Table 1 Computational Raman frequencies (in cm⁻¹) for Na₃PS₄ (\(P\overline{4}{2}_{1}c\), ICSD No. 121566) calculated with different levels of theory compared to experimental Raman frequencies measured at 100 K.

Mode No.	Mode Symmetry	PBE0	HSE06	R²SCAN	PBE0-D3	PBEsol	PBE	Exp.¹⁰
4–5	E	25	25	31	33	28	27	32
6	A1	71	71	79	77	70	67	70
7–8	E	72	72	80	92	80	71	84
9	B2	87	86	100	111	97	84	84
10–11	E	97	97	102	114	99	94	—
12	B1	100	100	105	116	100	96	—
13–14	E	120	120	125	127	117	116	—
15–16	E	123	123	131	154	137	120	—
18	A1	140	139	146	165	149	135	—
19–20	E	152	152	158	171	158	148	—
21–22	E	156	156	161	173	161	151	157
23	B1	157	156	162	188	164	152	157
24	B2	169	170	175	198	177	165	—
26	B1	175	175	180	207	184	170	—
27–28	E	196	196	200	218	198	188	—
29–30	E	198	197	203	224	203	190	—
31	A1	210	210	211	227	208	202	214
33	B1	227	226	227	239	219	216	226
34	B2	229	229	229	242	221	218	226
35	B1	272	271	269	280	261	258	276
36	B2	272	271	271	283	261	258	276
37–38	E	283	282	282	293	272	268	283
39–40	E	284	283	283	296	273	270	293
42	A1	415	413	404	421	392	387	413
43	B2	538	535	517	546	507	497	537
44–45	E	539	536	517	547	507	498	537
46	B1	569	567	552	579	541	531	567
47–48	E	571	568	553	580	542	533	570
Mean Absolute Error		3 [2]	3 [2]	8 [9]	11 [12]	14 [16]	17 [21]	—
Maximum Absolute Error		12 [9]	12 [10]	20 [20]	31 [31]	30 [30]	40 [40]	—
Mean Absolute Percentage Error		3% [1%]	3% [1%]	4% [2%]	7% [5%]	5% [4%]	6% [6%]	—

Mode number and mode symmetry are from calculations on the PBE0 level. The statistics in square brackets are for the frequencies >100 cm⁻¹.

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