bonding orbital doubly occupied in hf wavefunction at r e antibonding orbital unoccupied in hf...

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bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and 0.2 amplitude contours as computed at the MCSCF/aug-cc-pVTZ level for r e + n 0.1 Å for n = 0 to 20. The nuclei are indicated with + symbols. Teal and dark magenta indicate positive and negative amplitude, respectively. Individual frames are available. Molecular (“natural”) Orbitals for H 2 molecule (amplitude contours, color indicates +/- sign)

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Page 1: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

bonding orbitaldoubly occupied in HF wavefunction at re

antibonding orbitalunoccupied in HF wavefunction at re

The animations depict 0.1, 0.15, and 0.2 amplitude contours as computed at the MCSCF/aug-cc-pVTZ level for re + n 0.1 Å for n = 0 to 20. The nuclei are indicated with + symbols. Teal and dark magenta indicate positive and negative amplitude, respectively. Individual frames are available.

Molecular (“natural”) Orbitals for H2 molecule

(amplitude contours, color indicates +/- sign)

Page 2: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Natural Orbitals for H2 molecule

(This time plotted as Ψ along the y-axis)

Animations of the amplitudes along the bond axis for the H2 bonding and antibonding (natural) orbitals.

Page 3: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

GVB Orbitals for H2(X1g+)

1R GVB orbital

singly occupied for all r

2L GVB orbital

Singly occupied for all r

The animations depict 0.1, 0.15, and 0.2 amplitude contours as com-puted for re + n 0.1 Å for n = 0 to 20. The nuclei are indicated with + symbols. Individual frames are available.

Page 4: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Animations of the amplitudes along the bond axis for the H2 R and L GVB orbitals.

GVB orbitals effectively show the degree to which the atomic orbitals involved in bonding are polarized toward the other nucleus during bond formation in order to maximize electron-proton interactions.

The following sequence of slides shows GVB orbitals and their overlap for H2 at various point along the potential energy curve (and animated along the entire curve on the final slide).

GVB Orbitals for H2(X1g+)

Page 5: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Transforming NOs to GVB orbitals

The GVB wavefunction for H2 is the smallest subset of all the terms of the full configuration interaction wavefunction that allows for proper dissociation to H+H. Approximate GVB orbitals can be transformed from the natural orbitals of the equivalent MCSCF wavefunction using the CI vector coefficients for the 20 and 02 configurations ofb a, which converge upon 2-½ as r as shown in the figure.

Page 6: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Transforming NOs to GVB orbitals

MCSCF orbitals b/a can be transformed straightforwardly into approximate GVB orbitals R/L:

The GVB overlap is:

c’1 and c’2 are renormalized CI vector coefficients

(See previous slide for plot of SRL for H2.)

Page 7: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Bonding in H2 1Σ+ – GVB model – 2.75 Å

HH

1L

1R

Page 8: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Bonding in H2 1Σ+ – GVB model – 1.65 Å

HH

1L

1R

Page 9: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Bonding in H2 1Σ+ – GVB model – 1.35 Å

HH

1L

1R

Page 10: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Bonding in H2 1Σ+ – GVB model – 1.05 Å

HH

1L

1R

Page 11: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Bonding in H2 1Σ+ – GVB model – 0.75 Å

HH

1L

1R

Page 12: Bonding orbital doubly occupied in HF wavefunction at r e antibonding orbital unoccupied in HF wavefunction at r e The animations depict 0.1, 0.15, and

Bonding in H2 1Σ+ – GVB model – ANIMATION

HH

1L

1R

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bonding orbital doubly occupied in HF wavefunction at r e