integrals, was set to 6.0 so as to address the numerical problems that can arise, due to linear dependencies, through inclusion of diffuse functions in calculations on large molecules.

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RESULTS AND DISCUSSION Geometry Optimization. For purposes of computational expedience, the symmetry identified in Table 1 was applied to

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COMPLEXES SURVEYED Table 1 details the organometallic data set used for assessment purposes in the present work. All 11 complexes in this table (see Figure 1) have been studied experimentally, including

Figure 2. Lowest-energy conformers of complex 11, ranked in order of increasing energy. The notation used for axial group conformation is A (“aligned”) for those phenylethynyl moieties coplanar with the dppm methylene C atoms and O (“opposed” or “orthogonal”) for those perpendicular to this plane, with the lower-case variants analogously denoting orientation of the terminal NO2 moiety.

each target complex. For most of these complexes, several different conformers of this symmetry are possible. For example, for complex 11, each of the three phenyleneethynylene rings and the peripheral NO2 group can be in either a coplanar or a perpendicular orientation with respect to the mirror plane containing the dppm methylene C atoms, with the result that there are 16 feasible conformers of 11 with C2v symmetry. In such cases, all conformers were optimized independently, so as to ascertain the lowest-energy structure. Figure 2 displays the four lowest-energy conformations determined for 11, at the BP/TZP level of theory. These optimizations, which were performed in the vacuum phase, repeatedly found the lowest-energy conformers to be those in which all axial phenyl or phenylene (and NO2) moieties were constrained to be coplanar with each other. NLO Properties. Measurements of NLO properties tend to be quite research-group-dependent. Thus, it was felt inappropriate, in the present work, to compare experimental measurements obtained by different research groups, out of a concern that differences in the measurement techniques (as well as differences in the conventions employed to determine hyperpolarizability values) might swamp any qualitative trends in β value across a series of related structures. The data set that we have adopted (see Table 1) consists of complexes synthesized and characterized by some of us and measured by the Persoons group, thereby ensuring consistency of experimental technique and of conventions used.

Figure 1. Complexes 1−11.

laboratory determination of the β value for each complex. Complexes 1−3 are a series of (η5-cyclopentadienyl)metal complexes possessing p-nitrophenylalkynyl ligands with the group 8 metals Fe, Ru, and Os. Complexes 4 and 5 involve triphenylphosphine- and trimethylphosphine-ligated group 11 gold alkynyl complexes. Complexes 6 and 7 vary in the coligandsviz., bis(diphenylphosphino)methane (dppm) and 1,2-bis(diphenylphosphino)ethane (dppe)coordinated to the ligated metal center. Finally, complexes 8−11 explore the influence of phenylalkynyl chain lengthening upon the measured β value. The β values for the complexes in Table 1 were obtained through hyper-Rayleigh scattering (HRS) measurements reported in the indicated studies. The βHRS derived data are frequency dependent and need to be extrapolated to zero frequency to estimate the static (frequency independent), intrinsic first hyperpolarizability β. The dispersion due to resonance enhancement is estimated by the two-level model 2436


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Table 2. Calculated βo Values for Complexes 1−11 at the BP/TZP, SAOP/TZP, and GRACLB/TZP Levels of Theory calcd βtota,b

a

βveca,b

complex

BP

SAOP

GRACLB

BP

SAOP

GRACLB

exptl/HRS βtota

1 2 3 4 5 6 7 8 9 10 11

157.80 155.26 149.38 31.54 27.89 26.42 26.15 167.79 1006.24 1954.67 9656.21

153.56 156.17 148.87 38.99 33.27 19.99 25.42 156.17 977.61 1922.73 11536.31

158.65 155.81 150.64 32.69 36.13 25.81 25.72 166.76 998.04 1933.90 10602.03

89.62 93.16 89.62 18.92 16.74 15.85 15.69 100.67 603.77 1172.78 5793.77

92.13 93.70 89.32 23.39 19.96 11.99 15.25 93.70 586.57 1153.61 6921.72

95.19 93.49 90.38 19.61 21.68 15.49 15.43 100.06 598.81 1160.34 6361.03

64 161 181 12 27 12 3 129 178 161 365

In units of 10−30 esu. bCalculated in the vacuum phase.

Table 3. Effect on Calculated Hyperpolarizability of Ligand Modification (R = H, CH3, Ph) in dppm-Like (R2PCH2PR2) and dppe-Like (R2PCH2CH2PR2) Ligands β0,tota calcd complex

symmetry

Hb

CH3b

Phb

β0,tota exptl

C1 C1 C1 C2v C2v C2v

146.51 150.88 148.95 20.97 830.82 6145.78

154.00 161.86 153.58 37.59 1033.00 10243.38

153.56 156.17 148.87 19.99 994.73 11562.00

64 161 188 12 178 365

5

[Fe(CCC6H4-4-NO2)(dppe)(η -C5H5)] [Ru(CCC6H4-4-NO2)(dppe)(η5-C5H5)] [Os(CCC6H4-4-NO2)(dppe)(η5-C5H5)] trans-[RuCCPh)Cl(dppm)2] trans-[Ru(CCC6H4-4-C6H4-4-NO2)Cl(dppm)2] trans-[Ru(CCC6H4-(4-CC6H4)2-4-NO2)Cl(dppm)2]

1 2 3 6 9 11 a

formula

In units of 10−30 esu. bCalculated in the vacuum phase.

Table 4. Influence on Calculated β Values of Phosphine Ligand Substitution in a Set of trans-[Ru(CCPh)(4-C CC6H4CCPh)L2] Complexes ligand (L) dppe dppm Me2PCH2CH2PMe2 Me2PCH2PMe2 a

symmetry

βtota

βvec

Cs C2 C2v Cs C2 C2v

391.33 505.91 423.39 380.99 382 425.22

234.8 303.55 254.03 228.6 229.2 255.14

Table 5. β Values for PNA, Calculated for Different Solvent Media

a

β value, in units of 10−30 esu, calculated in the vacuum phase.

An additional concern with many of the group 8 metal complexes featured in Table 1 is that the HRS measurements may be subject to resonance enhancement, due to proximity of the optical absorption maximum to the second harmonic of the fundamental laser frequency appropriate to the measurement. The inclusion of the gold complexes 4 and 5 allows us to assess the scope for such concerns in the other cases: the gold complexes possess optical transitions in the UV and are optically transparent at the second-harmonic frequency, which should result in realistic intrinsic off-resonance β values.62 While the simple two-level model outlined above has some known limitations, we expect it to be largely sufficient for our purposes: the focus of our study is as much on the elucidation of qualitative trends in β value and comparison across a set of related structures as it is on the quantitative characterization of this property. Choice of Density Functional. Wu and co-workers have compared the calculated β values for three typical TM aromatic

solvent

ε

βtot(calcd)

βtot(exptl)b

gas n-hexane benzene chloroform tetrahydrofuran dichloromethane acetone ethanol methanol DMSO formic acid water

1 1.88 2.3 4.8 7.58 8.9 20.7 24.55 32.6 46.7 58.5 78.39

14.57 29.35 34.75 53.62 63.14 66.02 76.5 77.9 79.97 81.63 82.68 84.04

15.44

42.76

62.16 76.8

Calculated at the BP/TZP level of theory, in units of 10−30 esu. Reference 81, with λ 1064 nm. Obtained using the EFISH technique, in units of 10−30 esu.

a b

carbonyl complexes (the two tungsten pentacarbonyl derivatives [W(CO)5L], L = NC5H5, NC5H4CHO-4, and the chromium tricarbonyl arene derivative [Cr(CO)3(η6-C6H6)]) and found little significant difference between values obtained using orthodox generalized gradient approximation (GGA) approaches and those determined using meta-GGA functionals. 63 In the present work, we have assessed the performance of six widely used functionals: the GGA functionals BP,44,45 PBE,64 BLYP,51,65 and LB9466 and the asymptotically correct XC potentials GRACLB67 and SAOP68 (see Table S1 in the Supporting Information). 2437


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Table 6. Influence of Solvation (THF) on Calculated β Values for Complexes 1−11 complex

methoda

βtot(gas)b

βtot(THF)b

βvec(gas)b

βvec(THF)b

1

BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB BP SAOP GRACLB

149.38 153.56 158.65 155.26 156.17 155.81 149.38 148.87 150.64 31.54 38.99 32.69 27.89 33.27 36.13 26.42 19.99 25.81 26.15 25.42 25.72 167.79 156.17 166.76 1006.24 977.61 998.04 1954.67 1922.73 1933.90 9656.21 11536.31 10602.03

651.91 609.15 645.97 680.23 666.20 672.67 635.27 599.24 631.83 165.65 194.38 164.54 173.85 195.55 178.02 99.90 76.75 97.07 82.79 81.21 81.63 764.47 701.60 751.91 4321.22 3942.17 4268.94 8638.56 8012.13 8528.17 49109.29 54196.94 48081.45

89.62 92.13 95.19 93.16 93.70 93.49 89.62 89.32 90.38 18.92 23.39 19.61 16.74 19.96 21.68 15.85 11.99 15.49 15.69 15.25 15.43 100.67 93.70 100.06 603.77 586.57 598.81 1172.78 1153.61 1160.34 5793.77 6921.72 6361.03

391.14 365.49 387.58 408.14 399.72 403.60 381.17 359.55 379.10 99.40 116.63 98.72 104.31 117.34 106.82 59.94 46.05 58.24 49.67 48.73 48.98 458.69 420.97 451.14 2592.74 2365.27 2561.38 5183.15 4807.34 5116.97 29465.20 32518.33 28849.21

2

3

4

5

6

7

8

9

10

11

a

Figure 3. Different orientations of 4-dimethylamino-4′-nitroazobenzene (DANA) and 4-dimethylamino-4′-nitrostilbene (DANS) employed in hyperpolarizability calculations. The notation used for axial group conformation is as delineated for Figure 2. The notation “em” versus “sm” refers to “eclipsed” and “staggered” conformations of the dimethylamino methyl groups relative to the axial N−C bond.

GRACLB and BP β values for any of the complexes in Tables S1 and S2 (Supporting Information), there would appear to be little reason to prefer GRACLB over BP as a method for calculating the hyperpolarizabilities of larger TM-containing complexes (expecially since the additional calculations required of GRACLB may well be prohibitive for significantly larger complexes). Of the 10 β components, βzzz generally has the largest value for the complexes in our data set. This is largely an artifact of the orientation convention adopted by ADF, for which the “standard orientation” places the molecule largely in the yz plane and assigns the z axis to a C2 axis of symmetry (where present) or in alignment with the structure’s permanent dipole moment. Therefore, the major contribution to the first hyperpolarizability arises from the βzzz component, and the major charge transfer is along the z direction. Apart from the total β tensor βtot, for which HRS values exist for all complexes 1−11, another property widely reported in the literature is βvec, the vector component of β along the dipole moment direction (i.e., the z axis as discussed above). The relevant expression for βvec is

Using the TZP basis set in all calculations. bIn units of 10−30 esu.

According to the complexes surveyed in Table S1, there is very little difference among the β values computed using the BP, GRACLB, BLYP, and PBE functionals, while the SAOP and LB94 functionals show a somewhat greater propensity to deliver results divergent from this grouping (and from each other). Table 2 shows the β values obtained for complexes 1−11 in calculations using the BP, SAOP, and GRACLB functionals in conjunction with the TZP basis set. Again, generally close correspondence can be seen between GRACLB and BP (and in most cases also SAOP) values. The best results for spectroscopic properties, including β, are expected to be provided by “asymptotically correct” functionals such as GRACLB and SAOP (that is, those with good asymptotic behavior in −1/r for r → ∞). Calculations on the hyperpolarizabilities of small molecules69 support this expectation, as does the recent literature for sizable TM complexes. However, one disadvantage of GRACLB is that it requires a further argument, the ionization potential (IP) of the molecule. Assuming that the IP must be calculated from a pair of totalenergy calculations on the complex in both the reduced and oxidized states, this indicates that GRACLB is effectively a more computationally demanding method than the others surveyed here. Since there are only minor differences between the

βvec =

∑ i=x ,y,z

μi βi |μ|

(4)

where βi is defined as in eq 2, μi is the dipole moment along the direction i, and μ is the ground-state molecular dipole moment. The value of βvec is often used to evaluate and compare the second-order NLO responses of TM complexes and is generally measured in the laboratory using the electric field induced second-harmonic generation (EFISH) technique. As seen in Table 2, both βtot and βvec give similar trends for their calculated values. For metal alkynyl complexes with a dominant charge2438


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Table 7. Comparison, with Experimental β Values, of Computed β Values for DANA and DANS as a Function of Molecular Geometry calcd βtotb geometry

a

symmetry

E (kJ mol−1)

em-Aa

C2v

0

em-C6H4NO2(45°)

C2

6.44

em-Oo

C2v

11.03

sm-Aa

C2v

9.12

sm-C6H4NO2(45°)

C2v

3.15

sm-Oo

C2v

20.59

em-Aa

Cs

em-Oo

Cs

34.40

sm-Oo

Cs

43.40

sm-Aa

Cs

8.29

0

functionala BP SAOP GRACLB BP SAOP BP SAOP BP SAOP GRACLB BP SAOP BP SAOP BP SAOP GRACLB BP SAOP BP SAOP BP SAOP GRACLB

βvecb

in vacuo (a) DANA 371.45 389.64 372.57 407.43 444.75 70.33 77.44 385.96 405.64 388.99 427.9 467.97 72.35 80.45 (b) DANS 328.14 340.22 330.51 41.00 42.60 42.30 44.75 339.74 353.07 344.24

exptlb,c

solvent (THF)

in vacuo

solvent (THF)

β0,HRS

β0,EFISH

1702.49 1776.03 1692.63 1850.1 2069.49 175.29 198.65 1756.84 1827.67 1747.52 1977.21 2199.64 184.54 208.96

222.89 233.81 223.56 244.48 266.87 42.2 46.47 231.6 243.41 233.42 256.74 280.78 43.41 48.28

1021.59 1065.74 1015.63 1110.15 1241.83 105.18 119.2 1054.25 1096.68 1048.64 1186.35 1319.83 110.73 125.39

257

47

1472.54 1494.15 1467.41 94.93 96.29 102.35 104.19 1533.16 1548.13 1528.56

196.9 204.15 198.32 24.60 25.56 25.39 26.87 203.87 211.86 206.56

883.61 896.57 880.50 56.97 57.78 61.45 62.58 919.99 928.97 917.22

597

63

Using the TZP basis set. bIn units of 10−30 esu. cReference 82.

transfer axis, we have previously shown that βEFISH and βHRS values are equivalent within experimental error.70 Further, it is apparent from Table 2 that neither βtot nor βvec is particularly sensitive to the choice of BP, SAOP, or GRACLB functional. Ligand Simplification. Response property calculations for large complexes are highly computationally intensive in time and memory. Since many of the organometallic complexes surveyed here, and studied elsewhere, incorporate large bulky ligands such as dppm and dppe, which add significantly to the computational cost, it is desirable to assess whether such ligands can be satisfactorily modeled by simpler homologues which not only reduce the total number of basis functions required for calculation but also, in the circumstance where a dppe ligand is being replaced, may well allow the calculation to proceed at a higher degree of symmetry. This is a strategy that has been adopted fairly widely. Ivanov et al., in computational studies on Au4(PR3)42+ and Au4(μ2-I)2(PR3)4 clusters (R = PH3, PMe3, PPh3), concluded that substitution of PPh3 by PH3 or PMe3 had negligible effect on the optimized geometries, though the smaller ligands were not entirely suitable as PPh3 models for calculation of the cluster excitation spectra.71 Some of us,25,72 in studies on Os− and Ru−alkynyl complexes, have used PH3 as a model for bulky dppe ligands in calculations of excitation properties. Similarly, the ligand PH2CH2PH2 has been used as a model for dppe and dppm.73,74 The use of simpler ligands (phosphine, PMe3, etc.) as models for dppm or dppe is largely trouble-free when computation is sought purely to address or to understand the structural

properties of an organometallic complex but might present some problems (as suggested by Ivanov et al.71) where the focus is on electronic properties, particularly if ligand−ligand interactions are of significance. Indeed, such ligand simplification has been offered as a justification for discrepancies observed between experimental and theoretical observations of the excitation spectra.73,74 In this work, we investigate the feasibility of ligand simplification as an aid to the calculation of NLO properties. For dppm (PPh2CH2PPh2) and dppe (PPh2CH2CH2PPh2), the Ph rings on the ligand were replaced with simple CH3 or H fragments. The calculated βtot values are displayed in Table 3. The results given in Table 3 show minor variation between βtot values for R2PCH2CH2PR2 ligands (R = H, CH3, Ph) for complexes 1−3. For the R2PCH2PR2-ligated complexes 6, 9, and 11, there is some divergence between βtot values calculated with R = H and with R = CH3; the methyl substituent gives values closer to those of the full dppm ligand for the two larger complexes 9 and 11, though not for 6. The values in Table 3 suggest that methylation performs better on large complexes, which might be expected to have intrinsically large NLO properties. It is also useful to assess the consequences of seeking to model dppe with a smaller (and potentially more symmetric) dppm-like ligand. Comparison of complexes 6 and 7 in Table 1 suggest that such substitution is likely to have little effect on λmax but may influence the measured hyperpolarizability. We have addressed this question in Table 4, which explores the 2439


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Table 8. Computed βtot Values for Selected Complexes (6, 8, 10, and 11), at the BP/TZP and SAOP/TZP Levels of Theory, as a Function of Molecular Geometry BP/TZP structure trans-[Ru(CCPh)Cl(dppm)2] (6) trans-[Ru(CCC6H4-4-NO2)Cl(dppm)2] (8)

trans-[Ru(CCC6H4-4-CCC6H4-4-NO2)Cl(dppm)2] (10)

trans-[Ru(CCC6H4-(4-CCC6H4)2-4-NO2)Cl(dppm)2] (11)

a

SAOP/TZP

conformationa

Erelb

μc

ΔEH‑Ld

βtote

ΔEH‑Ld

βtote

A O Aa Ao Oo Oa AAa AAo AOo AOa OOo OOa OAa OAo AAAa AAAo AAOo AAOa AOAa AOAo AOOa AOOo OOOo OOOa OAOo OAOa OAAa OAAo OOAa OOAo

0.00 10.40 0.00 40.09 20.75 53.58 0.00 28.61 19.82 37.51 14.52 49.35 27.46 58.99 0.00 18.62 9.12 27.93 20.56 35.25 29.88 0.58 9.75 39.52 27.46 53.01 17.00 48.59 16.51 47.17

1.34 2.06 10.20 6.65 10.67 7.35 14.59 9.93 11.13 8.46 14.59 10.39 10.94 9.22 16.96 11.87 13.37 10.76 11.16 8.81 9.19 11.80 16.29 12.27 11.28 9.51 12.47 9.82 13.13 11.30

2.02 2.12 1.58 1.13 1.48 1.16 1.03 0.85 0.62 0.71 1.03 0.92 0.67 0.79 0.71 0.72 0.49 0.64 0.37 0.55 0.57 0.42 0.75 0.80 0.46 0.64 0.50 0.50 0.57 0.74

26.42 21.86 167.79 39.05 159.25 45.47 1954.67 583.94 360.08 425.03 1760.18 493.59 559.67 256.59 9656.21 2672.30 1396.72 1457.15 4159.13 234.71 320.21 995.62 8376.18 2136.30 1079.96 209.34 1692.35 290.34 1137.41 1076.12

2.21 2.34 1.49 0.90 1.42 0.95 0.95 0.62 0.51 0.51 0.99 0.73 0.60 0.61 0.65 0.49 0.38 0.42 0.28 0.36 0.38 0.36 0.73 0.61 0.41 0.48 0.48 0.66 0.49 0.55

19.99 17.05 156.17 50.39 155.66 75.22 1922.73 533.73 444.95 1381.23 1831.76 468.47 770.89 670.30 11536.31 2335.75 1244.53 3064.85 11164.66 220.43 313.07 1179.85 9692.27 1950.09 2639.99 207.35 1923.12 306.46 1058.59 1647.71

Conformational nomenclature adopted is as described for Figure 2. bIn kJ mol−1. cIn D. dIn eV. eIn units of 10−30 esu.

Table 9. Effect of Range Separation on Calculated β Values for the Compounds trans-[Ru((CC6H4)n-4-X)Cl(dppm)2] calcd structure

formula

exptla,b

BP86b

LC-BP86b,c

B3LYPb

CAM-B3LYPb,c

6 8 10 11

trans-[RuCCPh)Cl(dppm)2] trans-[Ru(CCC6H4-4-NO2)Cl(dppm)2] trans-[Ru(CCC6H4-4-CC6H4-4-NO2)Cl(dppm)2] trans-[Ru(CCC6H4-(4-CC6H4)2-4-NO2)Cl(dppm)2]

12 (0.09) 129 161 (1.25) 365 (2.83)

21.7 (0.15) 147.0 1771 (12.05) 8659 (58.92)

10.9 (0.18) 60.2 203.0 (3.37) 285.0 (4.73)

18.2 (0.14) 130.9 1039 (7.93) 2552 (19.49)

13.9 (0.16) 86.9 382.8 (4.40) 602.1 (6.93)

a Determined via HRS. See Table 1 for primary reference. bβ0(exptl) or βtot(calcd) is given in units of 10−30 esu. The ratio β(for the indicated compound):β(structure 8), obtained using the method specified, is shown in parentheses. cLC-BP86 is a range-separated analogue of the BP86 functional. CAM-B3LYP is a range-separated analogue of B3LYP.

influence on calculated β values of phosphine ligand substitution in a set of trans-[Ru(CCPh)(4-CCC6H4C CPh)L2] complexes. The complex trans-[Ru(CCPh)(4-C CC6H4CCPh)(dppe)2] has been measured experimentally with a reported |β| value of 34 × 10−30 esu.75 On the basis of our calculations in Table 4, it would seem that replacement of larger, bulky, and possibly less symmetric ligands (e.g., dppe) by smaller ligands (e.g., Me2PCH2PMe2) should have minor impact on the accuracy of the results, for the benefit of a saving in computational effort. An additional virtue of Me2PCH2PMe2 as a model ligand is that it delivers values between the Cs and C2 symmetry values for the widely used dppe ligand, in very close agreement with the dppm values.

Solvent Effects. According to previous studies, solvation has a substantial influence on the excitation spectral properties of a compound, although there is generally little difference found between geometries optimized in vacuo or in the presence of a solvent field (indeed, the results from solvatochromic studies of linear optical absorption properties in solvents of varying polarity and dielectric constant, in combination with measurements of the ground-state dipole moment, and an assumption of the applicability of the two-level model can be used to estimate the first hyperpolarizability; see ref 76). Several studies, both experimental and theoretical, have explored the spectral and NLO properties of p-nitroaniline (PNA),77−80 which would appear to be the only medium-sized compound for which a reliable gas-phase value of β has been determined 2440


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Figure 4. UV/vis spectra for 1 and 8 with the BP, SAOP, and GRACLB density functionals and with various basis sets, modeled via Gaussian broadening with a 2300 cm−1 fwhm.

phase to a solvent such as water), and absolute values also agree well. We have also applied solvent corrections to our calculations of β values for complexes 1−11, as shown in Table 6. As with PNA, incorporation of solvent effects (modeling the solvent THF) for these compounds is seen to increase βtot in a fairly consistent manner, and as for the gas-phase values, the solventcorrected values are not strongly dependent on the choice of functional used (BP/SAOP/GRACLB). The broadly consistent influence of solvent effects suggests that, while the treatment of such effects is expected to be important in principle for calculation of the NLO properties of solvated substances, in

experimentally, thus permitting direct comparison with the absolute β values calculated in vacuo. Additionally, PNA forms a convenient (if simplified) prototype for our NLO response calculations, featuring donor/acceptor moieties connected by a π-conjugated bridge. In Table 5, we have compared our calculated results of β, for PNA in different solvents, with the set of experimental values recommended by Reis.81 Comparison with experiment is possible only for the gas phase and for chloroform, acetone, and methanol. Nonetheless, both laboratory and computational results show a consistent increase in βtot with increasing solvent polarity (by approximately a factor of 6 in going from the gas 2441


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Figure 5. UV/vis spectra for 1, 6, 10, and 11 at the SAOP/TZP level of theory, using various P-substituted ligands, and modeled via Gaussian broadening with a 2300 cm−1 fwhm.

phenyl moiety. Independent rotation of the nitro group is also feasible, but numerous calculations suggest this is a more energetically demanding rotational mode and thus considered less likely to be important from the point of view of surveying the accessible conformational space. The results of our calculations on DANA and DANS (see Table 7) suggest, not surprisingly, that rotation of an aromatic subunit (nitrophenyl or nitrostilbenyl) has a significant effect on the calculated β0tot and β0vec values. It is more surprising to note that methyl group rotation, which should have negligible effect on the molecule’s π conjugation, the dipole moment, or any other parameter expected to be significant to the hyperpolarizability, does have a marked influence on β. The influence of conformation on β is also readily apparent in our calculations for complexes 6, 8, 10, and 11, reported in Table 8. These complexes were chosen because they have the same Cl−Ru(dppm)2−C2−metal−ligand core. Thus, any NLO differences are due to either the length of the chain or the interaction of adjacent Ph groups. The BP/TZP results show that βtot is generally largest for geometries which offer the greatest opportunity for π delocalization along the principal molecular axis; such conformations often also feature a comparatively small HOMO/LUMO gap and a comparatively large dipole moment, other factors that favor a substantial hyperpolarizability value. These findings are generally well matched by the SAOP/TZP calculations for the same conformations, except that for some of the conformations in Table 8, the disparity between BP and SAOP determinations of

practice there may be little impact on the trends in hyperpolarizability of a series of related compounds. Stereochemistry. For complexes featuring oligo(phenyleneethynylene) linkages, there is clearly scope for nearly free intramolecular rotation about the molecular axis. Since such rotation may influence both the spatial relationship between donor−acceptor groups and the π-conjugation pathways for electron transfer between these groups, the influence of different orientations on NLO properties such as hyperpolarizability cannot be discounted. This is true even for complexes for which techniques such as X-ray crystallography (XRD) reveal the existence of one preferred conformer in the crystalline state, since in solution a different conformer may be preferred, or low rotational barriers may “smear out” the structure over a wide range of energetically accessible conformations. The influence of conformation upon hyperpolarizability can be assessed by sampling a few different conformers of a given compound. We have explored this issue for the model πconjugated compounds 4-dimethylamino-4′-nitroazobenzene (DANA) and 4-dimethylamino-4′-nitrostilbene (DANS) (see Figure 3), for which the hyperpolarizabilities have been determined experimentally, using both HRS and EFISH, by Flipse et al.82 For molecules of this type, the hyperpolarizability component along the main molecular axis considerably exceeds all the others and thus the orientation of groups along the main axis has a significant impact on β. Our assessment includes rotation of dimethylamino methyl groups and of the nitro2442


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Figure 6. Some possible orientations of 8 and 10 resulting from phenylenethynylene rotation. The notation used for axial group conformation is as delineated for Figure 2

βtot approaches a factor of 3. Such mismatches occur when the SAOP/TZP determination of the HOMO/LUMO gap is significantly narrower than the corresponding BP/TZP value (such as, for example, in the case of the AOa conformation of 10). While there is no definitive method of determining which level of theory is more reliable in this instance, we are inclined to give greater credence to the BP/TZP results, since in other respects (as discussed in the preceding sections) this functional gives results which concur well with those from various other functionals, while SAOP results are often outliers. Regardless, the results in Table 8 illustrate the importance of considering conformational effects, since for larger complexes different conformations can have βtot values that differ by more than one order of magnitude. Range Separation. Several studies have recently addressed the use of range-separated density functionals in calculation of nonlinear optical properties. It has been found that “conventional” DFT methods (those lacking treatment of range separation) often overestimate the hyperpolarizabilities of πconjugated systems and that incorporation of range separation often mitigates this tendency to overestimation.83−86 Such range-separated calculations that have been reported to date have focused largely on the NLO properties of organic molecules, with little coverage yet devoted to organometallic systems.

In Table 9, we report the results of range-separated DFT calculations (at the LC-BP86 and CAM-B3LYP levels of theory) for the homologous sequence of complexes 8, 10, and 11 and for the related structure 6, all of which contain the Cl− Ru(dppm)2−C2− core. It can be seen that all methods deliver broadly comparable βtot values (in fair agreement with the experimental β0 values) for complexes 6 and 8 but overestimate the ratios βtot(10):βtot(8) and βtot(11):βtot(8). Nonetheless, the overestimation of βtot(11):βtot(8) in particular is very much less pronounced for the range-separated methods than for the methods lacking range separation. A complicating factor (which we have not yet had the opportunity to explore for the rangeseparated approaches) is that of axial conformation: the values reported in Table 9 are those for the coplanar conformations of each species. As we have shown above, the conformation can significantly influence the β value obtained, and in the absence of a detailed evaluation of the performance of range-separated functionals for a variety of oligo(phenyleneethynylene) conformations, we would recommend caution in the use of range separation for organometallic complexes of the kind investigated here. In this context also, it is worth noting that our previously reported DFT calculations on a set of broadly analogous Os-containing oligo(phenyleneethynylene) complexes87 have found that the laboratory UV/vis spectra for such compounds are significantly better matched by computed spectra of conformers lacking multiple phenyl-ring coplanarity, 2443


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Figure 7. UV/vis spectra obtained for different configurations of 8 and 10. The notation used for axial group conformation is as delineated for Figure 2

characterization of LO properties, specifically the computation of UV/vis spectra, to ascertain the influences on computation of the main electron transitions at energies less than approximately 40000 cm−1. Choice of Density Functional and Basis Set. In Figure 4, we show computed UV/vis spectra for complexes 1 and 8, obtained using the BP, SAOP, and GRACLB functionals with a variety of basis sets (DZ, DZP, TZP, TZ2P, and QZ4P for structure 1; DZ, DZP, and TZP for the larger structure 8). It is apparent from Figure 4 that the choice of density functional has little influence on the computed peak positions and intensities for either structure. For complex 1 the spectra appear similarly insensitive to choice of basis set, while for structure 8, there is good agreement between the DZP and TZP results, although the spectra obtained using the smallest basis set (DZ) display some variance (in both peak position and calculated intensity) from the results obtained with DZP and TZP, in particular above 30000 cm−1. We conclude that, while TZP is a “safe” choice of basis set in that the computed spectra are very similar to those obtained using larger basis sets, the choice of a smaller basis set (by preference DZP over DZ) should also give very similar results, a consideration that may be useful in pursuing spectra for large, computationally demanding organometallic species. Ligand Simplification. To assess the implications of substituting simpler, more symmetric ligands for dppm and dppe, we have calculated UV/vis spectra for compounds 1, 6, 10, and 11 with H- and CH3-substituted dppm or dppe. The spectra obtained are shown in Figure 5. An obvious difference among the spectra, and a consequence of ligand substitution, is

and such considerations may well impinge upon the nonlinear optical properties of these complexes. Notwithstanding the above cautionary statements, we would contend that the application of range-separated methods to the calculation of organometallic β values shows considerable promise, once a thorough exploration of these methods’ performance has been undertaken. Linear Optical (LO) Properties. While our primary focus here is on the performance of DFT in determining NLO properties, the computational characterization of LO propertiesviz., peak positions and calculated intensities in UV/vis spectra, dipole moment, and static polarizabilityis also of relevance because useful NLO materials are those possessing a wide transparency window in addition to efficient electron delocalization. The two-level model, widely used to rationalize NLO properties, can be expressed as β∝

Δμge fge 2 Ege 2

(5)

where fge, Ege, and Δμge are the oscillator strength, the transition energy, and the difference in dipole moment between the ground state and the excited state, respectively. The two-level model assumes that the dominant contribution to β arises from one intense, low-energy electronic absorption peak. As has been shown above, the trends in β values for our series of complexes vary depending on the functional and basis set used and as a function of solvent field inclusion, stereochemistry, and ligand treatment. In this section, we adopt a similar approach to the 2444


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(2) The size of ligands can have a substantial impact on computational expense. Where such ligands are not directly associated with the complex’s identified donor or acceptor groups, it is desirable to use simpler homologues. In the present work, substitution of dppm and dppe by their hydrogenated and methylated homologues was found to have a generally modest effect on computed β values. Among the larger complexes surveyed here, replacement of dppe and dppm by Me2PCH2CH2PMe2 or Me2PCH2PMe2 appeared to give better agreement than did the use of the yet simpler hydrogenated homologues. Use of Me2PCH2PMe2, in particular, in place of dppe or dppm, would appear to offer optimal efficiency of calculation for an acceptable return on accuracy. (3) While solvation has an undeniable effect on the absolute β values calculated, it has much less impact on the trend in calculated values for a set of related structures. Thus, in instances where comparison between related structures is the principal intent, there is little value in pursuing solvent corrections. (4) Different conformations of a given complex can exhibit dramatic differences between calculated β values, due to factors such as interruption of the π-conjugation pathways and modification of the structure’s instantaneous dipole moment. Neither XRD nor geometry optimization may provide an entirely reliable description of the complex’s conformational space under laboratory conditions (e.g., in solution), and this may be one of the principal causes for the generally poor quantitative agreement between computed and laboratory values of β, although there are some indications that the use of range-separated functionals may yield estimates of hyperpolarizability more reliable than methods that lack range separation. Regardless of the methodology employed, efforts to survey a range of conformers for any given structure are more likely to produce calculated β values which encompass the experimental measurement. (5) Limitations in experimental procedures and techniques also have an effect on β measurements. In HRS, measured β values at the incident laser wavelength are often considerably resonance-enhanced, a phenomenon with the potential to introduce uncertainty and error into laboratory values. Techniques such as EFISH have other limitations. For these reasons, considerable caution must be taken in assessing and comparing laboratory β values, especially values obtained using different techniques. (6) Notwithstanding points 4 and 5 above, calculation on only one (consistently adopted) conformer for a series of related compounds is likely to give a broadly reliable trend in computed β values. Thus, DFT is assessed to be a useful tool in guiding laboratory studies toward structures of particular promise for NLO purposes. (7) Since the simplest models of NLO properties make use of parameters that can be derived through calculations on optical spectroscopic properties, calculations of the UV/vis spectra can also shed light on the NLO behavior of a given complex. Many of the conclusions reached in points 1−6 above can analogously be applied also to the computation of optical spectroscopic properties (though we have not pursued UV/vis spectral calculations incorporating solvent-field corrections as a component of the present work).

that the H-substituted and CH3-substituted models do not display the broad and reasonably intense spectral features, typically centered at around 35000 cm−1 in the computed spectra, which characterize the dppm- and dppe-containing complexes. However, at lower frequencies (i.e., in the spectral region expected to be most useful for the prediction of NLO properties), agreement of calculated peak positions and intensities is extremely good for 1, 10, and 11 and fair for 6 (for which it would appear that the peak position is more strongly influenced by ligand simplification than is the calculated intensity). When they are assessed against the experimental λmax values (see Table 1), computed peak positions for 1, 6, and 11 all have their most intense feature red-shifted by ∼40006000 cm−1 from the experimental value; there is also a peak within this range for 10, although it is not the most intense spectral feature. The generally close correspondence between spectra obtained for ligand-simplified models and “full” structures suggests that such simplified models can usefully be pursued to obtain a theoretical appraisal of the spectroscopic properties of larger organometallic complexes. Furthermore, other things being equal, it would appear sensible to adopt the same ligand simplification strategy for optical spectra as for hyperpolarizability calculation, suggesting that Me2PCH2PMe2 would be the preferred simplified ligand of choice. Stereochemistry. We have explored the influence of changes in intramolecular orientation (see Figure 6) on the calculated spectra (see Figure 7) for compounds 8 and 10. These calculations show that the influence of conformation on the calculated spectra is considerable, with conformers which may differ only slightly in relative energy. The substantial influence of conformation on spectroscopic properties is problematic, in the sense that it appears to require computational characterization of several different conformers (including conformers which may be of low or no symmetry) in order to properly assess the spectroscopy of a large organometallic complex which may or may not have been studied experimentally. We would suggest, by analogy with our recommendations on NLO property calculations, that the consistent use of only one conformer across calculations on a series of related compounds is likely to reveal reliable spectroscopic trends, even if absolute agreement with experimental measurements is only fair. On the basis of the present results, it appears that an “orthogonal” conformation of phenyleneethynylene moieties generally gives better agreement with the observed optical spectra than does an “coplanar” conformation. Nonetheless, the issue of molecular conformation, and its treatment in calculations on optical and NLO properties, is one which we are currently pursuing further.

■

CONCLUSIONS Calculations of NLO properties of organometallic compounds via quantum chemical methods are not yet routine, and there are several important considerations for such calculations. Our results here can be summarized as follows: (1) A comparison of basis set and density functional options leads us to deduce that the BP/TZP level of theory is a reasonable compromise between computational expense and efficiency of calculation, for organometallic complexes of experimental interest or for structures large enough to be useful as models of such complexes. Use of larger basis sets and of other density functionals such as SAOP, GRACLB, and BLYP typically has only a minor effect on the β values calculated. 2445


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(24) Curreli, S.; Deplano, P.; Faulmann, C.; Lenco, A.; Mealli, C.; Mercuri, M. L.; Pilia, L.; Pintus, G.; Serpe, A.; Trogu, E. F. Inorg. Chem. 2004, 43, 5069. (25) Powell, C. E.; Cifuentes, M. P.; McDonagh, A. M.; Hurst, S. K.; Lucas, N. T.; Delfs, C. D.; Stranger, R.; Humphrey, M. G.; Houbrechts, S.; Asselberghs, I.; Persoons, A.; Hockless, D. C. R. Inorg. Chim. Acta 2003, 352, 9. (26) Jacquemin, D.; Perpete, E. A.; Ciofini, I.; Adamo, C. Chem. Phys. Lett. 2005, 405, 376. (27) Lin, J.; Wu, K.; Zhang, M. J. Comput. Chem. 2008, 30, 2056. (28) van Gisbergen, S. J. A.; Schipper, P. R. T.; Gritsenko, O. V.; Baerends, E. J.; Snijders, J. G.; Champagne, B.; Kirtman, B. Phys. Rev. Lett. 1999, 83, 694. (29) Jacquemin, D.; Andre, J. M.; Perpete, E. A. J. Chem. Phys. 2004, 121, 4389. (30) Champagne, B.; Perpete, E. A.; Jacquemin, D.; van Gisbergen, S. J. A.; Baerends, E. J.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. J. Phys. Chem. A 2000, 104, 4755. (31) Bruschi, M.; Fantucci, P.; Pizzotti, M. J. Phys. Chem. A 2005, 109, 9637. (32) (a) Cammi, R.; Tomasi, J. J. Comput. Chem. 1995, 16, 1449. (b) Cossi, M.; Barone, V.; Cammi, R.; Tomasi, J. Chem. Phys. Lett. 1996, 255, 327. (33) (a) Cramer, C. J.; Truhlar, D. G. Science 1992, 256, 213. (b) Cramer, C. J.; Truhlar, D. G. J. Comput. Chem. 1992, 13, 1089. (34) (a) Klamt, A.; Schuurmann, G. J. Chem. Soc., Perkin Trans. 2 1993, 799. (b) Andzelm, J.; Kolmel, C.; Klamt, A. J. Chem. Phys. 1995, 103, 9312. (35) Ray, P. C. Chem. Phys. Lett. 2004, 395, 269. (36) Ray, P. C.; Leszczynski, J. Chem. Phys. Lett. 2004, 399, 162. (37) Inerbaev, T. M.; Belosludov, R. V.; Mizuseki, H.; Takahashi, M.; Kawazoe, Y. J. Chem. Theory Comput. 2006, 2, 1325. (38) Calaminici, P.; Koster, A. M.; Jug, K.; Gray, D.; Blau, W. J. Mol. Struct. (THEOCHEM) 2006, 762, 87. (39) Li, Q.; Wu, K.; Sa, R.; Wei, Y. Chem. Phys. Lett. 2009, 471, 229. (40) Sainudeen, Z.; Ray, P. C. J. Phys. Chem. A 2005, 110, 9095. (41) te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A; Guerra, C. F.; Baerends, E. J.; Snijders, T.; Ziegler, J. G. J. Comput. Chem. 2001, 22, 931. (42) ADF2010.01; SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands; http://www.scm.com. (43) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (44) Becke, A. D. Phys. Rev. A 1998, 38, 3098. (45) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (46) (a) Klamt, A. J. Phys. Chem. 1995, 99, 2224. (b) Klamt, A.; Jones, V. J. Chem. Phys. 1996, 105, 9972. (47) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision D.01; Gaussian, Inc., Wallingford, CT, 2009. (48) Andrae, D.; Haeussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chem. Acc. 1980, 77, 123. (49) (a) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639. (b) Raghavachari, K.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (50) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.

ASSOCIATED CONTENT

S Supporting Information *

Text, figures, tables, and a .xyz file giving key computed molecule Cartesian coordinates for convenient visualization. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail for R.S.: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Australian Research Council (ARC) for financial support. M.G.H. thanks the ARC for an Australian Professorial Fellowship.

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REFERENCES

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