Tao Jianmin, Perdew John P
Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA.
Phys Rev Lett. 2005 Nov 4;95(19):196403. doi: 10.1103/PhysRevLett.95.196403. Epub 2005 Nov 1.
Density-functional approximations for the exchange-correlation energy Exc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current jp(r) is present, Vignale and Rasolt have extended the Kohn-Sham theorems and presented an additive correction valid to second order in the gauge-invariant vorticity nu=Delta x (jp/n):Exc[n, jp]=Exc[n, jp=0] + DeltaE(VR)(xc)[n, nu]. Apart from spin-polarization effects, their correction is unambiguous for a generalized gradient approximation (GGA). But for a meta-GGA (MGGA), one needs to know how to go back from the orbital kinetic energy density tau([n, jp];r) to tau([n,0];r); we show how to do this here. Numerical tests on the degeneracies for open-shell atoms show that current-density corrections reduce the error of GGA from 2 to 1 kcal/mol, and of MGGA from 5 to 2 kcal/mol.
多电子基态交换关联能Exc[n]的密度泛函近似已高度发展且用途广泛。当存在顺磁电流jp(r)时，维尼亚莱（Vignale）和拉索尔特（Rasolt）扩展了科恩-沈（Kohn-Sham）定理，并给出了一个在规范不变涡度nu = Δ×(jp/n)中二阶有效的加性修正：Exc[n, jp] = Exc[n, jp = 0] + ΔE(VR)(xc)[n, nu]。除自旋极化效应外，对于广义梯度近似（GGA），他们的修正是明确的。但对于元广义梯度近似（MGGA），需要知道如何从轨道动能密度tau([n, jp];r)回到tau([n,0];r)；我们在此展示如何做到这一点。对开壳层原子简并性的数值测试表明，电流密度修正将GGA的误差从2千卡/摩尔降低到1千卡/摩尔，将MGGA的误差从5千卡/摩尔降低到2千卡/摩尔。
