Ab-initio assessment of conventional standard-state thermodynamic properties of geochemically relevant gaseous and aqueous species M. Vetuschi Zuccolini n , G. Ottonello, D. Belmonte Laboratorio di Geochimica, DIPTERIS, Universit  a di Genova, Corso Europa 26, 16132 Genova, Italy article info Article history: Received 24 March 2009 Received in revised form 17 February 2010 Accepted 13 March 2010 Available online 4 November 2010 Keywords: Thermodynamics First principles methods Implicit solvation PCM abstract After some introductory remarks on the essential basic concepts concerning isolated (gas state) atoms and molecules (adiabatic vs. vertical ionization potential and electron affinity; dissociation energy), we will show how their (absolute) internal energy and enthalpy (i.e. ‘‘thermal corrections’’ to the energy of the molecule) may be converted into the conventional counterparts of common use in thermochemistry through an appropriate thermochemical cycle. The first-principles acceptation of entropy, in terms of translational, rotational, vibrational, and electronic contributions to the bulk partition function, will then be briefly restated, emphasizing that, for practical calculations, the V-dependency of the translational terms can be converted into a P-dependency with the perfect gas law. The entropy of ‘‘aqueous’’ species will then be discussed after some preliminary remarks on the significance of the ‘‘solvation entropy’’ in terms of a Polarized Continuum Model (PCM) conceptual framework, and some comments on the energy of the ‘‘hydronium ion’’ H 3 O + . Some comments on the nature of the electrostatic portion of the solvation entropy, in terms of the Born solvation theory, and the non-electrostatic portion (solvent collapse + cavity formation+dispersion+repulsion+liberation entropy terms), will then be made, showing how this last term may be computed practically by exploiting its analogy with the Helgeson–Kirkham–Flowers electrostatic approach. After some elementary application of the various concepts to the gaseous state, we will present a potential application of major use in geochemistry, i.e. the possibility of computing ab-initio the interaction parameters (i.e. individual activity coefficients) of complex ions in solution through PCM procedures. We will then discuss the state of the art attained in determining ab-initio the pK a scale of organic and inorganic acids, perhaps the most demanding task, due to the high level of internal precision required. Finally, we will give some examples of the application of the assessment of the Gibbs free energy of formation from the elements (G f 1), the enthalpy of formation from the elements (H f 1), and entropy (S1) at standard state (hypothetical 1-molal solution referred to infinite dilution at 298.15 K and 10 5 Pa) on geochemically relevant aqueous species of heavy metals. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction Improvements in computing capability and the development of accurate computational codes have made it possible to investigate the structure and energy of gaseous and aqueous species with ab-initio all-electron approaches. Textbooks, reviews and single applications to the realm of geochemistry have appeared over the years (see for instance Tossel and Vaughan, 1992; Rosso, 2001, and references therein; Di Tommaso and de Leeuw, 2009). Although quite demanding, in some circumstances computational results also offer an independent way of assessing thermodynamic proper- ties based on ab-initio molecular orbital theory. Details of the various procedures may be found in such textbooks as Hehre et al. (1986), Irikura and Frurip (1998), and Mennucci and Cammi (2008), which we would refer the reader to. Here we have limited ourselves to drawing the reader’s attention to some practical aspects encountered when performing the appropriate absolute-to-con- ventional conversions that are necessary to obtain values consistent with the extensive thermodynamic tabulations at our disposal. To do this, we must make some introductory remarks on several basic concepts (probably obvious to the majority of the readers). We will then discuss some potential applications of major use in geochem- istry, such as the possibility of computing ab-initio the interaction parameters (i.e. activity coefficients) of complex ions in solution through Polarized Continuum Model (PCM) procedures and we will then give some examples of applications to the assessment of the Gibbs free energy of formation of the elements (G1 f ), enthalpy of formation from the elements (H1 f ) and entropy (S1) at standard state (hypothetical 1-molal solution referred to infinite dilution at 298.15 K and 10 5 Pa) based on the results we have obtained from an elementary investigation of some aqueous heavy metal complexes of geochemical interest. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/cageo Computers & Geosciences 0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2010.03.024 n Corresponding author. Tel.: + 39 10 3538136; fax: + 39 10 352169. E-mail address: zucco@dipteris.unige.it (M. Vetuschi Zuccolini). Computers & Geosciences 37 (2011) 646–661