4-component Relativistic Calculations in a Multiwavelet Basis with Improved Convergence

Autor:	Tantardini, Christian, Eikås, Roberto Di Remigio, Frediani, Luca
Rok vydání:	2023
Předmět:	Physics - Chemical Physics
Druh dokumentu:	Working Paper
Popis:	The many-body wave function of an $N$-electron system within a relativistic framework can be described by the Dirac equation. Unfortunately, the Dirac operator $\hat{\mathfrak{D}}$ is unbounded and in case we would describe anions we will observe the variational collapse of wavefunction of $N+1$ electron. Thus, it is necessary to avoid it and an alternative approach is based on applying the square of the Dirac operator $\hat{\mathfrak{D}}^{2}$. This approach is especially suitable for a multiwavelet framework: its implementation in an integral equation form is readily available and the completeness of the multiwavelet basis guarantees that the matrix representation of $\hat{\mathfrak{D}}^{2}$ in the occupied space is identical to the square of the matrix representation of $\hat{\mathfrak{D}}$. This equivalence is not valid in a finite basis set. The use of the $\hat{\mathfrak{D}}^{2}$ operator within a multiwavelet framework is able to achieve higher precision compared to the $\hat{\mathfrak{D}}$, consistent with the quadratic nature of the error estimates in a variational framework. Comment: Submitted to Theoretical Chemistry Accounts
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.03290 Zobrazit plný text záznamu View this record from Arxiv