Question
Kato’s theorem states that this quantity exhibits a cusp at the location of the nucleus. For 10 points each:
[10h] Name this quantity, which uniquely specifies an atom’s ground-state properties per the first Hohenberg-Kohn theorem. A common computational chemistry approach involves solving for functionals of this quantity.
ANSWER: electron density [accept density functional theory; prompt on DFT]
[10e] A brute-force approach to DFT involves not using the molecular type of these constructs. The atomic type of these constructs specify the location of an electron in “shells” around the nucleus and come in s, p, d, and f types.
ANSWER: orbitals [accept atomic orbitals or molecular orbitals; reject “orbit(s)”]
[10m] To explain the symmetric structure of methane, Linus Pauling posited this phenomenon, where orbitals mix to create symmetric bonds by forming namesake sp and sp2 orbitals.
ANSWER: orbital hybridization [or hybridized orbitals or hybrid orbitals]
<Chemistry>
Summary
| 2024 ACF Fall at Cornell | fall | Y | 9 | 14.44 | 100% | 44% | 0% |
| 2024 ACF Fall at Ohio State | fall | Y | 8 | 20.00 | 100% | 100% | 0% |
| 2024 ACF Fall at Washington | fall | Y | 6 | 16.67 | 100% | 67% | 0% |
| 2024 ACF Fall at Georgia | fall | Y | 12 | 13.33 | 75% | 50% | 8% |
| 2024 ACF Fall at North Carolina | fall | Y | 9 | 18.89 | 100% | 89% | 0% |
| 2024 ACF Fall at Claremont Colleges | fall | Y | 4 | 15.00 | 75% | 75% | 0% |
| 2024 ACF Fall at Rutgers | fall | Y | 8 | 21.25 | 100% | 88% | 25% |
| 2024 ACF Fall at Illinois | fall | Y | 9 | 20.00 | 100% | 89% | 11% |
Data
| Maryland B (DII) | Bard A (UG) | 0 | 10 | 10 | 20 |
| Columbia A (UG) | Penn B (DII) | 10 | 10 | 10 | 30 |
| Columbia B | Lehigh A (UG) | 0 | 10 | 10 | 20 |
| Fordham A | Princeton A (UG) | 0 | 10 | 0 | 10 |
| Maryland A (DII) | Penn A (DII) | 0 | 10 | 10 | 20 |
| Columbia J (DII) | NYU A (UG) | 10 | 10 | 10 | 30 |
| Rutgers A (UG) | Rowan A (DII) | 0 | 10 | 10 | 20 |
| Rutgers B | NYU B | 0 | 10 | 10 | 20 |