From owner-chemistry@ccl.net Sat Jun 3 11:45:00 2023 From: "Cheng Fei Phung feiphung%hotmail.com" To: CCL Subject: CCL: Understanding ADAPT-VQE-SCF Message-Id: <-54934-230603114337-14052-pOtZeWOXuWATeYS6VUOWig]_[server.ccl.net> X-Original-From: "Cheng Fei Phung" Date: Sat, 3 Jun 2023 11:43:36 -0400 Sent to CCL by: "Cheng Fei Phung" [feiphung.:.hotmail.com] Could anyone explain what equations 12 to 15 are trying to tell for `ADAPT-VQE-SCF` https://arxiv.org/abs/2212.11405 ? From owner-chemistry@ccl.net Sat Jun 3 15:39:01 2023 From: "Susi Lehtola susi.lehtola#alumni.helsinki.fi" To: CCL Subject: CCL: Understanding ADAPT-VQE-SCF Message-Id: <-54935-230603153128-22226-WbWCWhg3Z9KFRS3nrE0i2A-*-server.ccl.net> X-Original-From: Susi Lehtola Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=UTF-8 Date: Sat, 3 Jun 2023 22:31:12 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola{:}alumni.helsinki.fi] On 6/3/23 18:43, Cheng Fei Phung feiphung%hotmail.com wrote: > > Sent to CCL by: "Cheng Fei Phung" [feiphung.:.hotmail.com] Could anyone > explain what equations 12 to 15 are trying to tell for `ADAPT-VQE-SCF` > https://arxiv.org/abs/2212.11405 ? Equation 12 is the second-quantized molecular Hamiltonian. Equation 13 is the one-electron part of the Hamiltonian. Equation 14 are the two-electron integrals. Equation 15 is the second-quantized Hamiltonian of Eq 12 rewritten in terms of the two-particle reduced density matrix. All of the above is standard textbook second quantization. If you wish to understand this, I recommend e.g. the classic book Molecular Electronic-Structure Theory by Trygve Helgaker, Poul Jørgensen, and Jeppe Olsen, which discusses second quantization in its very first chapter and also discusses in detail many of the core methods and algorithms of wave function based electronic structure theory. https://onlinelibrary.wiley.com/doi/book/10.1002/9781119019572 -- ------------------------------------------------------------------------------ Mr. Susi Lehtola, PhD Academy of Finland research fellow susi.lehtola*o*helsinki.fi Associate professor, computational chemistry http://susilehtola.github.io/ University of Helsinki, Finland ------------------------------------------------------------------------------ Susi Lehtola, FT akatemiatutkija susi.lehtola*o*helsinki.fi dosentti, laskennallinen kemia http://susilehtola.github.io/ Helsingin yliopisto ------------------------------------------------------------------------------