پاورپوینت نظریه اوربیتال مولکولی هوکل (pptx) 24 اسلاید
دسته بندی : پاورپوینت
نوع فایل : PowerPoint (.pptx) ( قابل ویرایش و آماده پرینت )
تعداد اسلاید: 24 اسلاید
قسمتی از متن PowerPoint (.pptx) :
1-4-نظریه اوربیتال مولکولی هوکل
در مولکول های مسطح مزدوج، سیستم pرا می توان مستقل از چارچوب s در نظر گرفت.
(اسکلت s سیستم های مزدوج مسطح درصفحه گرهی سیستم p قرار دارد ودر نتیجه با هم برهم کنش ندارند.)
سیستم پی در تعیین خواص شیمیایی و طیف نگاری پلی ان های مزدوج وترکیبات آروماتیک اهمیت ویژه دارد.
در تقریب HMO تابع موج الکترون های p به صورت ترکیب خطی اوربیتال های p بیان میشود.
ترازهای انرژی وضرایب اتمی از جمله اطلاعاتی هستند که از محاسبات بدست می آیند .
Molecular orbitals for polyatomic systems
The Hückel approximation
Here, we investigate conjugated molecules in which there is an alternation of single and double bonds along a chain of carbon atoms.
In the Hückel approach, the orbitals are treated separately from the orbitals, the latter form a rigid framework that determine the general shape of the molecule.
All C are considered similar only one type of coulomb integral for the C2p atomic orbitals involved in the molecular orbitals spread over the molecule.
A. The secular determinant
The molecular orbitals are expressed as linear combinations of C2pz atomic orbitals (LCAO), which are perpendicular to the molecular plane.
Ethene, CH2=CH2: =cAA + cBB, where A and B are the C2pz orbitals of each carbon atoms.
Butadiene, CH2=CH-CH=CH2: =cAA + cBB+ccC + cDD
The coefficients can be optimized by the same procedure described before: express the total energy E as a function of the ci and then minimize the E with respect to those coefficients ci. Inject the energy solutions in the secular equations and extract the coefficients minimizing E.
(1)
Numerator:
Denominator:
(1)
(1)
Energy in the LCAO approach
1 is a Coulomb integral: it is related to the energy of the e- when it occupies atome 1. ( < 0)
is a Resonance integral: it is zero if the orbital don’t overlap. (at Re, <0)
is the overlap integral related to the overlap of the 2 AO
Let’s find the “zeros” or roots of the polynomial vs. cA and cB
We want the cA minimizing E, we then impose:
We want the cB minimizing E, we then impose:
Secular equations
In order to have a solution, other than the simple solution cA= cB= 0, we must have:
Secular determinant should be zero
The 2 roots give the energies of the bonding and antibonding molecular orbitals formed from the AOs
Homonuclear diatomic molecules: =cAA + cBB with A= B A= B=
(1)
(2)
(2)
(1)
antibonding
bonding
antibonding= {2(1-S)}-1/2(A - B)
bonding= {2(1+S)}-1/2(A + B)
0
0
Eantibonding= - E-
Ebonding = E+-
Since: 0 < S < 1 Eantibonding > Ebonding
Note 1: He2 has 4 electrons ground-state configuration: 12 2*2 He2 is not stable!
Note 2: If we neglect the overlap integral (S=0), Eantibonding = Ebonding =
The resonance integral is an indicator of the strength of covalent bonds
Following these methods and since A= B= , we obtain those secular determinants:
Ethene, CH2=CH2:
Butadiene, CH2=CH-CH=CH2:
Hückel approximation:
1) All overlap integrals Sij= 0 (i j).
2) All resonance integrals between non-neighbors, i,i+n=0 with n 2
3) All resonance integrals between neighbors are equal, i,i+1= i+1,i+2 =
Severe approximation, but it allows us to calculate the general picture of the molecular orbital energy levels.
B. Ethene and frontier orbitals
Within the Hückel approximation, the secular determinant becomes:
E- = - energy of the Lowest Unoccupied Molecular Orbital (LUMO)
E+ = + energy of the Highest Occupied Molecular Orbital (HOMO)
LUMO= 2*
HOMO= 1
HOMO and LUMO are the frontier orbitals of a molecule.
those are important orbitals because they are largely responsible for many chemical and optical properties of the molecule. Note: The energy needed to excite electronically the molecule, from the ground state 12 to the first excited state 11 2*1 is provided roughly by 2|| ( is often around -0.8 eV) Chap 17
2||
Butadiene and delocalization energy
4th order polynomial 4 roots E
= E4
= E3
= E2
= E1
There is 1e- in each 2pz orbital of the four carbon atoms 4 electrons to accommodate in the 4 -type molecular orbitals the ground state configuration is 12 22
The greater the number of internuclear nodes, the higher the energy of the orbital
Butadiene C4H6: total -electron binding energy, E is E = 2E1+2E2= 4 + 4.48 with two -bonds
Ethene C2H4:E = 2 + 2 with one -bond
Two ethene molecules give: E = 4 + 4 for two separated -bonds.
The energy of the butadiene molecule with two -bonds lies lower by 0.48 (-36kJ/mol) than the sum of two individual -bonds: this extra-stabilization of a conjugated system is called the “delocalization energy”
3 nodes
2 nodes
1 node
0 node
LUMO= 3*
HOMO= 1
Top view of the MOs
