Spectroscopic Properties of Ni²⁺ Ions in Octahedral Complexes Enhanced Publication

Spectroscopic Properties of Ni 2+ Ions in Octahedral Complexes 八面体配合物中Ni 2+ 离子的光谱性质 1 2 3 4 corresp first-author E-mail： mikhail.brik@ut.ee E-mail： mikhail.brik@ut.ee BRIK Mikhail G (1969 - ), received his PhD from Kuban State University (Russia) in 1995 and his DSc (habilitation) from the Institute of Physics, Polish Academy of Sciences (Poland) in 2012. Since 2007 he is a professor at the Institute of Physics, University of Tartu, Estonia. Before that, he worked at Kyoto University (Japan) from 2003 to 2007, Weizmann Institute of Science (Israel) in 2002, Asmara University (Eritrea) from 2000 to 2001, and Kuban State University from 1995 to 2000. He is also a distinguished visiting professor at Chongqing University of Posts and Telecommunications (China) and Professor at Jan Długosz University (Poland). Since 2015 he serves as one of the editors of Optical Materials (Elsevier). Prof. Brik’s scientific interests cover theoretical spectroscopy of transition metal and rare earth ions in optical materials, crystal field theory, and ab initio calculations of the physical properties of pure and doped functional compounds. He is a coeditor of two books and author of 12 book chapters and about 410 papers in international journals. According to Google Scholar (June 2020), he has more than 8 500 citations with h index 45. He received the Dragomir Hurmuzescu Award of Romanian Academy in 2006 and the State Prize of the Republic of Estonia in the field of exact sciences in 2013. In 2018 he received the state professor title from the President of Poland. http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822370&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822375&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822372&type= 24.89202881 29.88732910 BRIK Mikhail G (1969 - ), received his PhD from Kuban State University (Russia) in 1995 and his DSc (habilitation) from the Institute of Physics, Polish Academy of Sciences (Poland) in 2012. Since 2007 he is a professor at the Institute of Physics, University of Tartu, Estonia. Before that, he worked at Kyoto University (Japan) from 2003 to 2007, Weizmann Institute of Science (Israel) in 2002, Asmara University (Eritrea) from 2000 to 2001, and Kuban State University from 1995 to 2000. He is also a distinguished visiting professor at Chongqing University of Posts and Telecommunications (China) and Professor at Jan Długosz University (Poland). Since 2015 he serves as one of the editors of Optical Materials (Elsevier). Prof. Brik’s scientific interests cover theoretical spectroscopy of transition metal and rare earth ions in optical materials, crystal field theory, and ab initio calculations of the physical properties of pure and doped functional compounds. He is a coeditor of two books and author of 12 book chapters and about 410 papers in international journals. According to Google Scholar (June 2020), he has more than 8 500 citations with h index 45. He received the Dragomir Hurmuzescu Award of Romanian Academy in 2006 and the State Prize of the Republic of Estonia in the field of exact sciences in 2013. In 2018 he received the state professor title from the President of Poland. mikhail.brik@ut.ee 1 1 corresp macg@cqupt.edu.cn macg@cqupt.edu.cn MA Chong⁃geng g（1980-）, received his PhD from University of Science and Technology of China in 2008. He spent three years（2010—2013）as a post⁃doctor in University of Tartu with the financial support of Eu⁃ropean Social Fund. He was also a visiting professor at University of Verona in 2017. His area of scientific interests covers the first ⁃ principles and crystal-field design of luminescent materials. He has published one book and more than 100 papers in international journals, which attracted more than 2 500 citations（hindex=27）. Currently he is a full professor and the director of CQUPT ⁃BUL Innovation Institute at Chong ⁃qing University of Posts and Telecommunications.Email: macg@cqupt.edu.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822384&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822384&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822384&type= 24.89202881 29.88732910 MA Chong⁃geng g（1980-）, received his PhD from University of Science and Technology of China in 2008. He spent three years（2010—2013）as a post⁃doctor in University of Tartu with the financial support of Eu⁃ropean Social Fund. He was also a visiting professor at University of Verona in 2017. His area of scientific interests covers the first ⁃ principles and crystal-field design of luminescent materials. He has published one book and more than 100 papers in international journals, which attracted more than 2 500 citations（hindex=27）. Currently he is a full professor and the director of CQUPT ⁃BUL Innovation Institute at Chong ⁃qing University of Posts and Telecommunications.Email: macg@cqupt.edu.cn macg@cqupt.edu.cn 重庆邮电大学 光电工程学院 & “重庆邮电大学⁃伦敦布鲁内尔大学”交叉创新研究院， 重庆　400065 重庆邮电大学 光电工程学院 & “重庆邮电大学⁃伦敦布鲁内尔大学”交叉创新研究院， 重庆　400065 School of Optoelectronic Engineering & CQUPT-BUL Innovation Institute， Chongqing University of Posts and Telecommunications， Chongqing 400065， China School of Optoelectronic Engineering & CQUPT-BUL Innovation Institute， Chongqing University of Posts and Telecommunications， Chongqing 400065， China 塔尔图大学 物理研究所， 爱沙尼亚 塔尔图　50411 塔尔图大学 物理研究所， 爱沙尼亚 塔尔图　50411 Institute of Physics， University of Tartu， Tartu 50411， Estonia Institute of Physics， University of Tartu， Tartu 50411， Estonia 琴斯托霍瓦师范大学 科学与技术学院， 波兰 琴斯托霍瓦　42200 琴斯托霍瓦师范大学 科学与技术学院， 波兰 琴斯托霍瓦　42200 Faculty of Science and Technology， Jan Długosz University， PL-42200 Czę stochowa， Poland Faculty of Science and Technology， Jan Długosz University， PL-42200 Czę stochowa， Poland 罗马尼亚国家科学院， 罗马尼亚 布加勒斯特　050044 罗马尼亚国家科学院， 罗马尼亚 布加勒斯特　050044 Academy of Romanian Scientists， Bucharest 050044， Romania Academy of Romanian Scientists， Bucharest 050044， Romania Based on an up-do-date literature data， we consider an empirical trend between the energy of the spin-forbidden 3 A 2 - 1 E transition of the octahedrally coordinated Ni 2+ ions and a new nephelauxetic parameter <math id="M1"><mtext>  </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>C</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mtext> </mtext></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822390&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822387&type= 36.83000183 6.68866634 （ B ， C （ B 0 ， C 0 ） are the Racah parameters of Ni 2+ ions in a crystal（free state）， respectively）. It is demonstrated that the energy of the Ni 2+ 1 E state is a linear function of the <math id="M2"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822394&type= 2.96333337 3.80999994 parameter. These findings prove importance of a simultaneous consideration of reduction of both Racah parameters B and C due to the nephelauxetic effect. Such an approach is more accurate in estimating the energy position of the 1 E level. The commonly used nephelauxetic ratio <math id="M3"><mi>β</mi><mo>=</mo><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822402&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822401&type= 12.61533356 3.30200005 ， which completely ignores the reduction in the values of the Racah parameter C ， is not accurate enough for this purpose. The collected in the present paper experimental data and their analysis can be useful for researchers working with the crystalline materials doped with Ni 2+ ions. 基于最新的文献数据，我们研究了八面体配位下Ni 2+ 离子自旋禁止跃迁 3 A 2 ⁃ 1 E的能量与新的电子云膨胀效应参数 <math id="M4"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>C</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mtext> </mtext></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822410&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822406&type= 35.81399918 6.68866634 之间的经验关系，其中（ B 、 C ）和（ B 0 、 C 0 ）分别是Ni 2+ 离子在晶体中和自由离子状态下描述3d电子间库仑作用的拉卡参数。研究结果表明，Ni 2+ 离子 1 E态的能量是 <math id="M5"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822417&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822415&type= 2.96333337 3.80999994 参数的线性函数。这样的发现确认了完全处理电子云膨胀效应需要同时考虑两个拉卡参数 B 和 C 约减贡献的重要事实。通常使用的电子云膨胀效应参数 <math id="M6"><mi>β</mi><mo>=</mo><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822423&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822421&type= 12.61533356 3.30200005 由于完全忽略了拉卡参数 C 的约减贡献，在估计 1 E态能级位置上是不准确的。相比而言，我们构建的理论方法则更好。本文所收集的实验数据以及实施的理论分析均将会对Ni 2+ 离子掺杂材料的光谱学研究有一定的参考价值。 Ni 2+ 自旋禁戒跃迁 共价性 Ni 2+ spin-forbidden transitions covalency 1　Introduction 1 Theoretical and experimental studies of the transition metal（TM） ions spectroscopic properties in a free state and in solids are still actively being performed, which can be readily explained by numerous applications in science and technology [ 1 1 - 3 3 1-3 ] . In particular, the TM ions with an unfilled 3d electron shell are of special importance. These ions can be stabilized in solids in different oxidation states and in different coordination, and this circumstance contributes to the variety and complexity of the optical spectra of these ions in various crystalline materials. Since the 3d electron shell is the outer one, its electrons strongly interact with nearest neighbors in the crystal lattice. The overall appearance of the absorption and luminescence spectra of these TM ions is determined by a combination of the spin-allowed broad emission bands and narrow spin-forbidden peaks. The former ones are used for getting tunable laser generation [ 4 4 ] , whereas the latter ones are important for lighting [ 5 5 - 8 8 5-8 ] , as well as for lasing （like ruby laser that operates on the sharp spin-forbidden 2 E- 4 A 2 emission transition of Cr 3+ ions）. One of those 3d TM ions is a divalent nickel, Ni 2+ , with its 3d 8 electron configuration. An interest to this ion has been revived recently because of its infrared emission in the second（1 000-1 350 nm） and third（1 550-1 870 nm） biological windows [ 9 9 - 11 11 9-11 ] , which facilitates applications of these ions in optical thermometry and bioimaging. The Ni 2+ electron configuration（3d 8 ） in terms of the number of allowed states is equivalent to the 3d 2 electron configuration. Both configurations have 45 allowed microstates, which obey the Pauli exclusion rule. These 45 states produce five LS terms, whose properties are summarized in Tab.1 Tab.1 . In that table the standard 2 S +1 L notation is used, where S and L stand for the total spin and orbital momenta, respectively. These five terms make the energy level scheme of a free ion. Term symbols Orbital degeneracy 2 L +1 Total degeneracy （2 L +1）×（2 S +1） Energy（in terms of Racah parameters B ， C ） 3 F （ L =3） 7 21 0 3 P （ L =1） 3 9 15 B 1 D （ L =2） 5 5 5 B + 2 C 1 G （ L =4） 9 9 12 B + 2 C 1 S （ L =0） 1 1 22 B + 7 C The free ion's energy levels split, when such an ion is placed into a crystal field. The splitting pattern depends on the symmetry properties of the crystal lattice site occupied by an impurity ion. An analysis of the energy levels schemes of the TM ions in crystal field of cubic symmetry can be performed with the help of the so-called Tanabe-Sugano diagrams [ 12 12 ] . Three main parameters are needed for this purpose: the crystal-field strength Dq （which describes the crystal field effects）, and two Racah parameters B and C （which determine the energy intervals between the free ion terms due to the Coulomb interaction between the electrons in the unfilled electron shell）. The horizontal axis in all such diagrams is the Dq / B ratio, the vertical axis is the energy E of the split states in terms of the Racah parameter B （or the E / B ratio）, and the diagrams are plotted for a fixed C / B ratio. Fig.1 Fig.1 depicts the Tanabe-Sugano diagram for a 3d 8 ion in an octahedral crystal field. When Dq / B ratio is equal to zero, the free ion's energy level scheme is restored. When Dq / B > 0, the energy levels are split, and the split levels depend on the Dq / B value. It can be noted, however, that the energy separation between the ground state spin-triplet 3 A 2 and the first spin-singlet 1 E state is practically independent of the crystal-field strength. Moreover, at some Dq / B value the first excited spin-triplet state 3 T 2 and the first spin-singlet 1 E intersect with each other. This allows to consider two special cases: （1）a weak crystal-field, where the first excited state 3 T 2 originates from the same 3 F term as the ground state 3 A 2 and, （2）a strong crystal-field, where the first excited state is 1 E, which comes from the 1 D term of a free ion. The Dq / B value, at which the energies of the 3 T 2 and 1 E states are equal, is a separation between these two situations, as shown by a vertical dashed line in Fig.1 Fig.1 . Since the energy of the 1 E state is very close to that of the 1 D free ion's term, it is possible to assume that only two Racah parameters B and C are needed to describe its energy position. The Racah parameters of the TM ions in crystals are considerably reduced relative to their “free ion” counterparts due to the so-called nephelauxetic effect [ 13 13 ] ; the degree of such a reduction depends on the peculiarities of the chemical bonds between the TM ions and ligands. The Racah parameters are reduced greatly in the covalent crystals, and their reduction is not so pronounced in the ionic compounds. As a result, the 1 E state will be lowered in covalently bonded systems and will be located higher in ionic crystals. This observation allowed to introduce a new parameter <math id="M7"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822447&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822444&type= 4.23333359 4.48733330 to the description of the spin-forbidden transitions [ 14 14 - 20 20 14-20 ] . It has been shown that the energy of the spin-doublet 2 E of the Mn 4+ and Cr 3+ ions（or the 1 E state of the Ni 2+ ions） is a linear function of this new parameter <math id="M8"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>C</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn><mtext> </mtext></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822454&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822450&type= 41.23266602 7.61999989 （where B and C are the Racah parameters in the crystal and B 0 and C 0 are the corresponding free ion's values）. In the present paper we give an extended overview of the Ni 2+ spectroscopic properties（in the octahedral coordination）, based on the recent publications, and demonstrate this linear behavior. The collected in the present paper experimental data on the Ni 2+ -doped solids provide a valuable source of reference information for the experimentalists, whereas the established linear trend between the 1 E level position and new parameter <math id="M9"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822456&type= 3.38666677 4.48733330 allows for a meaningful estimation of the Ni 2+ spectroscopic properties in new hosts. 2　Analysis of Spectroscopic Data on The Spin⁃forbidden 3 A 2 → 1 E Absorption Transition of Ni 2+ Ions in Solids 1 Tab.2 Tab.2 contains the values of the Racah parameters B and C for Ni 2+ ions in various solids. In addition, the energetical positions of the Ni 2+ 1 E state （calculated from the crystal field theory） and measured experimentally are also listed, along with the corresponding literature references. Notes: The chemical compositions of the glasses listed in the table are as follows: ZAS glass: 58SiO 2 + 21ZnO + 10Al 2 O 3 + 5TiO 2 + 3Ga 2 O 3 + 3K 2 O; ZLKB1: 19.9ZnO + 5Li 2 O + 25K 2 O + 50B 2 O 3 + 0.1NiO; ZLKB2: 19.9ZnO + 10Li 2 O + 20K 2 O + 50B 2 O 3 + 0.1NiO; ZLKB3: 19.9ZnO + 15Li 2 O + 15K 2 O + 50B 2 O 3 + 0.1NiO; ZLKB4: 19.9ZnO + 20Li 2 O + 10K 2 O + 50B 2 O 3 + 0.1NiO; ZLKB5: 19.9ZnO + 25Li 2 O +5K 2 O + 50B 2 O 3 + 0.1NiO; ZLNB1: 19.9ZnO + 5Li 2 O + 25Na 2 O + 50B 2 O 3 + 0.1NiO; ZLNB2: 19.9ZnO + 10Li 2 O + 20Na 2 O + 50B 2 O 3 + 0.1NiO; ZLNB3: 19.9ZnO + 15Li 2 O + 15Na 2 O + 50B 2 O 3 + 0.1NiO; ZLNB4: 19.9ZnO + 20Li 2 O + 10Na 2 O + 50B 2 O 3 + 0.1NiO; ZLNB5: 19.9ZnO + 25Li 2 O + 5Na 2 O + 50B 2 O 3 + 0.1NiO. 2 Crystal 2 B /cm -1 2 C /cm -1 2 <math id="M13"><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822480&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822478&type= 2.96333337 3.80999994 3 Position of the 1 E level/cm -1 2 Ref. Calculated Experimental Calc., Eq.（1） AgBr 708 2 615 0.885 27 10 223 10 700 10 765 ［ 22 22 ］ AgCl 807 3 141 1.033 25 12 206 12 470 12 411 ［ 23 23 ］ Al 2 O 3 900 4 250 1.272 56 15 009 15 840 15 072 ［ 24 24 ］ β⁃BaB 2 O 4 850 3 500 1.118 08 13 351 — 13 354 ［ 25 25 ］ BaLiF 3 1 062 3 865 1.319 39 15 504 15 504 15 593 ［ 26 26 ］ Ca 3 Sc 2 Ge 3 O 12 935 3 503 1.176 51 13 841 — 14 004 ［ 27 27 ］ CdBr 2 675 2 975 0.919 24 11 963 12 104 11 143 ［ 28 28 ］ CdCl 2 750 3 150 0.996 32 13 147 13 065 12 000 ［ 28 28 ］ CdI 2 730 3 450 1.032 65 12 419 12 450 12 404 ［ 29 29 ］ CsCdBr 3 776 3 041 0.996 39 11 781 11 780 12 001 ［ 30 30 ］ CsCdCl 3 799 3 142 1.027 67 12 132 12 700 12 349 ［ 31 31 ］ CsMgBr 3 782 3 026 0.998 54 11 800 11 800 12 025 ［ 30 30 ］ CsMgBr 3 886 3 952 1.214 27 14 555 14 700 14 424 ［ 32 32 ］ CsMgCl 3 868 3 869 1.189 15 14 435 — 14 145 ［ 32 32 ］ CsMgI 3 879 3 918 1.204 22 14 346 — 14 312 ［ 32 32 ］ KMgF 3 950 3 990 1.262 15 247 15 156 14 955 ［ 33 33 ］ KNiF 3 952 4 188 1.295 18 15 002 15 454 15 324 ［ 34 34 ］ KZnF 3 880 3 696 1.169 01 13 891 - 13 921 ［ 35 35 ］ K 2 ZnF 4 1 028 3 794 1.284 96 15 061 15 313 15 210 ［ 36 36 ］ LiCl 830 3 980 1.183 8 14 048 14 330 14 085 ［ 37 37 ］ LiGa 5 O 8 881 3 225 1.097 29 12 986 12 987 13 123 ［ 23 23 ］ α ⁃LiIO 3 913 4 069 1.250 71 15 304 — 14 829 ［ 38 38 ］ LiNbO 3 816 3 224 1.052 15 12 120 12 120 12 621 ［ 39 39 ］ MgAl 2 O 4 865 3 254 1.090 42 13 002 12 987 13 047 ［ 40 40 ］ MgBr 2 800 3 200 1.037 58 12 274 12 200 12 459 ［ 41 41 ］ MgF 2 995 4 192 1.323 85 15 583 15 600 15 643 ［ 23 23 ］ MgGa 2 O 4 869 3 150 1.077 76 12 814 12 870 12 906 ［ 42 42 ］ MgO 935 3 330 1.150 94 13 196 13 535 13 720 ［ 43 43 ］ 20MoO 3 ⁃80TeO 2 780 3 675 1.101 48 13 222 13 440 13 170 ［ 44 44 ］ Ni 3 （BO 3 ） 2 ， 2a site 915 3 797 1.208 21 9 611 — 14 357 ［ 45 45 ］ Ni 3 （BO 3 ） 2 ， 4f site 871 2 964 1.052 31 8 728 — 12 623 ［ 45 45 ］ NiBr 2 763 2 772 0.947 21 12 550 — 11 454 ［ 46 46 ］ NiCl 2 785 4 045 1.167 87 13 907 13 800 13 908 ［ 46 46 ］ NiCl 2 （H 2 O） 4 928 3 764 1.211 7 14 359 14 803 14 395 ［ 47 47 ］ NiF 2 697 4 035 1.116 03 13 799 — 13 331 ［ 48 48 ］ NiI 2 646 3 851 1.054 71 11 171 11 165 12 649 ［ 46 46 ］ RbCaF 3 1 034 3 816 1.292 44 15 040 15 000 15 293 ［ 49 49 ］ RbCdF 3 950 4 000 1.263 6 14 075 — 14 972 ［ 50 50 ］ WO 3 ⁃TeO 2 958 3 330 1.167 4 13 831 — 13 903 ［ 51 51 ］ ZAS 940 3 919 1.244 11 14 124 14 124 14 756 ［ 52 52 ］ ZLKB1 770 3 250 1.025 44 12 294 12 269 12 324 ［ 53 53 ］ ZLKB2 765 3 200 1.014 18 12 126 12 162 12 199 ［ 53 53 ］ ZLKB3 770 3 260 1.027 03 12 284 12 315 12 342 ［ 53 53 ］ ZLKB4 790 3 250 1.038 69 12 404 12 419 12 471 ［ 53 53 ］ ZLKB5 790 3 200 1.030 84 12 308 12 311 12 384 ［ 53 53 ］ ZLNB1 780 3 250 1.032 04 12 334 12 297 12 397 ［ 54 54 ］ ZLNB2 795 3 290 1.048 33 12 521 12 623 12 578 ［ 54 54 ］ ZLNB3 800 3 285 1.050 87 12 544 12 575 12 607 ［ 54 54 ］ ZLNB4 810 3 285 1.057 56 12 614 12 623 12 681 ［ 54 54 ］ ZLNB5 810 3 285 1.057 56 12 616 12 575 12 681 ［ 54 54 ］ ZnF 2 972 3 586 1.214 76 14 162 — 14 429 ［ 55 55 ］ ZnO⁃CdS nanocomposite 820 3 250 1.058 88 12 621 12 626 12 696 ［ 56 56 ］ ZnSiF 6 ·6H 2 O 932 4 155 1.276 95 15 239 — 15 121 ［ 57 57 ］ It is easy to see from the data presented in Tab. 1 Tab. 1 that all listed parameters vary in wide ranges. Thus, the value of B varies from 646 cm -1 in NiI 2 to 1 062 cm -1 in BaLiF 3 , the value of C changes from 2 615 cm -1 in AgBr to 4 250 cm -1 in Al 2 O 3 and the energy of the 1 E state is in between 10 700 cm -1 in AgBr and 15 840 cm -1 in Al 2 O 3 . Such wide limits can be explained by differences in chemical bonding: in highly covalent iodides and bromides the nephelauxetic effect is strong and the Racah parameters are reduced considerably. At the same time, the highly ionic fluorides are characterized by a weaker nephelauxetic effect and, correspondingly, greater values of the Racah parameters. Therefore, the degree of covalency of the chemical bonds between the Ni 2+ ions and ligands is the primary reason for the observed variations of the spectroscopic parameters in Tab.1 Tab.1 . The data in the “calculated” column correspond to the values obtained from the Tanabe-Sugano matrices in the cubic crystal field approximation. Since the Ni 2+ sites very often are characterized by a lower symmetry （trigonal or tetragonal）, such calculated values can deviate from the experimental data. Fig.2 Fig.2 shows the variation of the experimental positions of the Ni 2+ 1 E state against the <math id="M14"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>C</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot><mtext>  </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822491&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822488&type= 42.41799927 7.61999989 parameter. The data points were fitted to the linear function <math display="block" id="M16"><mi>E</mi><mfenced separators="|"><mrow><mmultiscripts><mrow/><mprescripts/><mrow/><mrow><mn mathvariant="normal">1</mn></mrow></mmultiscripts><mi mathvariant="normal">E</mi></mrow></mfenced><mo>=</mo><mn mathvariant="normal">920</mn><mo>+</mo><mn mathvariant="normal">11121</mn><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822519&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822514&type= 36.49133301 4.31799984 ， the value of the correlation coefficient R 2 is rather high（0.903）, which indicates a good quality of the fit. To assess the quality of the fit and variance of the data presented, we calculated the energy of the Ni 2+ 1 E state using Eq.（1） Eq.（1） in the various compounds that are listed in Tab.1 Tab.1 and then determined the root-mean-squared deviation <math display="block" id="M17"><mi>σ</mi><mo>=</mo><mroot><mrow><mfrac><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>i</mi><mo stretchy="false">(</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo>.</mo><mo stretchy="false">)</mo></mrow></msub><mo>-</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>i</mi><mo stretchy="false">(</mo><mi mathvariant="normal">E</mi><mi mathvariant="normal">q</mi><mo>.</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow><mrow><mi>N</mi></mrow></mfrac></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822523&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822520&type= 41.82533264 13.88533401 ， where E i （exp.） and <math id="M18"><msub><mrow><mi>E</mi></mrow><mrow><mi>i</mi><mo stretchy="false">(</mo><mi mathvariant="normal">E</mi><mi mathvariant="normal">q</mi><mo>.</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></msub><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822527&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822526&type= 10.92199993 3.80999994 are the corresponding experimental value and the calculated with the help of Eq.（1） Eq.（1） . The numerical estimations returned the value <math id="M19"><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822530&type= 2.45533323 2.62466669 =407 cm -1 . Two dashed straight lines in Fig.1 Fig.1 are parallel to the fit line （ Eq.（1） Eq.（1） ） and correspond to its upward/downward shift by the value of <math id="M20"><mi>σ</mi><mo>.</mo><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822538&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822536&type= 5.07999992 2.79399991 It should be noted that this value is of the order of magnitude of the phonon frequencies on solids and practically all data points in Fig.1 Fig.1 are within the <math id="M21"><mo>±</mo><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822544&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822542&type= 4.48733330 2.62466669 interval from the fit line. However, some data points, which correspond to NiI 2 , CdBr 2 , CdCl 2 , Al 2 O 3 compounds are outside of that area. The first three halides in this group are characterized by a layered structure and the chemical bonds are highly covalent. To illustrate the validity of our choice of the <math id="M22"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>C</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822551&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822546&type= 40.80933380 7.61999989 parameter, we also show in Fig.3 Fig.3 the dependence of the experimental energy position of the Ni 2+ 1 E state on the “old” nephelauxetic ratio <math id="M23"><mi>β</mi><mo>=</mo><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822556&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822553&type= 14.73200035 3.80999994 , which for a long time was considered as a qualitative measure of covalency. It can be easily seen from Fig.3 Fig.3 , that the data points are much more scattered than in Fig.2 Fig.2 . The linear fit returns a much smaller value of the correlation coefficient（only 0.728）. A similar result was obtained by us when considering the Mn 4+ ions and dependence of their 2 E level on the same parameter. Therefore, consideration of only one parameter B for the covalency description is insufficient, and both Racah parameters B and C have to be used when relating the energies of the spin-forbidden transitions of the TM ions chemical bonds covalency. Moreover, the present empirical finding has been confirmed and supported by our theoretical derivation based on the parameterized Tanabe-Sugano formula of 1 E energy level position of 3d 8 ions in octahedral complexes, as shown by Ref. [ 19 19 ]. We note that the linear relation between the 1 E level and <math id="M25"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn><mtext>  </mtext></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822567&type= 4.23333359 4.48733330 parameter holds true for the zero-phonon transitions. Quite often identification of the zero-phonon line（ZPL） position in the TM ions spectra is not an easy task, since the Stokes and anti-Stokes vibronic progressions that are observed in the experimental emission/absorption spectra can mask the true ZPL position. We consider this as an important factor that can cause deviation of some experimental data points in Fig.2 Fig.2 from the straight line determined by Eq.（1） Eq.（1） . In addition, such a linear relation can be also expected to be held for the case of 3d 2 ions in tetrahedral complexes because of the electron-hole complementarity between both 3d 8 and 3d 2 electronic configurations. 3　Conclusion 1 A thorough analysis of the recent publications on the spectroscopic properties of solids doped with Ni 2+ ions allowed to compile a database that collects the values of the Racah parameters B , C and energetic positions of the Ni 2+ 1 E level. We have re-examined an empirical trend between the lowest energy spin-forbidden Ni 2+ 3 A 2 - 1 E transition and a new covalency parameter <math id="M26"><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mrow><mrow><mi>C</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822574&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822572&type= 39.96266937 7.61999989 , which allows to account for a decrease of both Racah parameters because of nephelauxetic effect. The <math id="M27"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822577&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822575&type= 3.38666677 4.48733330 parameter describes the covalent effects much better than the commonly used nephelauxetic ratio <math id="M28"><mi>β</mi><mo>=</mo><mrow><mrow><mi>B</mi><mtext> </mtext></mrow><mo>/</mo><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822581&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39822579&type= 14.39333248 3.80999994 , which omits the second Racah parameter, C . It is hoped that the collected in the present paper data and their treatment will be useful for the description of the spectroscopic properties of Ni 2+ ions in solids. 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G BRIK Mikhail,S KURBONIYON Mekhrdod,MA Chong-geng.Spectroscopic Properties of Ni 2+ Ions in Octahedral Complexes[J].Chinese Journal of Luminescence,2022,43(09):1459-1468. G BRIK Mikhail,S KURBONIYON Mekhrdod,MA Chong-geng.Spectroscopic Properties of Ni2+ Ions in Octahedral Complexes[J].Chinese Journal of Luminescence,2022,43(09):1459-1468. 国家科技部外专局“一带一路”创新人才交流外国专家项目（DL2021035001L）； 2021年度中国博士后科学基金国外交流引进项目（重庆专项）； 国家自然科学基金（52161135110）资助项目 Supported by National Foreign Experts Program for “Belt and Road Initiative” Innovative Talent Exchange（DL2021035001L）；2021 Chongqing Postdoctoral International Exchange Program of China Postdoctoral Science Foundation； National Natural Science Foundation of China（52161135110） 2022-06-06 2022-07-04 2022-09-05 2023-02-13 发光学报 9 43