Permutationally Invariant Potential Energy Surfaces

Over the past decade, about 50 potential energy surfaces (PESs) for polyatomics with 4–11 atoms and for clusters have been calculated using the permutationally invariant polynomial method. This is a general, mainly linear least-squares method for precise mathematical fitting of tens of thousands of electronic energies for reactive and nonreactive systems. A brief tutorial of the methodology is given, including several recent improvements. Recent applications to the formic acid dimer (the current record holder in size for a reactive system), the H 2 -H 2 O complex, and four protonated water clusters H + (H 2 O) n=2,3,4,6 are given. The last application also illustrates extension to large clusters using the many-body representation.