INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 10, OCTOBER 2019 ISSN 2277-8616 Calculation Of Eigen Values And Atomic Orbital Electron Population Of Isomeric Benzodiazines By Density Functional Theory Method M.B. Kalhans, A.K. Singh, N.B. Singh Abstract: The concept of reactivity got advance treatment when Parr et al. published a paper on the application of density functional theory. In the present paper we have calculated the Eigen values and AOEP of the three isomeric Benzodiazines, which provided important results about the coordination trend of the said compounds. Key words: Density Functional theory, Eigen value, AOEP, Coordination, Benzodiazines. ———————————————————— 1. Introduction now by putting the value of ionization potential of an atom in DFT emerged as an important tool in quantum chemistry molecules IP, we get electron affinity of that atom in the 1 calculations. In DFT the function electron density (r) and molecule as EA = 2 -IP (5) the external potential V(r) are used to describe the ground state energy of an atom or a molecule. According to Koopman’s theorem the I and A are simply the ( ) ( ) ∫ ( ) ( ) (1) where F( )=T( ) + V ( ), T( ) is the electronic kinetic eigen value of HOMO and LUMO respectively with change ee in sign.9 energy function and Vee( ) is the electron - electron interaction energy function. The minimization of the total energy, subject to the condition that the total number of 2. Methodology/Experimental electron is fixed, i.e. The multipole model has been used to calculate the ∫ ( ) (2) molecular electrostatic potential for magnetic neglect of Equation (2), gives an Euler- Lagrange equation of the diatomic overlap like wave functions and the definitions for all the multiples for the 4s charge distribution that rise with form, 10-12 an s-p-d basis set have been listed . ( ) ( ) ( ) (3) ( ) where the Lagrange multiplier is the chemical potential2 The Hamiltonian from of Schrodinger wave equation is Hartree-Fock introduced a solution for ab-initio which has ( ) been used for DFT3 to add a classical two centre potential So, a general equation can be written in the following form. with a damping function for short distances to DFT ( ) Hamiltomian. The solution of equation (3) leads to the Eigen function is that wave function which when operated ground state density. The ground state energy is by an operator generates the same function multiplied by a determined by using this equation, Parr, etal.4 defined the constant. This constant is known as Eigen value of that electro negativity as the negative value of chemical particular function. For a general square matrix A of order n, potential viz. the corresponding equation satisfied by the Eigen values is ( ) (4) ( ) ( ) when a nth order determinant is expanded it gives a Although, Pearson was first to give the hard & soft acid polynomial in whose highest power is . This base concept the first unambiguous definition was given by 5 characteristic polynomial has n roots for , so a square Parr and Pearson. With the help of DFT we have matrix of order n has n eigen values.10 The eigen values of developed a method to evaluate the electron affinity of an 6,7 different molecular orbitals of the sample compounds as atom in a molecule. Density Functional theory provides a calculated by MNDO method are given in table 1&2. quantum mechanical justification for electronegativity. A concept used intutively for long time and validates 8 Table 1 Eigen values of various molecular orbitals of Sanderson’s postulates that when two or more atoms isomeric Benzodiazines combine to form a molecule their electronegativities gets Molecular Cinnoline Quinoxaline Quinazoline equalized and unique electronegativity exists everywhere in Orbital a molecule, C9=N10 ( ) -40.69117 -40.23188 -40.59563 C9=N10 ( ) -35.35357 -35.55180 -35.15218 C8=N7 ( ) -31.16657 -30.73839 -31.2288 C8=N7 ( ) -28.53501 -28.75524 -28.55443 C2=C1 ( ) -27.96398 -27.69129 -27.71341 _______________________ C2=C1 ( ) -22.95965 -23.01170 -22.87588 M B Kalhans and N B Singh: Department of Chemistry, Bareilly C3=C4 ( ) -22.32593 -22.50071 -22.31768 College Bareilly, U.P., India-243005 C3=C4 ( ) -21.52821 -20.95032 -21.53817 A K Singh: Department of Physics, Bareilly College Bareilly, U.P., C5=C6 ( ) -19.14658 -18.85743 -19.03011 C =C ( ) -17.91998 -18.4006 -18.31557 India-243005 5 6 C5-N10 ( ) -17.43101 -17.49555 -17.40303 1922 IJSTR©2019 www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 10, OCTOBER 2019 ISSN 2277-8616 C6-C7 ( ) -16.34090 -16.39579 -16.16300 C4-C5 ( *) Cinnoline > Quinoxaline > Quinazoline C2-C3 ( ) -15.55134 -15.53271 -15.79203 C6-C1 ( *) Quinoxaline > Quinazoline > Cinnoline C6-C1 ( ) -15.27805 -15.10767 -15.19151 C2-C3 ( *) Quinoxaline > Cinnoline > Quinazoline C4-C5 ( ) -14.92990 -14.81914 -14.82875 C6-C7 ( *) Quinoxaline > Quinazoline > Cinnoline C8-C9 ( ) -14.49950 -14.75112 -14.50674 C5-N10 ( *) Quinoxaline > Quinazoline > Cinnoline C3-H13 ( ) -13.49403 -15.15271 -13.45650 C5=C6 ( *) Quinazoline > Quinoxaline > Cinnoline C2-H12 ( ) -13.12603 -13.06695 -13.07328 C5=C6 ( *) Quinoxaline > Quinazoline > Cinnoline C1-H11 ( ) -12.97643 -12.64006 -12.81449 C3=C4 ( *) Quinoxaline > Quinazoline > Cinnoline C4-H14 ( ) -11.93268 -11.80837 -11.63203 C3=C4 ( *) Quinoxaline > Quinazoline > Cinnoline C7-H15 ( ) -11.55628 -11.32440 -11.17478 C2=C1 ( *) Quinoxaline > Quinazoline > Cinnoline C8-H16 ( ) -10.17351 -10.01415 -1021052 C2=C1 ( *) Quinoxaline > Quinazoline > Cinnoline Non Bonding -9.77652 -9.94285 -10.16667 C8=N7 ( *) Quinoxaline > Quinazoline > Cinnoline Non Bonding C8=N7 ( *) Quinoxaline > Quinazoline > Cinnoline (HOMO) -9.61188 -9.58517 -9.59238 C9=N10 ( *) Quinoxaline > Quinazoline > Cinnoline C8-H16 ( *) C9=N10 ( *) Cinnoline > Quinazoline > Quinoxaline (LUMO) -0.96512 -0.89793 -0.93332 C7-H15 ( *) -0.59148 -0.51607 -0.54831 Atomic orbital electron population represents the density of C -H ( *) 0.50114 0.61658 0.54737 4 14 electrons in various orbitals of an atom in bonded state. The C1-H17 ( *) 1.48370 1.54366 1.54079 C2-H12 ( *) 2.34501 2.36171 2.33507 contribution of electrons in each occupied molecular orbital C3-H13 ( *) 2.45123 2.41780 2.50609 are calculated by using the population analysis method of 11,12 C8-C9 ( *) 2.65779 2.61653 2.59285 Mulliken. AOEP values of different molecular orbitals of C4-C5 ( *) 2.86364 2.76806 2.70496 Pyran and its derivatives are calculated by MNDO C6-C1 ( *) 2.89090 3.03143 2.90210 technique Table 3 & 4. C2-C3 ( *) 3.18178 3.26181 3.07949 C6-C7 ( *) 3.28935 3.51931 3.35538 C5-N10 ( *) 3.53234 3.64588 3.55611 Table 3 AOEP values of different molecular orbitals of C5=C6 ( *) 3.70356 3.85895 3.99514 benzodiazines C5=C6 ( *) 4.24907 4.32597 4.31216 Molecular Orbital Cinnoline Quinoxaline Quinazoline C3=C4 ( *) 4.28730 4.38460 4.36757 C9=N10 ( ) 1.17679 1.17705 1.17448 C3=C4 ( *) 4.45307 4.57272 4.51670 C9=N10 ( ) 0.95111 0.94514 0.94921 C =C ( *) 2 1 4.71201 4.8806 4.84665 C8=N7 ( ) 0.95744 0.96150 0.95392 C8=N7 ( ) 1.00221 0.98088 0.98429 C2=C1 ( *) 4.86613 5.00987 4.93245 C2=C1 ( ) 1.18020 1.18096 1.18064 C8=N7 ( *) 4.999744 5.59738 5.31008 C2=C1 ( ) 0.94774 0.95023 0.94921 C8=N7 ( *) 5.58004 5.61110 5.60773 C3=C4 ( ) 0.97387 0.97351 0.97485 C9=N10 ( *) 5.75393 5.84933 5.77466 C3=C4 ( ) 0.97883 0.98984 0.99744 N9=N10 ( *) 7.44508 6.80485 6.95897 C5=C6 ( ) 1.18168 1.18097 1.18101 C5=C6 ( ) 0.98773 0.98660 0.98597 Table 2 Sequence of eigen values of different isomeric C5-N10 ( ) 0.93758 0.93714 0.93629 Benzodiazines C6-C7 ( ) 0.99403 0.98981 0.977 C -C ( ) 1.17659 1.17707 1.17888 M.O. Sequence 2 3 C6-C1 ( ) 0.92757 0.92823 0.93206 C9=N10 ( ) Quinoxaline > Quinazoline > Cinnoline C4-C5 ( ) 0.97814 0.97830 0.97957 C9=N10 ( ) Quinazoline > Cinnoline > Quinoxaline C8-C9 ( ) 0.96615 0.98091 0.98652 C8=N7 ( ) Quinoxaline > Cinnoline > Quinazoline C3-H13 ( ) 1.20038 1.19054 1.18579 C8=N7 ( ) Cinnoline > Quinazoline > Quinoxaline C2-H12 ( ) 0.95980 0.95413 0.94697 C2=C1 ( ) Quinoxaline > Quinazoline > Cinnoline C1-H11 ( ) 0.92090 0.91418 0.95684 C2=C1 ( ) Quinazoline > Cinnoline > Quinoxaline C4-H14 ( ) 1.01519 1.01162 0.96627 C3=C4 ( ) Quinazoline > Cinnoline > Quinoxaline C7-H15 ( ) 1.16473 1.19050 1.17463 C3=C4 ( ) Quinoxaline > Cinnoline > Quinazoline C8-H16 ( ) 0.94124 0.92501 0.95378 C5=C6 ( ) Quinoxaline > Quinazoline > Cinnoline Non Bonding 0.94728 0.92501 0.95378 C5=C6 ( ) Cinnoline > Quinoxaline > Quinazoline Non Bonding 1.00263 1.01167 0.95739 C5-C10 ( ) Quinazoline > Cinnoline > Quinoxaline C8-H16 ( *) 1.18223 1.60380 1.20516 C6-C7 ( ) Quinazoline > Cinnoline > Quinoxaline C7-H15 ( *) 0.94115 1.07072 0.91154 C2-C3 ( ) Quinoxaline > Cinnoline > Quinazoline C4-H14 ( *) 0.98091 1.30237 0.97290 C6-C1 ( ) Quinoxaline > Quinazoline > Cinnoline C1-H11 ( *) 0.98305 1.04554 0.90370 C4-C1 ( ) Quinoxaline > Quinazoline > Cinnoline C2-H12 ( *) 1.21722 1.21541 1.62662 C8-C9 ( ) Cinnoline > Quinazoline > Quinoxaline C3-H13 ( *) 1.00446 0.99625 1.41441 C3-H13 ( ) Quinoxaline > Quinazoline > Cinnoline C8-C9 ( *) 0.91934 0.91838 0.97196 C2-H12 ( ) Quinoxaline > Quinazoline > Cinnoline C4-C5 ( *) 0.99656 0.97209 1.10904 C1-H11 ( ) Quinoxaline > Quinazoline > Cinnoline C6-C1 ( *) 1.63810 1.21540 1.23643 C4-H14 ( ) Quinazoline > Quinoxaline > Cinnoline C2-C3 ( *) 1.03838 0.94179 0.96361 C7-H15 ( ) Quinazoline > Quinoxaline > Cinnoline C6-C7 ( *) 1.30354 0.97289 0.96490 C8-H16 ( ) Quinoxaline > Cinnoline > Quinazoline C5-N10 ( *) 1.03483 0.97208 0.91873 Non Bonding -I Cinnoline > Quinoxaline > Quinazoline