The gaseous sulfuric acid and its hydrates play an essential role in the formation and evolution of atmospheric aerosols via nucleation of binary sulfuric acid−water vapors. Recently, it has been pointed out that the dipole moment of vapor molecules and small preexisting clusters is a new parameter controlling the nucleation rates. In this paper, the dipole moments of the mono-, di-, and trihydrates of the sulfuric acid are calculated for the first time. We also report on the molecular structures, energies, vibrational frequencies, absorption intensities and dipole moments of the hydrates and compare our model predictions with the results of other studies. The density functional theory (DFT) calculations have been carried out using the PW91 method and TZP basis set. We have determined the optimized conformations of gas-phase sulfuric acid and mono-, di-, and trihydrates of sulfuric acid using different starting scenarios and computed their dipole moments. The obtained results can be utilized directly in the modeling of the atmospheric aerosol formation and they are applied for the analysis of the hydration thermodynamics.

Nadykto et al. Reply: In our Letter [1], we have applied a quantum approach for studying the sign preference and performed a first systematic quantum study of this puzzling phenomenon. Quantum methods have been progressing continuously since Schrödinger's original work [2], and their development has reached the stage when ''chemical properties can often be calculated with wave functionbased methods as well or better than they can be measured'' [3].Based on the additional information provided by Kathmann, Schenter, and Garrett [4], we can conclude that their curves [5] for positive and negative ions given in Fig. 2(b) should be simultaneously scaled by 8:63 kcal mole ÿ1 . Scaled curves for X (SM) and X ÿ (LG) are quite close to both our results and experimental data for Na H 2 O n and Cl ÿ H 2 O n , respectively. However, the simultaneous scaling of curves [5] for positive and negative ions does not affect G A i;iÿ1 ÿ G B i;iÿ1

Observed first in Wilson's pioneering experiments in the cloud chamber, the sign preference has remained a mystery for more than a century. We investigate the sign preference using a quantum approach and show that this puzzling phenomenon is essentially quantum in nature. It is shown that the effect of the chemical identity of the core ion is controlled by the electronic structure of the core ion through the influence on the intermolecular bonding energies during the initial steps of cluster formation. Our results demonstrate the superiority of the quantum approach and indicate fundamental problems of conventional ion-induced nucleation theories, in which the electronic structure of the core ion is either ignored or not treated rigorously.