Conseguences of soil crude oil pollution on some wood properties of olive trees Physics | 25 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 Theoretical Spectroscopic Study for Some Diatomic Molecules Adil Neama Ayyash Dept. of Physics/College of Science /University of Anbar Received in :2/April/2017,Accepted in:4/June/2017 Abstract In this work, four electronic states ( , , and ) of some diatomic molecules (InF and InCl) was studied by TD-DFT with energy represented by the exchange- correlation energy. The SAOP/ATZP model was applied here to determine all parameters (re, Be, De, , , Te , and were determined to creation reliable values for electron spectroscopy. Also, another set of this calculation has been used represented by two theoretical models: ATZP and et-QZ3P-xD model. Therefore these theoretical models for ( and , and ) of the molecules have been compared with many values, theoretical and experimental values, and appear convergence in values with simple error %. Our results showed that the TD-DFT with basis set in the present work is important for the estimation of spectroscopic parameters and constants for our molecules and the ATZP model is very close to et-QZ3P-xD model in all electronic states for InF and InCl molecules except some of the constants such as (Be). Keywords: spectroscopic parameters, diatomic molecules, DFT. Physics | 26 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 Introduction Indium halides are an important system to work with spectroscopic investigations and scientific lines in chemical, physical and astrophysical fields. For the last years, most researchers studies were about metal halides, that due to their potential applications. These are used in the lighting industry, for example diatomic indium halides have been subject to theoretical and experimental calculations [1]. The electronic spectrum of (InF and InCl) molecules appears in three band systems ( - , - , and - ) transitions and observed as first studied by researchers in 1952 [2]. At recent years, the physical and chemical properties of indium halides have great interest because of their application in the development of some semiconductor devices. In 1955, R.F. Barrow et al.[3] studied the rotational analyses of several bands of the A–X and B–X systems of InF molecule, In 1969, F.J. Lovas et al. [4] made high-temperature mass spectrometric studies of InF molecule of the dissociation energy. Recently spectroscopy offers direct determinations of parameters from the potential energy curves in which a molecule resides [5]. To know the properties of molecular spectroscopy we depend upon the molecular states for all electronic states. The ground state is more determined than the excited state, often with incomplete information available [6]. With a high exactitude, the spectroscopic parameters can be estimated, by curves fitting [5]. Spectroscopic parameters are very important to determine the spectrum, which is employed as a way to give new spectroscopic theoretical investigations, as the basis set influence, the electron correlation influence [7]. The spectroscopic parameters of all molecules are necessary for poorly characterized electronic states or yet experimentally unknown [8]. The Density Functional Theory (DFT)[9] has been used for calculating some of the spectroscopic electronic state parameters. Accordingly, DFT methods are used in many chemical applications [8]. Therefore, the advancement of DFT can be used for exactitude potentials, also, give the exactitude estimation of highest electronic states [8]. Some of the previous studies of the (TD-DFT) [10] have been used to calculate transition probability and excitation energy. Choosing TD-DFT methods is accessible in more theoretical packages, and in quantum chemical calculations, one needs a bigger number of the Gaussian-type basis than a Slater-type basis [11]. STO set has been improved and enter into theoretical calculations. Chong [7] evolved a method called by DZP (ADZP) method and TZP (ATZP) method in his calculations. In our study, another model (et-QZ3P-xD) [12] is compared with the improved ATZP set. The determination of spectroscopic parameters of the four states of InF and InCl molecules requires knowing the location of potential curves carefully. Method of computations In our study, we use the TD-DFT method for calculation, the electronic states ( , , and ) of our molecules (InF and InCl) can be studied by this method. The SAOP/ATZP model was used in this work to calculate all spectroscopic parameters and constants: Excitation energy (Te), bond length at equilibrium (re), the rotational constant (Be), harmonic vibrational frequency , vibrational anharmonicity , zero-point energy , centrifugal distortion constant ( De), the vibration–rotation constant . Also, another set of this calculation has been used represented by TD–DFT (SAOP)/et-QZ3P-xD model. which was used to model for ( and , and ) states of InF and InCl molecules. In this model, the advanced ATZP set [7] was applied. Three points determine the creation of our required parameters: (I) generation of the potential energy surfaces by two theoretical models ((SAOP)/et-QZ3P-xD and SAOP)/ATZP); (II) potential fitting of the electronic states, and (III) parameters calculation. The spectroscopic parameters and constants of all the electronic states are determined by fitted analytical potential curves. Physics | 27 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 By dependending on the Quantum approximation and the results of rovibrational energy levels, any potential energy Un(ρ) for the electronic states can be written as [13]: ∑ Where is spectral constant at ( =1,…,6), and is a spectral parameter equals to (r-re); n= 0,…, 7; ( i.e. ground = 0). For all ground and excited state determined, the calculations were done using two theoretical models. All calculations were done applying the ADF theoretical program [14,15], and TD-DFT. The potential energy curve was fitted to equation (1) for all electronic states. Then, in this work, two basis sets were examined, they are labeled as efficient and large basis sets; the established et-QZ3P-xD is the large basis set, where x = 1 or 2 according to atoms. The (ATZP) is the efficient basis set with x = 1or 0 [7].. The potential energy can be written as follows [16]: ( ) ( ) where is harmonic frequency, ) is anharmonic frequency and (v) is vibration quantum number . Also, vibrational zero-point energy (ZPE) can be written as[16]: Where, the vibrational term, (J): the angular momentum and the rotational constant at (v- state) [16]: ( ) Where : rotational constant at equilibrium and : vibrational– rotational constant. The total energy EnvJ can be written as[13] Where is the transitional energy, the spectroscopic constants were determined in a program called VIBROT [17]. Results and discussion The Spectroscopic investigation for all constants ( re, , , Te , De, Be, and ) have been estimated by two models ( ATZP and et-QZ3PxD) for ( , , and ) states of InF and InCl molecules and presented in tables 1 and 2. Also, errors % in the states for InF and InCl have been determined, which depended on constants above. These errors are given in figures (1–7). These parameters were created by dependending on (ATZP) and (et-QZ3P-xD) sets and were expressed in figures (8 – 11). The errors in re estimated by the TD- DFT(SAOP)/ATZP model and Figure 1 shows that. The errors are about of 0.45%, this is close to researcher’s results [18] for InCl and [19] for InF. The constant Be is associated to re as below[16]: Physics | 28 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 Where is Dirac constant, is reduced mass and re is bond length at equilibrium, they are the prospect to have symmetric alterations as re but in a reciprocal position, this is because of the inverse relationship between Be and re. The errors in Be have been expressed in figure 2 for all states of InF and InCl. However, in a ground state and excited state, the efficient basis set and the larger basis set gave bond lengths and rotational constants for InF and InCl molecules very convergent with the experimental values [18] for InCl and [19] for InF (see table 1 and 2). Figures (3-a and 3-b) provide an appraisement of the exactitude of the harmonic vibrational frequency , which is the theoretical result, with the two models. Also, our theoretical value of ( ) in the ground state is proximate to researcher’s results. The centrifugal distortion constant De (figure 4) exhibit fairly accurate agreement with experiment. The theoretical estimation of has its prominence in high exactitude estimations of experimental values. The vibrational– rotational constant depend upon the third derivative of the potential energy curves, but the fourth derivative is used to obtain on . The errors are the outcome of the first and second excited states. The errors in constants in ground states are by et-QZ3P-xD model less than ATZP model for InF molecule, but in InCl molecule, the errors were in ATZP model less than the et-QZ3P-xD model. The errors in other excited states were convergent as shown in figures (5-a and 5-b). The constant is associated with other parameters via [16] √ Figures (6-a and 6-b) show convergence in the performance of the effective set and performance of the larger set. For normal molecules, zero-point energy (ZPE) is small as shown in the tables. Also, producing the ZPE in this study as a “spectroscopic constant” is an important process. Figure 7 shows the errors of the estimation ZPE by these models, which also are convergent. Adiabatic excitation energy, (Te ) of molecules has been discussed in this study for InF and InCl molecule as showen in tables (1 and 2) and figures (8-11), where values of (Te ) were zero for ground states and convergent values for excited states with experimental values. Figure 8 shows a comparison between theoretical models in the ground states of InF molecule by depending on “absolute average percentage deviation (AAPD)” for the diatomic molecular parameters. From this figure, the SAOP give a good agreement with the experimental results in the ground states. The et-QZ3P-xD model shows error % less than the ATZP model for all constants. The high error % was clear in estimating the anharmonic and the rotational constant (Be) in this figure. Also, figure 9 shows a comparison between theoretical models in the three lowest-lying excited states of InF molecule. From this figure, the TD-DFT(SAOP)/et-QZ3P-xD model appears error % less than the TD-DFT(SAOP)/ATZP model for all constants except rotational constant (Be). In Figure 10, the results show convergence in errors% between theoretical models of the constants for ground states of InCl molecule except for the constants and (Be) which show high errors in the TD-DFT(SAOP)/et-QZ3P-xD model comparing with the TD- DFT(SAOP)/ATZP model, That is, due to the inverse relationship between the two constants (Be and re). In figure 11, the results show convergence in errors% between theoretical models of the constants for three lowest-lying excited states of InCl molecule except for the constants which show high errors in the ATZP model comparing with the et-QZ3P-xD model, therefore here et-QZ3P-xD model is better than ATZP model, and agree with experimental values. Physics | 29 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 In general, two theoretical models for state and next three low-lying electronic states , and ) of the molecules have been compared with theoretical and experimental values, and the results show convergence in values with simple error %. Our results have shown that the TD-DFT in conjunction with basis set in this study is an important for the estimation of spectroscopic parameters for ground and excited states of InF and InCl molecules, Conclusion The important conclusion from our results is the ATZP basis set which is very close to larger et-QZ3P-xD basis set, as shown in tables and figures in previous results section. That is in all electronic states of InF and InCl molecules except some of the constants such as (Be) which have different behavior in sometimes. Physics | 30 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 References 1- Ghalouci L.; Taibi F.; Ghalouci F. and Bensaid M.O., (2016), “ Ab initio investigation into structural, mechanical and electronic properties of low pressure, high pressure and high pressure-high temperature phases of Indium Selenide” Computational Materials Science, 124, 62-77. 2- Welti D. and Barrow R. F., (1952), “ The Absorption Spectra of Gallium”, and Indium Monofluorides”, Proc. Phys. Soc. A 65, 629. 3- Barrow R.F.; Glaser D.V. and Zeeman P.B., (1955), Proc. Phys. Soc. A 68, 962. 4- Lovas F.J., and Torring T., (1969), Microwave rotational spectrum of indium monofluoride, Naturfor. 24 a, 634. 5- Lin C. Y., George; M. W. and Gill P. M., (2004), “EDF2: A Density function for predicting molecular vibrational frequencies”, W. Aust. J. Chem., 57, 365-370. 6- Yang G.Y. and Huang D. G., (2017), Modern Inorganic Synthetic Chemistry (Second Edition), 219-246. 7- Chong. D. P., (2005), “Interpretation of the Kohn–Sham orbital energies as approximate vertical ionization potentials” Mol. Phys., 103, 479-492. 8- Sinnokrot M. O. and Sherrill C. D., (2001), “Density Functional Theory Predictions of Anharmonicity And Spectroscopic Constants for Diatomic Molecules”, J. Chem. Phys., 115, 2439-2448. 9- Kohn W. and Sham L., (1965), Phys. Rev., 140, A1133. 10- Runge E. and Gross E., (1984), “Density-Functional Theory for Time-Dependent Systems” Phys. Rev. Lett., 52, 997-1011. 11- Van Lenthe E. and Baerends E., (2003), “Optimized Slater-type basis sets for the elements 1–118” J Comput. Chem., 24, 1142-1156. 12- Chong D. P.; Lenthe E. Van; Gisbergen S. J., (2004), J Comput. Chem., 25, 1030. 13- Bernath P. F., (1995), Spectra of Atoms and Molecules; Oxford University Press: New York. 14- ADF Program System. Release (2003), Scientific Computing & Modelling: Amsterdam. 15- G.Te Velde; Bickelhaupt F. M.; Baerends E. J.; Fonseca Guerra C.; van Gisbergen S. J. A. and Snijders J. G., (2001), J Comput. Chem. 22, 931. 16- Basov N. G. and Bashkin G., (1990), Chem. Laser, (springer-Verlag), 33-34. 17- Dun T. H., (1978), Dunning, Jr. VIBROT: A Vibration-Rotation Analysis Program for Diatomic Molecules; private communication of DPC to C. N. Bauschlicher. 18- Mishra S.K.; Yadav K. S. and Singh V. B., (2004), J. Phys. Chem. Ref. Data, 33, 2. 19- Nampoori V. P.; Kamalasanan M.; Patel M., (1975), J. Phys. B: Atom. Molec. Phys., 8. 17. http://www.sciencedirect.com/science/article/pii/S0927025616303329 http://www.sciencedirect.com/science/article/pii/S0927025616303329 http://www.sciencedirect.com/science/article/pii/S0927025616303329 Physics | 31 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 Table(1): Spectroscopic constants for the electronic states of InF molecule. Stat e Method re (Å) Te (cm -1 ) (cm -1 ) (cm -1 ) De×10 8 (cm -1 ) (cm -1 ) Be (cm -1 ) (cm -1 ) et-QZ3P-xD ATZP Expt.[19] 1.972 1.976 1.985 0 0 0 534.112 544.144 535.350 2.5212 2.5000 2.6180 25.2400 25.1600 25.2096 185231 185200 187855 0.2470 0.2410 0.2628 266.42 271.44 267.02 et-QZ3P-xD ATZP Expt.[19] 1.932 1.933 1.985 29335 29156 28145 574.311 573.000 575.200 3.5800 3.5801 3.6700 25.1100 25.0000 25.0000 198011 198000 200000 0.2880 0.2720 0.2732 286.26 285.60 286.68 et-QZ3P-xD ATZP Expt.[19] 1.940 1.945 1.944 31221 31040 31255 588.000 582.300 572.200 2.9100 2.9000 2.6300 25.1112 25.1000 25.0000 201006 201004 201000 0.3050 0.2725 0.2736 293.19 290.42 285.44 et-QZ3P-xD ATZP Expt.[19] 1.952 1.962 1.967 41765 41534 42809 461.244 460.622 463.900 7.1311 7.2461 7.3500 36.5200 36.4100 36.5000 492000 491110 500000 0.2510 0.2441 0.2670 228.83 228.49 230.11 Table (2): Spectroscopic constants for the electronic states of InCl molecule. state method re (Å) Te (cm -1 ) (cm -1 ) (cm -1 ) De×10 8 (cm -1 ) (cm -1 ) Be (cm -1 ) (cm -1 ) et-QZ3P-xD ATZP Expt. [18] 2.413 2.417 2.402 0 0 0 316.324 311.881 317.389 1.3241 1.1022 1.0320 5.1100 5.0902 5.1612 51821 51744 51737 0.1277 0.1122 0.1089 157.83 155.66 158.43 et-QZ3P-xD ATZP Expt. [18] 2.330 2.334 2.333 27821 27423 27778 338.112 333.001 340.040 1.9442 1.9331 1.8800 5.2911 5.3477 5.2660 67992 64515 66780 0.1269 0.1392 0.1152 168.56 166.01 169.55 et-QZ3P-xD ATZP Expt. [18] 2.332 2.337 2.338 28001 28433 28563 337.901 335.551 339.100 2.3022 2.2717 2.1930 5.9141 6.0012 5.9000 79821 76999 78740 0.2824 0.9065 0.1149 168.37 167.20 169.00 et-QZ3P-xD ATZP Expt. [18] 2.441 2.462 2.458 37423 37200 37568 176.010 174.261 177.270 12.8220 12.0016 12.5890 14.2076 15.0333 14.9500 36879 35662 36654 0.4822 0.5666 0.1040 84.79 84.13 85.48 Physics | 32 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017 Physics | 33 2102( عام 2( العدد ) 30هجلة إبن الهيثن للعلىم الصرفة و التطبيقية الوجلد ) Ibn Al-Haitham J. for Pure & Appl. Sci. Vol.30 (2) 2017