Thermodynamics of Forming Water Clusters at Various Temperatures and Pressures by Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO Model Chemistries; Implications for Atmospheric Chemistry

The Gaussian-2, Gaussian-3, complete basis set- (CBS-) QB3, and CBS-APNO methods have been used to calculate ΔH° and ΔG° values for neutral clusters of water, (H2O)n, where n = 2−6. The structures are similar to those determined from experiment and from previous high-level calculations. The thermodynamic calculations by the G2, G3, and CBS-APNO methods compare well against the estimated MP2(CBS) limit. The cyclic pentamer and hexamer structures release the most heat per hydrogen bond formed of any of the clusters. While the cage and prism forms of the hexamer are the lowest energy structures at very low temperatures, as temperature is increased the cyclic structure is favored. The free energies of cluster formation at different temperatures reveal interesting insights, the most striking being that the cyclic trimer, cyclic tetramer, and cyclic pentamer, like the dimer, should be detectable in the lower troposphere. We predict water dimer concentrations of 9 × 1014 molecules/cm3, water trimer concentrations of 2.6 × 1012 molecules/cm3, tetramer concentrations of approximately 5.8 × 1011 molecules/cm3, and pentamer concentrations of approximately 3.5 × 1010 molecules/cm3 in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using Complete Basis Set and Gaussian-n Models combined with CPCM Continuum Solvation Methods

Complete basis set and Gaussian-n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pKa values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol, to calculate pKa values with cycle 1. The complete basis set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Accurate pKa Calculations for Carboxylic Acids Using Complete Basis Set and Gaussian-n Models Combined with CPCM Continuum Solvation Methods”

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pKa values for six carboxylic acids. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol to calculate pKa values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit.

Accurate relative pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with continuum solvation methods

The complete basis set methods CBS-4, CBS-QB3, and CBS-APNO, and the Gaussian methods G2 and G3 were used to calculate the gas phase energy differences between six different carboxylic acids and their respective anions. Two different continuum methods, SM5.42R and CPCM, were used to calculate the free energy differences of solvation for the acids and their anions. Relative pKa values were calculated for each acid using one of the acids as a reference point. The CBS-QB3 and CBS-APNO gas phase calculations, combined with the CPCM/HF/6-31+G(d)//HF/6-31G(d) or CPCM/HF/6-31+G(d)//HF/6-31+G(d) continuum solvation calculations on the lowest energy gas phase conformer, and with the conformationally averaged values, give results accurate to ½ pKa unit. © 2001 American Institute of Physics.

Shading Silhouettes of Smaller Ones

I am truly honored to have been given the amazing opportunity to create this original piece, this powerful journey through memory and emotive exploration of the loss of childhood. How do we feel about the loss of our child-self? Could we ever get them back? How long, how deep would one have to dig in the graveyards, the playgrounds of memory, to uncover what was buried there... to un-erase what waserased? shading silhouettes of smaller ones will ultimately encourage a reconnection with the Inner Child hidden inside all of us, as well as an intimate awareness of the adult version of the self by looking back to the smaller ones. The main inspiration for this piece is then of course, Inner Child Work. Most people may not be familiar with this therapeutic exploration of childhood... It wasimportant to me then, to present this concept in an imaginative, theatrical way, as a gift to you - a comprehensive and intensely moving gift. Speaking from experience, working on my Inner Child - my little Bianca - has been the most painful, frightening, yetrewarding and powerful experience within my personal life. Some people spend their entire lives trying to love themselves, to prove themselves, or be accepted. Some are too afraid to look back to where it all began. The characters within this piece will face thatfear... in a regression from the complexities of adulthood to the confusion of adolescence, all the way back to the wonder and bliss of childhood. They will reveal memories, of both joy and pain, love and abandonment, journeying backwards through time - through memory - through a playground - back to the beginning... We will enter a world where a push of a merry-go-round spins us to games of Truth or Dare after a high school dance at 16 - or the slam of a metal fence reminds us of the door Dad slammed in our face at 9 - where the sound of chain links swings us back to scrapping our knee by the sandbox at 5 This piece will attempt to connect everyone, both cast and audience, through a universal understanding and discussion of what it means to grow up, as well as a discovery of WHY we are the way we are - how experiences or relationships from our childhood have shaped our adult lives. We will attempt to challenge your honesty and nerve by inviting you to ask questions of yourselves, your past - to remember what it's like to have the innocence and hope of a child, to engage with and discover your Inner Child, to realize when or why you left them behind, and if you want to this magical part of yourself. It is my hope that you will join us in a collective journey - gather the courage to dig up the little kid you buried so long ago...* The creation, design, choreography, and direction for shading silhouettes of smaller ones mark the culminating experience of a year-long independent study in Theatre.