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Chimica Fisica I > Struttura molecolare > Flashcards

Struttura molecolare Flashcards

1
Q

What is the meaning of the total energy of the molecule?

A

It is the sum of the electronic energy and the nuclear repulsion energy.

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2
Q

What is the Hamiltonian for the electronics of a molecule?

A

It is the sum of the electron kinetic energy, electron-electron interaction and the electron-nucleus interaction.

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3
Q

What happens if the nuclear energy is changed?

A

If the nuclear energy is changed, we have different eigenvalues and eigenfunctions. Witch varies the electron function parametricaly

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4
Q

What is the essence of the Born-Oppenheimer approximation?

A

It is the separation of electronic and nuclear motion, with the electronic wavefunction being a slowly varying function.

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5
Q

What generates a pull force when the nuclei are moved from the equilibrium position?

A

The total energy generates a pull force, which is the sum of the core-core repulsion and the electronic energy.

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6
Q

What determines the movement of the cores?

A

The total energy determines the movement of the cores.

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7
Q

What does the equation for electron motion need to achieve?

A

It needs to be resolved separately for each core configuration to achieve a minimum structure.

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8
Q

What is the curve that can be built from calculating the electronic and total energy for all nuclear configurations?

A

It is a curve of the total energy, which shows the minimum energy and the dissociation energy.

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9
Q

What is the energy dependence of states with m ≠ 0 in the hydrogen-ion molecule?

A

States with m ≠ 0 in the hydrogen-ion molecule are doubly degenerate, and the energy depends on m^2.

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10
Q

What is the significance of the progressive index in the classification of states in the hydrogen-ion molecule?

A

The progressive index in the classification of states in the hydrogen-ion molecule plays the role of the main quantum number, similar to the case of atomic states.

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11
Q

What is the significance of the spherical symmetry in the hydrogen-ion molecule?

A

Unlike in atoms, the hydrogen-ion molecule does not have spherical symmetry, and therefore L^2 does not commute with H.

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12
Q

What is the form of the eigenfunctions in the hydrogen-ion molecule?

A

ψ(ξ)ψ(η) 1/√2π e^(imφ)
The eigenfunctions in the hydrogen-ion molecule are even or odd, and must be eigenfunctions of the parity operator.

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13
Q

What is the significance of the center of inversion in the hydrogen-ion molecule?

A

The hydrogen-ion molecule has the center of inversion, so the states must be symmetric or antisymmetric for inversion in the middle.

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14
Q

What is the significance of the axial symmetry in the hydrogen-ion molecule?

A

The axial symmetry in the hydrogen-ion molecule means that Lz will switch with H, and the self-functions will also be self-functions of Lz.

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15
Q

What is the variational method used in the MO method?

A

The variational method used in the MO method is the method of minimizing the energy with respect to suitable variational parameters.

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16
Q

What is the limit of the wave function for an electron in a dissociating molecule as the internuclear separation approaches infinity?

A

Nel limite invece di R tendente
ad infinito le funzioni saranno genuinamente funzioni dell’atomo di idrogeno
e quindi con esponente orbitale k = 1.

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17
Q

What is the goal of the LCAO method?

A

The goal of the MO method is to find the best approximation to the true wave function of a molecule using a linear combination of atomic orbitals.

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17
Q

What is the goal of the MO method?

A

The goal of the MO method is to find the best approximation to the true wave function of a molecule using a linear combination of atomic orbitals.

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18
Q

What is the determinant of the coefficients in the MO method?

A

The determinant of the coefficients in the MO method is the secular determinant, which must be equal to zero for non-trivial solutions.

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19
Q

What is the equation for the secular equation in the MO method?

A

The equation for the secular equation in the MO method is (Haa - W Saa) c1 + (Hab - W Sab) c2 = 0 and (Hba - W Sba) c1 + (Hbb - W Sbb) c2 = 0.

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20
Q

What is the equation for the Hamiltonian matrix elements in the MO method?

A

he equation for the Hamiltonian matrix elements in the MO method is Haa = <ϕa|H|ϕa>, Hab = <ϕa|H|ϕb> = Hba, and Hbb = <ϕb|H|ϕb>.

21
Q

What is the determinant of the secular equation in this case?

A

The determinant of the secular equation in this case is (Haa - W)(Hbb - W) - (Hab - W Sab)^2 = 0.

22
Q

What are the two possible values for the energy of the molecular orbitals?

A

The two possible values for the energy of the molecular orbitals are W1 = (Haa + Hab)/(1 + Sab) and W2 = (Haa - Hab)/(1 - Sab).

23
Q

How do we find the coefficients c for the first solution?

A

We find the coefficients c for the first solution by solving the equation (Haa - W1) c1 + (Hab - W1 Sab) c2 = 0 and using the expression c1/c2 = -(Hab - W1 Sab)/(Haa - W1), where c1=c2

24
Q

What is the expression for the first molecular orbital given the normalization condition?

A

The expression for the first molecular orbital is ψ1 = 1/sqrt(2 + 2Sab) (ϕa + ϕb).

25
Q

What is the expression for the second molecular orbital?name?

A

The expression for the second molecular orbital is ψ2 = 1/sqrt(2 - 2Sab) (ϕa - ϕb). stato eccitato

26
Q

What is the purpose of the matrix H’?

A

It is the transformed Hamiltonian matrix in the new orthogonal basis.

27
Q

What is the new basis obtained after diagonalizing the S-matrix?

A

ψa = 1/√2(ϕa + ϕb), ψb = 1/√2(ϕa - ϕb)

28
Q

What is the significance of the overlap integral of orbitals of different atoms in the formation of a bond?

A

It is essential that the overlap integral is not null

29
Q

What are the stages involved in the general procedure for solving the secular problem?

A
  1. Choose a feature base in which to expand molecular orbitals and calculate the integrals defining the H and S matrices; 2. Transform the base into an orthogonal base where S is a unit array; 3. Transform the H matrix into the new base by obtaining H’; 4. Diagonalize the H’ matrix to obtain energies (eigenvalues) and eigenvectors in the orthogonal base; 5. Get the linear combinations in the original base.
30
Q

What is the center of inversion?

A

The center of inversion is a point in space where any atom in a molecule is equidistant from its mirror image.

31
Q

Describe the symmetry of the autofunctions with respect to the center of inversion.

A

The autofunctions must be either symmetric or antisymmetric with respect to the inversion at the center.

31
Q

Describe the symmetry of the autofunctions with respect to the center of inversion.

A

The autofunctions must be either symmetric or antisymmetric with respect to the inversion at the center.

32
Q

Describe the type of combinations that the functions of symmetry must be.

A

The functions of symmetry must be linear combinations of the type ψ1 = c(ϕa + ϕb) and ψ2 = c(ϕa − ϕb) that have the correct symmetry.

33
Q

Define the normalization of the functions of symmetry.

A

The normalization of the functions of symmetry is the process of scaling the functions to ensure that the integral of the square of the function over all space is equal to one.

34
Q

What is the form of the Hamiltonian matrix in the functions of symmetry?

A

The Hamiltonian matrix in the functions of symmetry is in diagonal form as the integrals of the type <ψ1|H|ψ2> are null if the functions are of different symmetry.

35
Q

Describe the trend of density for the two auto-functions of the binding and antibinding orbital.

A

For the function of the ground state, the electronic density is greater than the sum of the electronic densities of the two separate functions, while in the excited it’s the opposite

36
Q

How to quantify the stabilization of the molecule between the dissociated and undissociated molecule ?

A

To quantify the stabilization of the molecule it is necessary to calculate the Coulombian and risonance integrals and choose the value of the orbital exponent.

37
Q

How is the dissociation energy value improved?

A

The dissociation energy value is improved by introducing hybrid orbitals s-p.

38
Q

Define the principle of maximum overlap.

A

he principle of maximum overlap states that the greater the density of the density tronic in the center between the two atoms, the stronger the bond.

39
Q

Define the Hab resonance integral.

A

The Hab resonance integral is a negative sign that determines the sequence for increasing energy levels and is of fundamental importance in determining the stability of the molecule and the formation of the chemical bond.

40
Q

What is the significance of atomic orbitals with |m| = 1?

A

The levels and states originating from atomic orbitals with |m| = 1 are doubly degenerate.

41
Q

What is the sequence of levels in order of increasing energy?

A

The sequence of levels in order of increasing energy is σg1s < u1s < σg2s < u2s < πu2p+1 = πu2p-1 < σg2p < g 2p+1 = g 2p-1 < u2p.

42
Q

What is the purpose of the symbol * in the molecular orbitals classification?

A

The symbol * in the molecular orbitals classification is used to identify antisymmetric orbitals for reflection with respect to a plane perpendicular to the axis of bond.

43
Q

What is the purpose of the symbol that identifies the value |m| = 1 of the z-component of the moment ?

A

to specify that the orbital is doubly degenerate and resulting from atomic orbitals px’e antisymmetric for reflection with respect to yz plane.

44
Q

What is the rule of non-crossing?

A

The rule of non-crossing states that some levels never cross each other as the internuclear distance varies, and this can never happen for levels of the same symmetry.

45
Q

Cos’è il limite dell’atomo unito?

A

È il limite in cui i due atomi si trovano a distanza nulla

46
Q

Che forma ha l’orbitale σu*1s nell’atomo unito?

A

2pz

47
Q

Cosa varia con la separazione internucleare?

A

Cambiano i livelli energetici, i quali si possono intersecare

48
Q

cosa indica Λ

A

ML |

Chimica Fisica I (21 decks)

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