The ab initio molecular dynamics simulations of metallic, charged, and electrochemical systems require, in principle, the inclusion of unequally occupied electronic states. In this contribution, the general approach to work with fixed but arbitrary occupations within the Car-Parrinello molecular dynamics scheme is revisited, focusing on the procedure which is required to maintain the orthonormality constraints in the commonly used position-Verlet integrator. Expressions to constrain also the orbital velocities, as it is demanded by a velocity-Verlet integrator, are then derived. The generalized unequal-occupation SHAKE algorithm is compared with the standard procedure for damped dynamics (energy optimization) of systems including fully unoccupied electronic states. In turn, the proposed unequal-occupation RATTLE algorithm is validated by the corresponding microcanonical ensemble simulations. It is shown that only with the proper orthogonalization method, a correct ordering of states and energy conserving dynamics can be achieved.

中文翻译：

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具有不等电子职业的Car-Parrinello分子动力学的类似Verlet的算法

该从头金属，带电和电化学系统的分子动力学模拟原则上要求包含不相等占据的电子态。在此贡献中，重新讨论了在Car-Parrinello分子动力学方案中处理固定但任意职业的一般方法，重点是在常用的位置-Verlet积分器中维持正交性约束所需的过程。然后推导也约束速度-速度letlet积分器要求的轨道速度的表达式。将广义的不等占用SHAKE算法与包括完全未占用电子状态的系统的阻尼动力学（能量优化）的标准过程进行了比较。反过来，相应的微规范集成仿真验证了所提出的不占空间的RATTLE算法。结果表明，只有采用正确的正交化方法，才能实现正确的状态排序和节能动力学。