# PHOTODETACHED ELECTRONIC WAVE FUNCTION OF HYDROGEN HALIDE ANIONS.

Byline: Ayesha Amjad, Afaq Ahmad, Maryam Nawaz and Sadia Ashiq

ABSTRACT:

The general expression of outgoing photo-detached electronic wave function for hydrogen halide anionsHX-(X= F, Cl, Br, I) has been derived by employing Two-center Model. The normalization constants in molecular wave function for bound or unbound states may be obtained from Linear Combination of Atomic Orbital (LCAO) or Molecular Orbital theory. This outgoing wave function provides us an excellent way to explore the structural properties of HX-anions.

I. INTRODUCTION

The well-known Schrodinger's wave equationdescribes quantum particledynamics beautifully emphasizing on the importance ofwave functions in terms of probabilities changing in time [1,2,3]. For each observable there correspondsa quantum mechanical operator,operating on the wave functionprovidingdesired information [4, 5].

In the theoretical study of photo-detachment of negative ions, the detached-electronicwave function is necessary to compute electron flux and total cross-section for the system under study. That would provide the electron affinities of neutral atoms or molecules by threshold calculations in the spectra [6, 7].

The Schrodinger's wave equation had been solved successfully for the simplest system of Hydrogen atom (Z=1).The wave function gave complete interpretation about allowed energies, radii, size of H-atom, ionization energies, electron affinities, and parity[3-5, 8]. Subsequentlythe wave equation was solved for Helium (Z=2) as two-electron system andmany different structural parameters were obtained [4, 9]. Other many-electron systems were also solved and studied via Schrodinger's wave equation [27-28]. To study HX-negative molecule system in photo-detachment process, we have to determineitswave functionsby Linear Combination of Atomic Orbitals (LCAO)of H- and X-[3]. It must be understood that the LCAO utilizing a limited number of atomic orbitals provides onlyguesstimate to the true molecular orbital. In a simple hetero-nuclear molecule, molecular orbitals form as an outcome of overlap betweeInI.

the atomic orbitals on each atom. For overlap to occur atomic orbitals must have almost the same orbital energy and they must possess the proper symmetry [9]. Nature of interaction among atomic orbitals finallyresults in bonding and anti-bonding molecular orbitals [10].

Negative ions are fragile fascinating quantum systems having lots of interesting physical and chemical properties.These are being studied due to their increasing importance in applied sciences[11, 12]. Here we want to study negative hydrogen halide ions by computing their photo-detached wave functions. Interactions between halide ions and atomic hydrogen or deuterium have recently fascinated new interest and curiosity for low-energy collisions (below 8 eV) leading to associative attachment, a process important in many plasmas. Associative attachment results in molecule formation parallel with detachment of electrons. The shapes of the electron spectra exhibit significant structures [13, 14].Hydrogen halides signify a particularly striking class of compounds for the study of electron-molecule collisions, because of a number of remarkable phenomena encountered in the cross sections. The cross sections are of practical prominence because hydrogen halides are used in industrial plasmas [15].

We have developed photo-detached electronic wave functions of negative hydrogen halide ions by employing

Two-center model. As we are dealing with the two centers system, so the two centers of hydrogen halide anion in the photo-detachment process will play the role of slits just like those in Young's double slit experiment [16]. There is an equal probability that either an electron can evolve from center H or center X in accordance with Quantum mechanical probabilistic theory [17]. Two centers of negative ion will act as coherent sources of outgoing waves and superposition of these two coherent detached waves will give the total photo-detached outgoing wave for the system in agreement with LCAO-MO method.

This article is organized in such a way that in the next section we will first discuss Two Center model of our hydrogen halide anion and then compute the total detached- wave function at large distances from the system. Atomic units are used throughout this article.

THEORY

The schematic diagram of two-center system is shown in figure 1. Thelaser light is polarized in the z-direction, and the system is placed y-axis such that H and X denote the two centers of the system. The origin of the Cartesian coordinates system is taken to be at the middle of the axis connecting the two centers of the system. The screen perpendicular to the z-axis is placed at a distance L from the two centers, whered is the interatomic distance. Here L(greater then)(greater then)d and usually equal to several thousand Bohr radii in the photo-detachment microscopy experiment [18]. Two outgoing waves PsH and PsX will evolve from hydrogen halide anion.

III. CONCLUSION

We studied the photo-detachment of HX- (X= F, Cl, Br, I)

REFERENCES

[1] P.W. Atkins, A hand book of concepts(Oxford University Press, 1974)

[2] E. Schrodinger, Phys. Rev., 28, 1049 (1926)

[3] Arthur Beiser, Perspective of Modern Physics (McGraw-Hill,1969)

[4]David J.Griffiths, Introduction to Quantum Mechanics(Second Edition, Pearson Higher Education and Professional Group, 2004)

[5]Richard Liboff , Introductory Quantum Mechanics (4th edition, Pearson Higher Education and Professional Group, 2002)

[6] L. C. Lee and G. P. Smith, J. Chem. Phys.70, 1727(1979)

[7] T. Andersen, Physics Reports., 394, 157 (2004)

[8] P.W. Atkins, An Introduction to Quantum Chemistry (Oxford University Press, 1977)

[9] Dr.Richard F.W.Bader, An Introduction to the Electronic Structure of Atoms And Molecules (Clarke, Irwin, 1970)

[10] deKock, Roger L., and Gray, Harry B., Chemical Structure and Bonding(University Science Books, 1980)

[11] David J. Pegg, Rep. Prog. Phys., 67, 857-905 (2004)

[12] Pontus Andersson, Laser Photodetachment of Negative Ions, (PhD thesis, 2009)

[13] S. Zivanov, M. Allan, M. Cizek, J. Horacek, F.A.U. Thiel, H. Hotop, Phys. Rev. Lett.89, 073201(2002) [14] S. Zivanov, M. Cizek, J. Horacek, M. Allan, J. Phys. B36, 3513 (2003)

[15] J. Fedor, O. May, and M. Allan, Phys. Rev. A 78, 032701 (2008)

[16] A.Afaq, M. L. Du, Commun. Theor. Phys., 50, 1401 (2008)

[17]NouridineZettili, Quantum mechanics: Concepts and Applications (2nd Edition, Wiley, 2009)

[18] C. Blondel, C. Delsart, and F. Dulieu, Phys. Rev. Lett.77, 3755(1996);C. Blondel, C. Delsart, and F. Dulieu, et al., Eur. Phys. J. D 5, 207 (1999);C. Blondel, W. Chaibi, C. Delsart, et al., Eur. Phys. J. D33, 335(2005)

[19] A.Afaq, Iftikhar Ahmad, International Journal of Quantum Chemistry, 111, 4067 (2011) [20] M.L.Du, Phys. Rev., A., 40,4983(1989)

[21] M.L. Du and J.B. Delos, Phys. Rev. Lett., 58, 1731 distance, size of the atom, binding energies etc. (1987)

[22] M.L. Du and J.B. Delos, Phys. Rev., A 38, 1896 (1988)

[23] M.L. Du and J.B. Delos, Phys. Rev., A 38, 1913 (1988)

[24] M.L. Du and J.B. Delos, Phys. Rev. A38,5609 (1988)

[25] A.Afaq and M. L. Du, Commun. Theor. Phys., 50, 1402(2008)

[26] J. Phys. Chem., Ref data, 4, 539(1975)

[27]Claes Johnson, Many-Minds Quantum Mechanics (Stockholm, 2001)

[28]Raymond A. Serway, John W. Jewett ,Physics for Scientists and Engineers (8 Edition, Mary Finch, 2009)

1Centre of Excellence in Solid State Physics, University of the Punjab, Lahore-54590, Pakistan

2Government Post Graduate College for Women Daska, Sialkot, Pakistan

Email: aafaq.cssp@pu.edu.pk

ABSTRACT:

The general expression of outgoing photo-detached electronic wave function for hydrogen halide anionsHX-(X= F, Cl, Br, I) has been derived by employing Two-center Model. The normalization constants in molecular wave function for bound or unbound states may be obtained from Linear Combination of Atomic Orbital (LCAO) or Molecular Orbital theory. This outgoing wave function provides us an excellent way to explore the structural properties of HX-anions.

I. INTRODUCTION

The well-known Schrodinger's wave equationdescribes quantum particledynamics beautifully emphasizing on the importance ofwave functions in terms of probabilities changing in time [1,2,3]. For each observable there correspondsa quantum mechanical operator,operating on the wave functionprovidingdesired information [4, 5].

In the theoretical study of photo-detachment of negative ions, the detached-electronicwave function is necessary to compute electron flux and total cross-section for the system under study. That would provide the electron affinities of neutral atoms or molecules by threshold calculations in the spectra [6, 7].

The Schrodinger's wave equation had been solved successfully for the simplest system of Hydrogen atom (Z=1).The wave function gave complete interpretation about allowed energies, radii, size of H-atom, ionization energies, electron affinities, and parity[3-5, 8]. Subsequentlythe wave equation was solved for Helium (Z=2) as two-electron system andmany different structural parameters were obtained [4, 9]. Other many-electron systems were also solved and studied via Schrodinger's wave equation [27-28]. To study HX-negative molecule system in photo-detachment process, we have to determineitswave functionsby Linear Combination of Atomic Orbitals (LCAO)of H- and X-[3]. It must be understood that the LCAO utilizing a limited number of atomic orbitals provides onlyguesstimate to the true molecular orbital. In a simple hetero-nuclear molecule, molecular orbitals form as an outcome of overlap betweeInI.

the atomic orbitals on each atom. For overlap to occur atomic orbitals must have almost the same orbital energy and they must possess the proper symmetry [9]. Nature of interaction among atomic orbitals finallyresults in bonding and anti-bonding molecular orbitals [10].

Negative ions are fragile fascinating quantum systems having lots of interesting physical and chemical properties.These are being studied due to their increasing importance in applied sciences[11, 12]. Here we want to study negative hydrogen halide ions by computing their photo-detached wave functions. Interactions between halide ions and atomic hydrogen or deuterium have recently fascinated new interest and curiosity for low-energy collisions (below 8 eV) leading to associative attachment, a process important in many plasmas. Associative attachment results in molecule formation parallel with detachment of electrons. The shapes of the electron spectra exhibit significant structures [13, 14].Hydrogen halides signify a particularly striking class of compounds for the study of electron-molecule collisions, because of a number of remarkable phenomena encountered in the cross sections. The cross sections are of practical prominence because hydrogen halides are used in industrial plasmas [15].

We have developed photo-detached electronic wave functions of negative hydrogen halide ions by employing

Two-center model. As we are dealing with the two centers system, so the two centers of hydrogen halide anion in the photo-detachment process will play the role of slits just like those in Young's double slit experiment [16]. There is an equal probability that either an electron can evolve from center H or center X in accordance with Quantum mechanical probabilistic theory [17]. Two centers of negative ion will act as coherent sources of outgoing waves and superposition of these two coherent detached waves will give the total photo-detached outgoing wave for the system in agreement with LCAO-MO method.

This article is organized in such a way that in the next section we will first discuss Two Center model of our hydrogen halide anion and then compute the total detached- wave function at large distances from the system. Atomic units are used throughout this article.

THEORY

The schematic diagram of two-center system is shown in figure 1. Thelaser light is polarized in the z-direction, and the system is placed y-axis such that H and X denote the two centers of the system. The origin of the Cartesian coordinates system is taken to be at the middle of the axis connecting the two centers of the system. The screen perpendicular to the z-axis is placed at a distance L from the two centers, whered is the interatomic distance. Here L(greater then)(greater then)d and usually equal to several thousand Bohr radii in the photo-detachment microscopy experiment [18]. Two outgoing waves PsH and PsX will evolve from hydrogen halide anion.

III. CONCLUSION

We studied the photo-detachment of HX- (X= F, Cl, Br, I)

REFERENCES

[1] P.W. Atkins, A hand book of concepts(Oxford University Press, 1974)

[2] E. Schrodinger, Phys. Rev., 28, 1049 (1926)

[3] Arthur Beiser, Perspective of Modern Physics (McGraw-Hill,1969)

[4]David J.Griffiths, Introduction to Quantum Mechanics(Second Edition, Pearson Higher Education and Professional Group, 2004)

[5]Richard Liboff , Introductory Quantum Mechanics (4th edition, Pearson Higher Education and Professional Group, 2002)

[6] L. C. Lee and G. P. Smith, J. Chem. Phys.70, 1727(1979)

[7] T. Andersen, Physics Reports., 394, 157 (2004)

[8] P.W. Atkins, An Introduction to Quantum Chemistry (Oxford University Press, 1977)

[9] Dr.Richard F.W.Bader, An Introduction to the Electronic Structure of Atoms And Molecules (Clarke, Irwin, 1970)

[10] deKock, Roger L., and Gray, Harry B., Chemical Structure and Bonding(University Science Books, 1980)

[11] David J. Pegg, Rep. Prog. Phys., 67, 857-905 (2004)

[12] Pontus Andersson, Laser Photodetachment of Negative Ions, (PhD thesis, 2009)

[13] S. Zivanov, M. Allan, M. Cizek, J. Horacek, F.A.U. Thiel, H. Hotop, Phys. Rev. Lett.89, 073201(2002) [14] S. Zivanov, M. Cizek, J. Horacek, M. Allan, J. Phys. B36, 3513 (2003)

[15] J. Fedor, O. May, and M. Allan, Phys. Rev. A 78, 032701 (2008)

[16] A.Afaq, M. L. Du, Commun. Theor. Phys., 50, 1401 (2008)

[17]NouridineZettili, Quantum mechanics: Concepts and Applications (2nd Edition, Wiley, 2009)

[18] C. Blondel, C. Delsart, and F. Dulieu, Phys. Rev. Lett.77, 3755(1996);C. Blondel, C. Delsart, and F. Dulieu, et al., Eur. Phys. J. D 5, 207 (1999);C. Blondel, W. Chaibi, C. Delsart, et al., Eur. Phys. J. D33, 335(2005)

[19] A.Afaq, Iftikhar Ahmad, International Journal of Quantum Chemistry, 111, 4067 (2011) [20] M.L.Du, Phys. Rev., A., 40,4983(1989)

[21] M.L. Du and J.B. Delos, Phys. Rev. Lett., 58, 1731 distance, size of the atom, binding energies etc. (1987)

[22] M.L. Du and J.B. Delos, Phys. Rev., A 38, 1896 (1988)

[23] M.L. Du and J.B. Delos, Phys. Rev., A 38, 1913 (1988)

[24] M.L. Du and J.B. Delos, Phys. Rev. A38,5609 (1988)

[25] A.Afaq and M. L. Du, Commun. Theor. Phys., 50, 1402(2008)

[26] J. Phys. Chem., Ref data, 4, 539(1975)

[27]Claes Johnson, Many-Minds Quantum Mechanics (Stockholm, 2001)

[28]Raymond A. Serway, John W. Jewett ,Physics for Scientists and Engineers (8 Edition, Mary Finch, 2009)

1Centre of Excellence in Solid State Physics, University of the Punjab, Lahore-54590, Pakistan

2Government Post Graduate College for Women Daska, Sialkot, Pakistan

Email: aafaq.cssp@pu.edu.pk

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Publication: | Science International |
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Date: | Dec 31, 2012 |

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