Симетрія парності в ряді проблем квантової та структурної хімії
Анотація
Дається синтетичний огляд і нові результати з теорії та застосувань альтернантної симетрії на засадах єдиного підходу, що базується на використанні операторів J-симетрії (симетрії парності). Останні, на відміну від типової комутації, антикомутують з гамільтоніанами або іншими придатними операторами. Ми трактуємо в виразах J-симетрії різноманітні теми та проблеми, котрі здебільша пов’язано з π-оболонками супряжених молекул. Зокрема окреслено різноманітні орбитальні теорії із систематичним використуванням блок-матричної техніки (матриці густини, операторні функції тoщо). В контексті проблем електричної провідності поодиноких молекул вивчено π-моделі та їхня J–симетрія поруч із способами розрахунку функцій Гріна та електронної трансмісії. Ми підкреслюємо принципову важливість врахування π-електронної кореляції для правильного описування π-спектру трансмісії. Розглянуто особливості електронної структури радикальних станів альтернантів та придатність спінового правила Ліба-Овчинникова, котре є результатом дії J–симетрії у згоді з ефектами електронної кореляції. Показано, як спрощена (заснована на хюккелівських МО) спін-поляризаційна модель забезпечує коректні оцінки числа ефективно розпарених електронів в полірадикалоїдних альтернантах. Інший тип задач стосується до проблеми молекулярної хіральності (взагалі структурної асиметрії). Аналіз спектру раніше впровадженого оператора хіральності дав можливість реінтерпретувати проблему у виразах J–симетрії. Це дозволило зконструювати новий оператор хіральності, який є невід’ємно визначеним та який зникає на ахіральних структурах. Його найпростіший інваріант, матричний слід, слугує за кількісну міру структурної або електронної хіральності. Попередні розрахунки свідчать, що новий індекс хіральності поводиться розумно, навіть для високо симетричних хіральних систем.
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