Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 1

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1 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 1 Journal of Computational Methods in Sciences and Engineering 5 (2005) IOS Press Molecular geometry, charge distribution and polarization in platinum nitrides. An ab initio and density functional theory study of PtNN, PtPtNN, NPtPtN, and NNPtNN Demetrios Xenides a and George Maroulis b, a Department of Theoretical Chemistry, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 52a, A6020 Innsbruck, Austria b Department of Computer Science and Technology, University of Peloponnese, GR Tripolis, Greece Abstract. We have calculated molecular geometries, atomic charges, dipole moments and polarizabilities for the linear platinum nitrides PtNN, PtPtNN, PtNNPt and NNPtNN. The calculation of the electric properties relies on finite-field Møller-Plesset perturbation theory and Coupled Cluster techniques. Our best values for the polar PtNN and PtPtNN molecules are calculated at the CCSD(T) level of theory and are µ/ea 0 = (PtNN) and (PtPtNN), α/e 2 a 2 0E 1 h = (PtNN) and (PtPtNN), α/e 2 a 2 0E 1 h = (PtNN) and (PtPtNN). For PtNNPt and NNPtNN we obtain α/e2 a 2 0E 1 h = (PtNN) and (PtPtNN), α/e 2 a 2 0E 1 h = (PtNN) and (PtPtNN). Compared to the best values, the performance of the DFT methods is rather erratic. 1. Introduction and theory Platinum compounds, such as Pt(N 2 ) n, have attracted early experimental attention [1,2]. More recently, model experimental work by Andrews and coworkers have brought forth an amazing wealth of new findings on platinum hydrides [3] and nitrides [4]. Although interesting theoretical studies on small platinum compounds are available, see for instance the work of Basch [5] and Cui et al. [6], we are aware of only one paper on the electric polarizability [7]. Nevertheless, experimental measurements of the hyperpolarizability of platinum polyynes are already known [8]. More recently, the possible use of platinum complexes as nonlinear optical (NLO) materials has been the object of high-level experimental investigations [9,10]. The purpose of this paper is to report a systematic study of the linear platinum nitrides PtNN, PtPtNN, NPtPtN, and NNPtNN. Our study relies on conventional ab initio and density functional theory (DFT) calculations to provide reliable theoretical data on the charge distribution and dipole polarizability. Previous experience on DFT calculations of electric properties shows that one should avoid generalizations on the predictive capability of these methods [13 17]. Our aim is to enrich current knowledge by providing new findings on the performance of DFT methods on the prediction of Corresponding author. maroulis@upatras.gr /05/$ IOS Press and the authors. All rights reserved

2 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 2 2 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides Fig. 1. NBO charges (above) and molecular geometries (below) of PtNN, PtPtNN, PtNNPt and NNPtNN at the MP2 level of theory with basis sets S0, S1 and S2 (reference bond lengths in bold, see text). molecular properties for platinum nitrides. The energy of neutral molecule interacting with a weak static, general electric field can be written in terms of the components of the field F α,f αβ,f αβγ,f αβγδ,..., as [18,19] E p E p (F α,f αβ,f αβγ,f αβγδ,...) = E 0 µ α F α (1/3)Θ αβ F αβ (1/15)Ω αβγ F αβγ (1/105)Φ αβγδ F αβγδ +... (1/2)α αβ F α F β (1/3)A α,βγ F α F βγ (1/6)C αβ,γδ F αβ F γδ (1) (1/15)E α,βγδ F α F βγδ +... (1/6)β αβγ F α F β F γ (1/6)B αβ,γδ F α F β F γδ +... (1/24)γ αβγδ F α F β F γ F δ +... E 0, µ α, Θ αβ, Ω αβγ and Φ αβγδ are the energy and the dipole, quadrupole, octopole and hexadecapole moment of the free molecule. The second, third and fourth-order properties (in bold) are the dipole and quadrupole polarizabilities and hyperpolarizabilities α αβ, β αβγ, γ αβγδ,a α,βγ,c αβ,γδ,e α,βγδ and

3 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 3 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides 3 Fig. 2. HOMO and LUMO of linear platinum nitrides at the MP2/S0 level of theory. B αβ,γδ. The subscripts denote Cartesian components. A repeated subscript implies summation over x, y and z. The number of independent components needed to specify the respective tensors is regulated by symmetry [11]. The properties of interest in this work are the dipole moment and static dipole polarizability. The dipole moment vanishes for the centrosymmetric NPtPtN and NNPtNN. For PtNN and PtPtNN µ α has only one independent component. With z as the reference molecular axis we specify µ α and α αβ by their components µ z µ, and α xx, α zz, respectively. In addition to the Cartesian components of the polarizability we also calculate the mean and the anisotropy, defined as [18] α =(α zz +2α xx )/3 α = α zz α xx (2) The use of a homogeneous electric field in reduces considerably the expansion of Eq. (1). E p = E 0 µ α F α (1/2)α αβ F α F β (1/6)β αβγ F α F β F γ (1/24)γ αβγδ F α F β F γ F δ +... (3) Equation (3) reduces to a even simpler form for centrosymmetric molecules, as µ α = β αβγ =0, E p = E 0 (1/2)α αβ F α F β (1/24)γ αβγδ F α F β F γ F δ +... (4) We have obtained the properties of interest in this work from Eqs (3) and (4), relying on a computational approach based on the finite-field method [20] and presented in sufficient detail elsewhere [21 23]. The computational tools employed in this work are widely used electronic structure methods. Their potential and basic characteristics may be found in standard textbooks [24 26]. Their use follows the available implementation in GAUSSIAN 03 [27]. The conventional ab initio methods are Møller-Plesset perturbation theory (MP) and the Coupled Cluster (CC) approach. The MP methods are: second-order MP (MP2), partial fourth-order MP with single, double and quadruple excitations from the reference

4 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 4 4 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides Table 1 Dipole moment and dipole polarizability values of PtNN molecule obtained with the [Pt/N] [5s4p4d/4s4p2d] basis set (reference results in bold) Method µ z α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE Table 2 Dipole moment and dipole polarizability values of PtPtNN molecule obtained with the [Pt/N] [5s4p4d/4s4p2d] basis set Method µ z α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE determinant (SDQ-MP4) and fourth-order MP (MP4). The CC methods are: CCSD (singles and doubles CC) and CCSD(T) (CCSD with an estimate of connected triple excitations by a perturbational treatment). The DFT based methods are B3LYP, B3P86, B3PW91, mpw1pw91, O3LYP and PBEPBE. A description of their composition has been given elsewhere [17]. 2. Computational strategy The choice of suitable basis sets is of central importance to theoretical calculations of molecular properties [28,29]. Experience shows that the design of such basis sets is no trivial matter [30 34]. The difficulty increases considerably in calculations of electric properties of compounds containing metals [35 37]. In this work, leaning heavily on previous experience [36,37], we chose the Stevens/Basch/Krauss (SBK) effective core potential triple-split basis set CEP-121G [38 40]. After considerable experimentation, we designed three basis sets for molecular geometry calculations and two more flexible ones for electric polarizability calculations. For the molecular geometry calculations we use the basis sets S0, S1 and S2 defined as follows (GTF

5 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 5 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides 5 Table 3 Dipole polarizability values of PtNNPt molecule obtained with the [Pt/N] [5s4p4d/4s4p2d] basis set Method α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE exponents in parentheses): S0 CEP-121G S1 = S0 + Pt:sp( ) + d( ) S2 = S1 + N: d(0.9424). Table 4 Dipole polarizability values of NNPtNN molecule obtained with the [Pt/N] [5s4p4d/4s4p2d] basis set Method α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE The exponents of the GTF added on Pt were chosen as the geometric mean of the two most diffuse in CEP-121G. The exponent on N was chosen to minimize the energy of the dinitrogen molecule. For the electric polarizability calculations we use the basis sets P1 and P2, defined as follows: P1 = CEP-121G + Pt: sp( ) + d( ) + N: sp( ) + d(0.9471, ) P2 = P1 + Pt: f(0.2527, , )

6 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 6 6 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides Table 5 Dipole moment and dipole polarizability values of PtNN molecule obtained with the [Pt/N] [6s5p5d3f/5s5p4d] basis set Method µ z α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE Table 6 Dipole moment and dipole polarizability values of PtPtNN molecule obtained with the [Pt/N] [6s5p5d3f/5s5p4d] basis set Method µ z α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE The exponents of the d-gtf on N were optimized on the dinitrogen molecule after the addition of a diffuse sp-gtf. The tight one was chosen to minimize the energy and the diffuse one to maximize the mean polarizability. The size of the two basis sets for all four molecules has as follows: 92 (PtNN), 132 (PtPtNN or PtNNPt) and 142 (NNPtNN) for P1 and 113 (PtNN), 174 (PtPtNN or PtNNPt) and 163 (NNPtNN) for P2. 5D and 7F basis sets were used in all cases. The GAUSSIAN 03 program was used in all calculations [27]. Unless otherwise noted, atomic units are used throughout this paper. SI conversion factors are: Energy, 1 E h = J, length, 1 a 0 = m, dipole moment µ, 1 ea 0 = Cm and dipole polarizability, α αβ,1e 2 a 2 0 E 1 h = C 2 m 2 J 1. Hereafter, property values are given as pure numbers, that is µ/ea 0 and α αβ /e 2 a 2 0 E 1 h. 3. Results and discussion Molecular geometry and charge distribution. We have calculated molecular geometries for the four linear platinum nitrides at the MP2 level of theory with basis sets S0, S1 and S2. We have also obtained

7 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 7 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides 7 Table 7 Dipole polarizability values of PtNNPt molecule obtained with the [Pt/N] [6s5p5d3f/5s5p4d] basis set Method α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE Table 8 Dipole polarizability values of NNPtNN molecule obtained with the [Pt/N] [6s5p5d3f/5s5p4d] basis set Method α xx α zz α α SCF MP SDQMP MP CCSD CCSD(T) B3LYP B3P B3PW mpw1pw O3LYP PBEPBE atomic charges from a full Natural Bond Orbital (NBO) analysis [41]. Our findings are given in Fig. 1. In Fig. 2 we show HOMO and LUMO for all four molecules obtained at the MP2/S0 level. Our best values for the geometrical parameters are the MP2/S2 ones (in bold). All subsequent calculations with basis sets P1 and P2 have been performed at the MP2/S2 geometry. Let us compare our best findings with the early SCF calculations of Basch [5] and the more recent BPW91 results reported by Citra et al. [4]. For PtNN Basch found R Pt N = and R N N = 1.120Å, in reasonable agreement with our and The respective values reported by Citra et al. [4] are and Overall, our values are in fair agreement with reported by Citra et al. [4], with the notable exception of the Pt-Pt bond length in PtPtNN. Polarizability calculations. Our values for the electric properties are shown in Tables 1 8. PtNN. Our SCF values for this molecule are µ = , α = and α = (basis P1) and µ = , α = and α = (basis P2). It is obvious that the extension of the basis set has a non-negligible effect on the electric properties. Electron correlation has a strong effect on all properties. Our best values are obtained at the CCSD(T)/P2 level and are µ = , α = and α = The increase in magnitude, in comparison to the SCF values is 11.2, 14.7 and 3.7 %, respectively. The DFT based methods predict systematically a larger dipole moment for basis P2 while the mean and the anisotropy are within a few percent from the reference CCSD(T)/P2.

8 Galley Proof 15/09/2006; 11:07 File: jcm108.tex; BOKCTP/wyy p. 8 8 D. Xenides and G. Maroulis / Molecular geometry, charge distribution and polarization in platinum nitrides PtPtNN. The SCF values for this tetraatomic are µ = , α = and α = (basis P1) and µ = , α = and α =98.37 (basis P2). Thus, we observe a persistence of the divergence between P1 and P2. Turning our attention to electron correlation effects we notice that the CCSD(T)/P2 values are µ = , α = and α = The effect is dramatic on the dipole moment. The post-hartree-fock values for the polarizability show a notable discrepancy between MP and CC methods for the longitudinal component. The non-uniform effect on the Cartesian components entails an increase for the mean but a drastic reduction for the anisotropy. What is more, we observe that the DFT methods diverge clearly from the ab initio ones for both the mean and the anisotropy. PtNNPt. For this molecule we report SCF values α = and α = (basis P1) and α = and α = (basis P2). The difference between P1 and P2 persists. The post-hartree-fock values calculated with basis P2 show a strong increase for both Cartesian components of the polarizability. It is instructing to notice again the absence of convergence pattern in the MP methods. Overall, both the mean and the anisotropy increase considerably. The DFT methods show a somehow systematic behaviour as, with notable exception of the PBEPBE, they predict a relatively low mean, α. For α all methods predict a reasonable value, again with the notable exception of the PBEPBE. NNPtNN. The SCF values α = and α = (basis P1) and α = and α = (basis P2). A difference of a few percent is still very much present. For the P2 basis set electron correlation has a small effect of the transversal but a strong one on the longitudinal one. The CCSD(T)/P2 values are α = and α = 76.75, or 11.6 and 34.0% above the respective SCF values. Compared to the reference CCSD(T)/P2 results, the DFT methods predict a very reasonable mean but a larger anisotropy. 4. Conclusions We have reported a systematic study of the molecular geometry, charge distribution, dipole moment and polarizability for the linear platinum nitrides PtNN, PtPtNN, PtNNPt and NNPtNN. Several elements of this investigation are worth reporting. These are the basis set dependence of the calculated values at the SCF and post-hartree-fock levels of theory, the unsatisfactory convergence of the MP series and the absence of clear pattern in the behaviour of DFT methods. The electric properties reported in this work are the first to appear in the literature. It should be noted that this is a non-relativistic study as the inclusion of relativistic effects was beyond the scope of this investigation. Acknowledgement Demetrios Xenides is happy to acknowledge his indebtedness to Dr. Michael Fink, system administrator of the Zentral Informatik Dienst (ZID) of the University of Innsbruck, for specific computer resources allocation. References [1] D.W. Green, J. Thomas and D.M. Gruen, J. Chem. Phys. 58(5453) (1973). [2] W. Klotzbuecher and G.A. Ozin, J. Am. Chem. Soc. 97(2672) (1975). [3] L. Andrews, X. Wang and L. Manceron, J. Chem. Phys. 114(1559) (2001). [4] A. Citra, X. Wang, W.D. Bare and L. Andrews, J. Phys. Chem. A 105(7799) (2001). [5] H. Basch, Chem. Phys. Lett. 116(58) (1985).

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