paper/result/perfect/non-polar/default.typ

@@ -45,21 +45,35 @@ It should be noted, however, that the observability in Raman experiment depends
 因此，拉曼张量的大小可以在进一步的第一性原理计算之前给出，结果总结在表中。
 我们的结果表明，756 附近的峰应该比其它峰具有更强的拉曼强度。
 
-A method to estimate the magnitudes of the Raman tensors based on symmetry analysis was proposed.
+A method to rapidly estimate the magnitudes of the Raman tensors was proposed (see appendix for details).
 This approach is founded on the symmetry analysis and incorporates the assumption
-  that the majority contribution of each atom to the Raman tensor is determined by its nearest neighbors
-    (denoted as $a_i$),
-  while contributions from more distant atoms are considered small (denoted as $epsilon_i$, $eta_i$, and $zeta_i$).
-Additionally, we neglect the absolute differences in amplitudes of the same type of atoms in a phonon mode,
-    focusing only on their vibrational directions.
-Consequently, the Raman tensors of the calculated phonon modes can be estimated
-    before additional first-principles computations (see appendix for details),
-  and the results are summarized in @table-nopol.
-The parameters $a_i$ exhibit significantly larger absolute values compared to $epsilon_i$, $eta_i$, and $zeta_i$,
-  indicating the E#sub[2] mode at 756.25 cm#super[-1] in simulation (mode 8)
-    possess a much higher Raman intensity than the others.
+  that the primary contribution from each atom to the Raman tensor arises from its nearest neighbors (denoted as $a_i$),
+  while contributions from more distant atoms are much smaller (denoted as $epsilon_i$, $eta_i$, and $zeta_i$).
+Furthermore, we neglect the absolute amplitude differences among atoms of the same type within a phonon mode,
+  considering only their vibrational directions.
+This enables a preliminary estimation of the Raman tensor magnitudes prior to detailed first-principles calculations,
+  with the results summarized in @table-nopol.
+Our analysis indicates that the E#sub[2] mode at 756.25 cm#super[-1] in simulation (mode 8)
+  should possess a much higher Raman intensity than the others.
 
-我们使用第一性原理计算得到了拉曼张量的大小，并与我们的结果进行了比较。
+#include "table-nopol.typ"
+
+我们使用第一性原理计算得到了频率和拉曼张量的大小，并与我们的结果进行了比较。
+
+声子频率和拉曼张量的大小被使用第一性原理计算，并与实验结果和理论预测进行了比较（@table-nopol）。
+计算的声子频率与实验数据有很好的吻合，误差在 2-5% 之间，这个误差可能是由于 PBE 泛函对原子间力的低估（cite）。
+计算的拉曼张量也与实验和理论结果基本一致，这包括
+  强度最高的模式 E#sub[2] 在 776 cm#super[-1] 的实验（模式 8），
+  其次是四个强度较低但在实验中清晰可见的模式，
+  包括 E#sub[2] 模式在 195.5 cm#super[-1]（模式 1）和 203.3 cm#super[-1]（模式 2），
+    E#sub[1] 模式在 269.7 cm#super[-1]（模式 3），
+    和 A#sub[1] 模式在 609.5 cm#super[-1]（模式 6）。
+在 746 cm#super[-1]（模式 7）计算的 E#sub[1] 模式
+  和 756.25 cm#super[-1]（模式 9）计算的 E#sub[2] 模式
+  被预测具有更弱的拉曼强度，并且位于最强模式（模式 8）附近，使得它们在实验光谱中难以区分。
+此外，在 812.87 cm#super[-1]（模式 10）计算的 A#sub[1] 模式
+  在基面极化配置（xx 和 yy，仅为 0.01）中具有非常弱的拉曼强度，
+  但当偏振沿 z 轴时（1.78）则显示出可观的强度。
 
 The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods,
   and the results are compared with both experimental data and theoretical predictions (@table-nopol).
@@ -97,8 +111,6 @@ Besides, there are small peeks at xxx,
 // 在论文中我们这样来称呼：phonon 对应某一个特征向量，而 modes 对应于一个子空间。
 // 也就是说，简并的里面有两个或者无数个 phonon，但只有一个 mode
 
-#include "table-nopol.typ"
-
 #include "figure-raman.typ"
 
 // TODO: 解释为什么 E1 可以看到