Born–Oppenheimer potential energy curves of NaK from the optimised atomic basis sets

Figures & data

Table 1. The optimised Gaussian exponents of atomic orbitals s, p, and d for sodium and potassium atoms.

Na			K
s	p	d	s	p	d
1.370519	0.311924	0.887695	1.082205	0.206216	0.979704
0.939692	0.129085	0.112686	1.069245	0.047287	0.323243
0.394043	0.040638	0.031485	0.605437	0.028605	0.086434
0.083874	0.016706	0.012876	0.255401	0.012394	0.028052
0.041838	0.007092	0.006103	0.048138	0.005074	0.010874
0.021195		0.003247	0.021701		0.003537
0.006804			0.005294		0.001150
0.006103			0.004217		0.000374
0.000153			0.001999

Table 2. Asymptotic values and ${\delta }_A$, i.e. the difference between the obtained results and the experimental data [39,40,42].

Na	K	Calculated asymptotic energies (cm${}^{-1}$)	${\delta }_A$ (cm${}^{-1}$)
$2p^{6}3s$	$3p^{6}4p$	13023.56	−0.10
$2p^{6}3p$	$3p^{6}4s$	16967.65	0.02
$2p^{6}3s$	$3p^{6}5s$	21026.22	−0.33
$2p^{6}3s$	$3p^{6}3d$	21535.28	−0.32

Figure 1. Adiabatic potential energy curves of the NaK molecule for five states with symmetry ${}^1{\mathrm{\Sigma }}^{+}$.

Figure 2. (a) The comparison of the current results of the adiabatic potential energy curves with the potentials derived from experimental data [25,27,28] for the 3–5${}^1{\mathrm{\Sigma }}^{+}$ (the graph is scaled by the value of the bond energy for the present ground state), (b) error plot, i.e. the value of the difference between the current results and the experimental data [25,27,28] for given distances.

Table 3. Spectroscopic constants of the ground and excited ${}^1{\mathrm{\Sigma }}^{+}$ states.

State	Reference	$R_e$ (Å)	$D_e$ (cm${}^{-1}$)	$T_e$ (cm${}^{-1}$)	${\omega }_e$ (cm${}^{-1}$)
$1^1{\mathrm{\Sigma }}^{+}$	Present	3.476	5252	0	123.72
	Experiment (2008) [44]	3.499	5273.62	0	–
	Experiment (2000) [45]	3.499	5273.67	0	124.03
	Experiment (1985) [13]	3.498	5275	0	124.01
	Theory (2016) [31]	3.537	5034	0	119.60
	Theory (2011) [43]	3.480	5186	0	123.50
	Theory (1996) [30]	3.477	5187	0	123.44
	Theory (1984) [46]	3.498	5170	0	123.80
	Theory (1984) [47]	3.413	5491	0	127.60
	Theory (1983) [48]	3.392	5000	0	132.00
$2^1{\mathrm{\Sigma }}^{+}$	Present	4.170	6171	12,105	81.59
	Experiment (1988) [14]	4.196	6220	12,137	81.25
	Theory (2016) [31]	4.236	6121	11,933	78.50
	Theory (1996) [30]	4.181	6121	12,089	81.00
	Theory (1984) [47]	4.064	6532	12,011	86.20
	Theory (1983) [48]	4.212	5888	12,300	76.00
$3^1{\mathrm{\Sigma }}^{+}$	Present	4.403	4359	17,861	69.12
	Experiment (2004) [28]	4.438	4443	17,787	69.61
	Experiment (1987) [17]	4.445	4455	17,787	69.66
	Theory (2016) [31]	4.457	4174	17,677	67.51
	Theory (2011) [43]	4.410	4322	17,818	69.00
	Theory (1996) [30]	4.403	4317	17,837	68.74
	Theory (1984) [47]	4.440	4104	18,368	61.70
	Theory (1983) [48]	4.419	4114	18,200	77.00
$4^1{\mathrm{\Sigma }}^{+}$	Present	7.184	4347	21,931	33.56
	Experiment (2003) [27]	–	–	22,583	–
	Theory (2011) [43]	6.700	4352	21,862	52.40
	Theory (1996) [30]	7.181	4331	21,874	33.92
	Theory (1983) [48]	7.250	4309	22,245	–
$5^1{\mathrm{\Sigma }}^{+}$	Present	4.294	3233	23,554	112.73
	Experiment (2002) [25]	4.307	–	23,531	115.61
	Theory (2011) [43]	4.290	3200	23,517	111.00
	Theory (1996) [30]	4.292	3195	23,527	112.00
	Theory (1983) [48]	4.329	3279	24,147	104.20

Figure 3. Adiabatic energy curves of the NaK molecules for three states with symmetry ${}^1\mathrm{\Pi }$ and one state with symmetry ${}^1\mathrm{\Delta }$.

Table 4. Spectroscopic constants of the excited ${}^1\mathrm{\Pi }$ and ${}^1\mathrm{\Delta }$ states.

State	Reference	$R_e$ (Å)	$D_e$ (cm${}^{-1}$)	$T_e$ (cm${}^{-1}$)	${\omega }_e$ (cm${}^{-1}$)
$1^1\mathrm{\Pi }$	Present	4.013	1209	17,067	68.82
	Experiment (1991) [49]	4.013	1324	16,993	71.46
	Experiment (1988) [50]	4.016	1306	16,993	71.50
	Theory (2016) [31]	4.105	1169	16,885	64.80
	Theory (2011) [43]	4.040	1213	17,016	67.60
	Theory (1996) [30]	4.038	1193	17,016	67.60
	Theory (1984) [47]	4.069	1079	17,365	61.30
	Theory (1983) [48]	4.069	726	17,500	65.00
$2^1\mathrm{\Pi }$	Present	4.133	2075	20,144	82.92
	Experiment (2008) [29]	4.155	2157	20,090	82.76
	Experiment (1986) [18]	4.191	2149	20,093	81.52
	Theory (2016) [31]	4.180	2057	19,794	82.05
	Theory (2011) [43]	4.130	2052	20,089	84.80
	Theory (1996) [30]	4.133	2072	20,082	83.00
	Theory (1984) [47]	4.011	1839	20,643	84.00
	Theory (1983) [48]	4.069	1291	21,000	71.00
$3^1\mathrm{\Pi }$	Present	4.480	1127	25,661	47.28
	Experiment (1998) [22]	4.449	1293	25,519	48.80
	Theory (1996) [30]	4.509	1155	25,568	47.20
	Theory (1984) [47]	4.789	738	26,690	46.00
$1^1\mathrm{\Delta }$	Present	3.794	3628	23,159	96.17
	Theory (2011) [43]	3.800	3751	22,969	97.00
	Theory (1996) [30]	3.794	3761	22,961	96.60
	Theory (1984) [47]	3.725	4076	23,352	103.60

Figure 4. Adiabatic potential energy curves of the NaK molecule for five states with symmetry ${}^3{\mathrm{\Sigma }}^{+}$.

Table 5. Spectroscopic constants of the excited ${}^3{\mathrm{\Sigma }}^{+}$ states.

State	Reference	$R_e$ (AA)	$D_e$ (cm${}^{-1}$)	$T_e$ (cm${}^{-1}$)	${\omega }_e$ (cm${}^{-1}$)
$1^3{\mathrm{\Sigma }}^{+}$	Present	5.461	194	5058	21.82
	Experiment (2008) [44]	5.448	208	–	22.82
	Experiment (1985) [13]	5.440	209	5066	22.99
	Theory (2016) [31]	5.498	253	4781	21.52
	Theory (2011) [43]	5.460	209	4977	22.50
	Theory (1996) [30]	5.451	197	4990	22.65
	Theory (1984) [47]	5.276	291	5200	26.90
	Theory (1983) [48]	5.588	161	4800	23.00
$2^3{\mathrm{\Sigma }}^{+}$	Present	4.303	2557	15,719	73.65
	Experiment (2000) [24]	4.308	2443	15,751	73.40
	Experiment (1995) [20]	4.450	2461	15,857	63.17
	Experiment (1990) [51]	4.260	2015	16,283	68.64
	Experiment (1989) [15]	4.100	2319	15,998	73.79
	Experiment (1988) [16]	–	2580	15,719	75.50
	Theory (2016) [31]	4.390	2478	15,576	70.18
	Theory (2011) [43]	4.310	2544	15,684	72.90
	Theory (1996) [30]	4.310	2541	15,669	73.40
	Theory (1984) [47]	4.240	2645	15,799	74.00
	Theory (1983) [48]	4.340	2097	16,100	77.00
$3^3{\mathrm{\Sigma }}^{+}$	Present (inner well)	3.930	800	21,420	94.47
	Present (outer well)	8.228	34	22,186	9.43
	Theory (2016) [31]	3.993	548	21,303	93.58
	Theory (2011) [43]	3.940	774	21,385	96.40
	Theory (1996) [30]	3.937	774	21,380	94.20
	Theory (1984) [47]	3.842	782	21,690	88.30
$4^3{\mathrm{\Sigma }}^{+}$	Present	4.204	2380	23,898	74.78
	Theory (2011) [43]	4.210	2358	23,854	74.40
	Theory (1996) [30]	4.212	2355	23,850	74.00
	Theory (1984) [47]	4.143	2282	23,649	70.90
$5^3{\mathrm{\Sigma }}^{+}$	Present	5.190	1862	24,926	98.01
	Theory (2011) [43]	5.190	1878	24,847	96.60
	Theory (1996) [30]	5.191	1855	24,868	97.00
	Theory (1984) [47]	5.234	2047	25,381	73.70

Figure 5. Adiabatic potential energy curves of the NaK molecule for three states with symmetry ${}^3\mathrm{\Pi }$ and one state with symmetry ${}^3\mathrm{\Delta }$.

Table 6. Spectroscopic constants of the excited ${}^3\mathrm{\Pi }$ and ${}^3\mathrm{\Delta }$ states.

State	Reference	$R_e$ (Å)	$D_e$ (cm${}^{-1}$)	$T_e$ (cm${}^{-1}$)	${\omega }_e$ (cm${}^{-1}$)
$1^3\mathrm{\Pi }$	Present	3.481	6722	11,553	120.49
	Experiment (1986) [18]	3.502	6698	11,562	120.37
	Theory (2016) [31]	3.555	6528	11,526	117.36
	Theory (2011) [43]	3.480	6663	11,503	125.70
	Theory (1996) [30]	3.461	6702	11,508	121.71
	Theory (1984) [47]	3.440	6910	11,534	122.20
	Theory (1983) [48]	3.450	6291	11,900	129.00
$2^3\mathrm{\Pi }$	Present	4.225	1980	20,241	67.27
	Experiment (1994) [52]	4.223	2012	20,248	67.38
	Experiment (1989) [15]	4.225	2001	20,248	67.38
	Theory (2016) [31]	4.333	1769	20,082	62.30
	Theory (2011) [43]	4.230	1968	20,192	66.40
	Theory (1996) [30]	4.233	1964	20,190	67.09
	Theory (1984) [47]	4.149	1964	20,508	69.30
	Theory (1983) [48]	4.461	1049	21,200	69.00
$3^3\mathrm{\Pi }$	Inner well
	Present	3.903	1574	25,213	95.06
	Theory (2011) [43]	3.910	1555	25,167	98.10
	Theory (1996) [30]	3.911	1558	25,165	101.00
	Outer well
	Present	5.589	2052	24,735	42.45
	Theory (1984) [47]	5.556	2329	25,099	51.70
$1^3\mathrm{\Delta }$	Present	3.889	2928	23,860	92.73
	Theory (2011) [43]	3.890	3068	23,651	93.70
	Theory (1996) [30]	3.889	3075	23,647	93.60
	Theory (1884) [47]	3.794	3132	24,296	97.70

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