Sunday, July 21, 2019
Quantum Chemistry: Molecular Geometry of Water Molecule
Quantum Chemistry: Molecular Geometry of Water Molecule Question 1: Optimize the molecular geometry of a water molecule (H2O) at HF/STO-3G level of theory in Gaussian-09 through the GaussView Visualization software package on the desktops provided. Give optimized bond length lengths and angles using this combination of methods and basis set. Ans. Bond Length = 0.98927 Ãâ¦ and the Bond Angle H-O-H is 100.035 degrees Recalculate the geometry using an alternative method of your own choice. Ans. Using Semi-empirical (PM6) we get a bond length of 0.94911 Ãâ¦ and a Bond Angle H-O-H is 107.488 degrees. Give molecular orbital diagram with drawings of the molecular orbitals. You may have to rerun the calculation with pop=full included. Ã Ans. Molecular orbitals for isolated H-O-H molecule were calculated using Hartree-Fock wave function and STO-3G basis set.  HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Occupied Molecular Orbital) HOMO LUMO HOMO: Mainly pz2 is character with no contribution from Hydrogen 1s orbital but contributes to lone pair effects. LUMO: O-H antibonding with greatest electron density around Oxygen atom. Lowest Energy Orbital 1a1 contributed by 1s orbital of Oxygen Atom (approximately spherical). 2nd Lowest Energy Orbital 2a1 (close to non-bonding) contributed mostly by 2s orbital of Oxygen Atom (approximately spherical). Also contributes to O-H bonds. Energy Orbital 1b2 (non-bonding) contributed by 1s orbital of Hydrogen Atom and 2s plus 2px orbitals of Oxygen Atom leading to O-H bonds. Energy Orbital 3a1 (non-bonding) contributed by 1s orbital of Hydrogen Atom and 2s plus 2pz orbitals of Oxygen Atom leading to O-H bonds. Highest occupied molecular orbital 1b1 (non-bonding) with pz2 character. No contribution from Hydrogen atoms. How will the geometry change when and electron from the highest occupied molecular orbital is removed? Calculate the energy of H2O+, i.e. water with a charge of 1 and multiplicity 2. Ans. Using Hartree-Fock Wave Function with STO-3G basis set for a Water molecule with +1 charge and multiplicity 2, we get Bond length = 0.96 Ãâ¦ Bond Angle H-O-H = 109.5 degrees Energy of H2O+ = -75.2017003581 A.U. (atomic units) How will the geometry change when an electron is removed from the second highest occupied molecular orbital of H2O? Ans. If an electron is removed from the second highest occupied molecular orbital and electron from the highest occupied molecular orbital will move down to stabilize the oxygen atom and giving it a negative charge leading to a single lone pair. The original water molecule has 2 lone pairs and repulsion leads to a bond angle approximately 104.5 degrees, on removing an electron the repulsion force decreases leading to a larger bond angle but the geometry will remain the same. Calculate the infrared spectrum of water Ans. For Hartree-Fock Wave Function and STO-3G basis set. How will the spectrum change when the hydrogen atoms are replaced by deuterium atoms? Ans. If the hydrogen atoms were replaced by deuterium the mass of the atoms bonding to the oxygen atom increases as deuterium is a heavier isotope that results in a drop in the frequency of vibration of the molecules with similar peaks. How will the spectrum change when the water molecule is in liquid phase rather than in the gas-phase? Ans. For Hartree-Fock Wave Function and STO-3G basis set. Question 2: Do a geometry optimization and frequency for cyclohexane in the chair and boat configurations in the gas phase. Template structures should be available in GaussView. Chose a density functional method and basis set. As this is a relatively large system, I would choose a modest basis set without polarization and diffuse basis functions. Which of the two structures is more stable? Ans. The chair conformer is more stable as compared to boat as the hydrogens in the chair conformation are well separated as compared to the boat conformer leading to less force of repulsion hence less energy and more stability.  Calculate the vibrational spectra of both structures. Give a comparison. Ans. Chair Conformation IR Spectra -> Boat Conformation IR Spectra -> More peaks in the IR spectra of the boat conformation due to more interactions. Higher energy due to more interactions as compared to chair conformation. The boat conformation is not stable and is only used for experimental purposes and cannot exist independently. How would you be able to identify percentages of chair and boat configuration from a mixture of the two? Ans. We can easily calculate the percentages of chair to boat by calculating the value of ÃÅ½Ã¢â¬ G between chair and boat and equating it to (- RT ln (Q)). The value of Q will give us the ratio of boat to chair conformer in a mixture of two. Chair Conformer Energy Boat Conformer Energy There will be a negligible difference between the energy for Chair Conformer at 10 cycles rather than 9 cycles. Hence, = 28.077 kJ/mol  Equating, where R= 0.008314 kJ/molK and T=273.15+27=200.15 K we get, Q=1.29866 * 10^-5 which is the ratio of boat to chair conformer present in the solution. Draw the dipole moment of the chair and boat configuration. Which of those structures will dissolve better in water and why? Ans. Chair conformer of cyclohexane has negligible dipole moment due to symmetry and equal charge distribution. On the other hand Boat conformation of cyclohexane has dipole moment due to the shape of the conformer making it polar due to charge distribution and steric effects. BOAT CONFORMER (Note: Grey spheres are C atoms and Blue spheres are H atoms) Hence the boat conformer is able to dissolve in water but stabilizes soon and turns into the chair conformer making it non-polar and separating it from water. How many different configurations of Fluoro-cyclohexane exist? Draw structures but do not minimize in Gaussian. Ans. Dipole moments of Fluoro-Cyclohexane have increased by a factor of 611.6 as compared to cyclohexane. This explains how the presence of a single fluoride atom instead of a hydrogen impacts the structure and charge distribution of the cyclic hydrocarbon. In turn adding a Fluoride atom also increases the energy of the cyclic hydrocarbon creating less stable structures in boat, twist and half chair increasing and decreasing the amount of other conformers in a solution compared to chair.  CHAIR CONFORMER BOAT CONFORMER (NOTE: Grey spheres are C atoms, White Spheres are H atoms and Blue Sphere is F atom) At room temperature only Chair Fluoro-Cyclohexane can exist but may transition between conformations that will be present for negligible time. REFERENCES: http://www.idc-online.com/technical_references/pdfs/chemical_engineering/Molecular_orbitals_for_water.pdf http://butane.chem.uiuc.edu/pshapley/GenChem2/A6/book.pdf https://en.wikipedia.org/wiki/Cyclohexane_conformation http://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/sterism2.htm http://www.virginia.edu/ep/Interactions/Constants_Units__Conversions.htm SOFTWARES: Gaussian(R) 09 Art in the Victorian Era | Analysis of Styles Art in the Victorian Era | Analysis of Styles The Victorian era was an age of peace and prosperity in Great Britain. The Victorian style is developed mainly in Great Britain during the reign of Queen Victoria, who became queen at the age of 18 years old. This movement takes place during the peak of the Industrial Revolution, in this moment, the science, as well as every other aspect of the society, were suffering big changes, with technological advances and a loss on the moral and religious values. This brought a search of rising the social dignity and tried to integrate all the arts in this harmonious and beautiful environment. The Victorian Era begins in 1837 and ends by the beginning of the 20th Century. The Victorian art is eclectic, it gathers the best of other styles, coming back to the Medieval. It uses richly ornamented objects and it has a taste for the naturalist inspired motifs, with great excess and saturation on the forms. A great interest for the daily spaces emerges, specially the dining room, for being a meeting point. The medieval themes are frequently used, full of knights and damsels, and comes back to the representation of religious scenes. Regarding to the painting, the Victorian era is a cult to the classical beauty, to counter the ugly modern world, result of an industrial revolution, where several topics are used, from the religious to the historical, and where the representation of women is recurrent. During the Victorian era, several artists tried to imitate the big former artists, previous the Industrial Revolution. The pre-Raphaelite movement is one of the most important of this period, formed by Dante Gabriel Rosetti, William Holman Hunt and John Everett Millais, mainly. The pre-Raphaelite tried to fight the teaching on the academies, and all the bad that the Industrial Revolution brought, wanting to recover a more spontaneous art, searching for inspiration on the natural, looking up to the big Reinassance artists. The Lady of Shalott, painted in 1888 by John William Waterhouse is a representative painting of this time. This oil on canvas is held nowadays at the Tate in London. This painting tells the story of Elena, the lady of Shalott, who was confined in a tower where she wove day and night. One day, a whisper announced that a terrible curse will await her if she ever looked at Camelot. In this painting we see Elena in a boat on her way to Camelot. The artist shows us a def enceless young lady, wearing a white tunic. She seems exhausted, a woman who has assumed her faith and her death, with a lost gaze and her arms lay in a surrender position. In the boat, Elena is carrying some of her fabrics, in these fabrics we can observe the adventures of the Knights of the Round Table, as well as the love she feels for Lancelot. The English landscape on the background is reduced to simple strokes. The rich colours and details are used to highlight the central figure. Waterhouse gives importance to the atmosphere, giving less importance to the design. It is a composition of isolation and despair. Waterhouse creates a balance in the composition by opposing the pale figure of the woman on one side of the painting with the horizon on the other. He uses warm and autumnal colours, maybe as a symbolism of Elenas imminent death. Waterhouse captures a sense of sorrow, giving Elena a bewildered look, a woman with no control in her life, a possible nod to the political powe r of women at the time. Victorian society was especially harsh on its female subjects, particularly regarding issues of sexuality and chastity. For instance, Augustus Eggs oil, Misfortune, caused a big shock when it was shown for the first time in 1858 at the Royal Academy. This painting is part of a triptych, which tells us the story of an infidelity and the consequences it had for a woman at the time. The subject of this painting was not only controversial but contemporary and topical. The scene happens in the living room, the husband is holding a letter, evidence of his wifes affair. He is looking to his wife, who is laying on the floor, she is wearing two bracelets in both arms that seem like handcuffs, maybe a symbolism of what the marriage supposed to her. There is religious symbolism as well, there is an apple cut in two, placed in two different spheres of the painting, one half on the floor next to the mother, and the other half by the knife on the table next to the father. On the left side of the p ainting, we see the two children playing with cards, they built a tower which is falling apart, symbolism of the marriage of their parents, only the big sister seems to acknowledge what is happening. We can also see a novel of Balzac at the base of the girls, as well as four small significant paintings on the wall, Adam and Eve expelled from the paradise hanging over the wifes portrait, and one of a shipwreck hanging over the husbands portrait. We can observe a pair of scissors on the table, maybe as a symbolism for the break up. The brushwork is precise, paying attention to the details. Dark colours are predominant in this painting, and the light comes from the left side of the painting, tenuously enlightening the room. Augustus Egg represents the deception of the fallen women, which became almost a trademark of the Victorian period, ex.: The Awakening Conscience by William Holman Hunt, in which we find similitudes such as the mirror in both scenes. The mirror in Eggs painting show s us an open door, through which the mother will soon leave. The mirror gives a sensation of depth by showing us the rest of the room. The Victorian era can be summed up in a series of changes caused by the Industrial Revolution. For many people this period represented a step back of all what had been achieved by the time, that will take artists to romanticize previous times, when everything seemed to be simpler, it was a fight against the progress and the unknown, marked by artistic tendencies which searched for a balance between the what it is beautiful and the new, resulting in a greater richness on the design. These two paintings are a representation of the artistic movement during the Victorian era. They both use recurring topics of the period. Bibliography. Rosenblum, R. Modern Painting and the Northern Romantic Tradition: Friederich to Rothko, Icon (Harpe), 1977. Rothenstein, J. Moder English Painters, Arrow Books, 1962. Treble, R. London: Victorian Paintings. The Burlington Magazine 122, no. 925 (1980): 274-77.