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)

Natural Orbitals for H 2 molecule (This time plotted as  along the y-axis) Animations of the amplitudes along the bond axis for the H 2 bonding and antibonding (natural) orbitals.

GVB Orbitals for H 2 (X 1  g + ) 1  R GVB orbital singly occupied for all r 2  L GVB orbital Singly occupied for all r The animations depict 0.1, 0.15, and 0.2 amplitude contours as com- puted for r e + n 0.1 Å for n = 0 to 20. The nuclei are indicated with + symbols. Individual frames are available.

Animations of the amplitudes along the bond axis for the H 2  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 H 2 at various point along the potential energy curve (and animated along the entire curve on the final slide). GVB Orbitals for H 2 (X 1  g + )

Transforming NOs to GVB orbitals The GVB wavefunction for H 2 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 of  b  a, which converge upon  2 -½ as r   as shown in the figure.

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 S RL for H 2.)

Bonding in H 2 1 Σ + – GVB model – 2.75 Å HH 1L1L 1R1R

Bonding in H 2 1 Σ + – GVB model – 1.65 Å HH 1L1L 1R1R

Bonding in H 2 1 Σ + – GVB model – 1.35 Å HH 1L1L 1R1R

Bonding in H 2 1 Σ + – GVB model – 1.05 Å HH 1L1L 1R1R

Bonding in H 2 1 Σ + – GVB model – 0.75 Å HH 1L1L 1R1R

Bonding in H 2 1 Σ + – GVB model – ANIMATION HH 1L1L 1R1R