INTRODUCTION
Analytical derivatives of the electronic energy of a chemical system are of utmost importance for the study of chemical properties, including but not limited to geometric and electric properties, vibrational-rotational spectra and reaction dynamics. In the last years, much effort has been put onto developing new quantum-chemical methods and computational algorithms, thus rendering ab initio energy-derivative calculations very efficient and almost transparent to the (computational) chemist.
One further step is still possible in the reduction of the time needed to evaluate second and higher energy derivatives: the use of floating basis functions, i.e., functions which are not necessarily centered on atoms, but whose positions are floated away from nuclei and optimized. Wavefunctions using floating basis functions have the important property of satisfying the Hellmann-Feynman theorem,1-3 which leads to important reductions in the time needed to evaluate energy derivatives. Hirao3. has recently taken profit of this property and shown the fast speed of calculating energy derivatives for wavefunctions which obey the theorem. This faster methodology implies thus the possibility of studying much larger molecules.
Use of floating functions brings about another major advantage, because the separation between atomic and basis centers may result into polarization4 taking place. Therefore, chemical systems where polarization basis functions are needed for reaching a certain level of quality in non-floating, nuclei-following basis set calculations may be studied with a smaller basis set (at least at a semiquantitative level) if floating functions are employed.
The literature on floating functions is not especially large, but has received renewed attention lately. Hurley5 was one of the first researchers to attack the problem long time ago. Later, Frost 6 used floating spherical gaussian orbitals in which the exponents and centers were optimized. In turn, electric-field variant gaussian orbitals were used by Sadlej. 7 Gerratt and Mills9,10 showed later how energy second derivatives can be calculated taking profit of the Hellmann-Feynman theorem, leading to the development of the so-called coupled- perturbed Hartree-Fock equations. Early applications to chemical structure and reactivity were carried out by Nakatsuji,11,12 Also, Moccia13 and Huber14-17 dealt with optimization techniques of function centers.
A recent paper by Helgaker and Almlöf4 studied systematically molecular properties using floating Gaussian-type functions. Likewise, Hurley18 analyzed the use of floating functions in gradient calculations. Furthermore, Hirao3.A used the Hellmann-Feynman theorem for accelerating energy derivative calculations, whereas Hirao and Mogi19 discussed very recently the properties of various floating schemes and applied them to various levels of energy calculation to show how the Helmann-Feynman theorem was satisfied. Finally, Darling and Schlegel 20 studied how electric field-dependent functions can improve the calculated values of electric properties.
This paper focuses on one aspect which still remains rather unclear from earlier studies: the difficulty (i.e., cost) of obtaining wavefunctions using floating basis functions. Another goal of this paper is to assess the importance of using floating basis functions when computing molecular properties. Special emphasis will be laid in estimating the vibrational Stark effect, the vibrational intensity effect and the vibrational contribution to electrical properties. The vibrational Stark effect and vibrational intensity effect are reported from the first order Stark tuning rate (þþE) and from the infrared cross section changes (þSE), respectively.21-24
