Ground-state potential energy

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a hamionic excited state is used because that is the way the first calculations were perfomied.) (a) The classical trajectory that originates from rest on the ground-state surface makes a vertical transition to the excited state, and subsequently undergoes Lissajous motion, which is shown superimposed, (b) Assuming a vertical transition down at time (position and momentum conserved) the trajectory continues to evolve on the ground-state surface and exits from chaimel 1. (c) If the transition down is at time 2 the classical trajectory exits from chaimel 2 (reprinted from [52]).

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

Figure 3. Relaxed triangular plot [68] of the U3 ground-state potential energy surface using hyperspherical coordinates. Contours, are given by the expression (eV) — —0.56 -t- 0.045(n — 1) with n = 1,2,..,, where the dashed line indicates the level —0.565 eV. The dissociation limit indicated by the dense contouring implies Li2 X Sg ) -t- Li.

If we require similar information regarding the ground state potential energy surface in a polyatomic molecule the electronic emission specttum may again provide valuable information SVLF spectroscopy is a particularly powerful technique for providing it. 

The photochemical behavior of butadienes has been closely studied. When these compounds are exposed to light, they move from the ground state to an excited state. This excited state eventually returns to one of the ground state conformations via a process that includes a radiationless decay (i.e., without emitting a photon) from the excited state potential energy surface back to the ground state potential energy surface. 

Iordanov TD, Davis JL, Masunov AE, Levenson A, Przhonska OV, Kachkovski AD (2009) Symmetry breaking in cationic polymethine dyes, part 1 ground state potential energy surfaces and solvent effects on electronic spectra of streptocyanines. Int J Quantum Chem 109 3592-3601... 

For a recent list of references to calculations of parts of ground state potential energy hypersurface see Salem, L. Accounts Chem. Res. 4, 322 (1971). 

Figure 4. Ground-state potential energy curves of Hs from 2-RDM and wavefunction methods are shown. MP2 and MP4 denote second- and fourth-order perturbation theories, while CCSD and CCSD) represent coupled cluster methods.

Comprehensive theoretical investigations of such retro-Diels-Alder reactions, with particular attention devoted to the very rapid transitions between photoexcited and ground-state potential energy surfaces at conical intersections, have appeared." ... 

Fig. 5. The pseudo-Jahn-Teller effect in ammonia (NH3). (a) CCSD(T) ground state potential energy curve breakdown of energy into expectation value of electronic Hamiltonian (He), and nuclear-nuclear repulsion VNN. (b) CASSCF frequency analysis of pseudo-Jahn-Teller effect showing the effect of including CSFs of B2 symmetry is to couple the ground and 1(ncr ) states to give a negative curvature to the adiabatic ground state potential energy surface for the inversion mode.

We also performed extensive DFT studies on both the full target system and the model for calibration purposes. For details of one-electron basis sets used please consult Ref. (55). We used the B3LYP functional but found the ground-state potential energy surface to be relatively insensitive to the chosen functional (note though that this does not mean that DFT gives the correct surfaces, as important nondynamical correlation effects are... 

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