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arXiv 0812.1669cond-mat.mtrl-sci
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振动量子化对晶体结构性质的影响

Effect of quantization of vibrations on the structural properties of crystals

I. Scivetti, N. I. Gidopoulos, J. Kohanoff

摘要:

研究了零温下周期晶体中振动自由度量子化所产生的结构效应。为此,我们介绍了一种方法的基础上映射一个合适的子空间的振动流形和解决Schroedinger方程在it.A数量越来越准确的近似范围从准谐波近似(QHA)的振动自洽场(VSCF)方法和精确解。一个彻底的分析模型单原子和氢键链的近似,并提出了一个线性HF链的势能面通过第一原理电子结构计算得到的结果。我们专注于量子核效应的晶格常数,并表明,VSCF是一个很好的近似,这意味着模式之间的相关性并不是非常重要的。QHA对于共价键、轻度非谐体系是极好的,但对于氢键体系则不适用。在后者中,零点能量在H原子中心的晶格常数处表现出非解析行为,这导致量子校正能量曲线中的假次最小值。一个廉价的非谐波近似的非相互作用的模式似乎产生相当好的结果氢键链,小系统的尺寸。然而,它收敛到不正确的QHA结果的大小增加。研究了第一性原理HF链的同位素效应。我们展示了晶格常数和HF距离如何随着质量的减小而增加,以及QHA如何被证明不足以再现这种行为。

英文摘要:

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schroedinger equation in it. A number of increasingly accurate approximations ranging from the quasi-harmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monoatomic and hydrogen-bonded chains, and results are presented for a linear HF chain where the potential energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant, and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently-bonded, mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a non-analytic behavior at the lattice constant where the H-atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic appoximation of non-interacting modes appears to produce rather good results for hydrogen-bonded chains, for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles HF chain. We show how the lattice constant and the HF distance increase with decreasing mass, and how the QHA proves to be insufficient to reproduce this behavior.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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