Quantum-Mechanical Hamiltonians for Constrained Systems: Application to Four-Body Systems

The Decoupling of Electronic and Nuclear Motions in the Isolated Molecule Schrödinger Hamiltonian

“…There has been much previous work along these lines, but most of it has been in the context of particular coordinate choices. However, both Chapuisat and his colleagues [26,27] and Handy and his [28,29], among others, for example, Lukka [30], have presented rather general and abstract accounts of the methodology. Additional reviews have been provided by Sutcliffe [31-331.…”

Quantum-Mechanical Description of Rigidly or Adiabatically Constrained Molecular Systems

“…2 ) The dynamics of an N-particle system in terms of curvilinear coordinates rests on the relations between the 3N body-({gggЉ} Å {xyz}, {yzx}, {zxy}) fixed (BF) Cartesian atomic coordinates x Å (x 1 (13)(14)(15). The following must be known: either 3N relationships of the type x Å x(q) and the BF frame is…”

“…small polyatomic molecules are the most difficult works that A general method for expressing with no approximation can be achieved. the kinetic energy operators for rigidly constrained systems In order to treat four-particle or larger systems, two ap-has been previously proposed (1). The topic is reviewed proaches are basically possible: (i) Consider all internal de-in Section 2.…”

“…However, the corresponding exact kinetic energy tion of the low-lying bands of the infrared spectra of four-operator cannot be straightforwardly written, even if the opatom molecules described in terms of curvilinear internal erator for the constraint-free system is known. Indeed comcoordinates (2), (ii) nearly ab initio dynamical calculations pelling model constraints modify the metric of the configurafor bimolecular systems (reactive or inelastic) involving ei-tion space; i.e., the Jacobian to be used in the differential ther diatomic molecules (3) or an atom and a small poly-element for the calculation of the Hamiltonian matrix eleatomic molecule (4), and (iii) the dynamical study of the ments is changed, so that the Hamiltonian operator must also relative degrees of freedom of dimers (5) or trimers (6) of be changed (1,10). small polyatomic molecules are the most difficult works that A general method for expressing with no approximation can be achieved.…”

The rovibrational kinetic energy for complexes of rigid molecules

“…A general analysis of internal constraints on n body systems has been given by Menou and Chapuisat [10] and by Gatti et al [11]. These authors observe that such a formalism may be applied to find the rovibrational kinetic energy of a rigid body complex, though they do not derive such a kinetic energy.…”