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A many-electron system’s state can be represented with a reduced form of this matrix for two electrons rather than with the full wave function. For 10 points each:
[10m] Name this matrix that is constructed by summing the outer products of state vectors. This matrix is often used to represent mixed states.
ANSWER: density matrix [or density operator; accept two-electron reduced density matrix; prompt on 2-RDM]
[10e] Methods based on the two-electron density matrix, or 2-RDM methods, compute this state for many-electron systems. In QM, electrons can absorb energy to transition from this state to an excited state.
ANSWER: ground state
[10h] Two answers required. A 2-RDM method resolved a discrepancy concerning energy barriers to these two possible pathways for the ring opening of two butadiene derivatives. These terms describe the ways end carbons are repositioned when a sigma bond forms.
ANSWER: disrotatory AND conrotatory [accept suprafacial AND antarafacial]
<Chemistry>
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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
British ColumbiaNYU010010E
Chicago BCornell A1010020ME
Georgia StateLSE010010E
Georgia TechMinnesota010010E
Illinois AColumbia A10101030MEH
Illinois BColumbia B010010E
Johns HopkinsIowa State010010E
MITTexas10101030MEH
MarylandVirginia010010E
North Carolina ANorthwestern1010020ME
North Carolina BMichigan010010E
Ohio StateCornell B010010E
Penn StateOttawa010010E
StanfordWUSTL A1010020ME
Toronto AChicago A010010E
Toronto CToronto B010010E
UC Berkeley AIndiana10101030MEH
UCFVanderbilt0101020EH
Virginia TechHarvard010010E
WUSTL BArizona State1010020ME
Waterloo ARutgers10101030MEH
Waterloo BFlorida010010E
Winona StateRIT010010E
YaleUC Berkeley B010010E

Summary

TournamentExact Match?HeardPPBEasy %Medium %Hard %
2025 ACF NationalsYes2415.42100%33%21%