Er(III) Complexes ** Supplementary Information Field Design ...Supplementary Information Table S1. Selected structural-parameters of complex 1, 2, and 3.Selected structural parameters

Supplementary Information

Key Role of Higher Order Symmetry and Electrostatic Ligand Field Design in the Magnetic Relaxation of Low-coordinate Er(III) Complexes **

Saurabh Kumar Singh, Bhawana Pandey, Gunasekaran Velmurugan and Gopalan Rajaraman[a]

Electronic Supplementary Material (ESI) for Dalton Transactions.This journal is © The Royal Society of Chemistry 2017


Table S1. Selected structural-parameters of complex 1, 2, and 3.

Selected structural parameters Complex 1 Complex 2 Complex 3Er–N1 (Å) 2.23118 2.22287 2.24883

Er–N1 (Å) 2.25056 2.37436 2.24660

Er–N1 (Å) 2.24634 2.30658 2.24184

Er–Cl (Å) 2.52846 2.38642 2.5712

N1-Er–N2 () 115.2 111.01 117.6

N2-Er–N3 () 118.1 113.1 114.6

N1-Er–N3 () 115.3 116.1 116.9

Cl-Er–N1 () 102.7 108.2 100.6

Cl-Er–N2 () 101.9 102.9 101.1

Cl-Er–N3 () 100.3 102.9 101.5

N1-N2–N3–Er () 23.1 30.1 20.8

(Å) 0.45 0.61 0.43

Table S2. SHAPE computed minimal distortion from the ideal geometry in coordination number four. vTBPY stands for axially vacant trigonal bipyramid and T-4 stands for the tetrahedral geometry.

Selected structural parameters vTBPY-4 T-4Complex 1 2.103 0.381

Complex 2 2.425 0.185

Complex 3 2.069 0.423


Figure S1. SINGLE_ANISO computed principal magnetization orientation of each KDs of complex 1a.

Figure S2. SINGLE_ANISO computed principal magnetization orientation of the ground state KD of complex 1a with different level of theory. Red line represent computed orientation using BS1 basis set, Blue line represent using BS2 level of theory, green represent the computed orientation for complex 1a + 4 layers of point charge at BS1 level of theory.

12

34

8

7

5

6


Table S3. SINGLE_ANISO computed composition of wave functions of the ground J=15/2 of Er(III) for complex 1a,@BS1 level of theory

wave function 1 wave function 2 wave function 3 wave function 4 wave function 5mJ real imag real imag real imag real imag real imag

-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2

-0.473976-0.0009150.000050-0.013635-0.0316960.012702-0.0109990.0023380.002682-0.0037830.000186-0.0007700.002117-0.000007-0.000105-0.000251

0.872206-0.006737-0.0227010.1052490.017402-0.005959-0.031893-0.0056020.002041-0.007150-0.0022890.0016050.0028150.000340-0.0014750.000000

-0.000120-0.001246-0.0003020.001463-0.001778-0.0021000.0044760.0005120.006038-0.0227710.0113000.030424-0.098987-0.0199700.0054820.992671

0.000220-0.000797-0.0001560.003205-0.000090-0.0009300.0067380.0033310.000621-0.024893-0.008315-0.019540-0.038274-0.0107960.0040200.000000

-0.000254-0.163976-0.0112380.0026090.0025110.0027680.0026770.013199-0.0075920.0036730.021540-0.042868-0.082305-0.0815510.543853-0.016042

-0.000282-0.0801320.0005640.013691-0.0104600.0001010.0081890.005050-0.044900-0.010280-0.0060060.018292-0.016334-0.0154990.8069340.000000

-0.010734-0.963583-0.0660840.067209-0.015089-0.009949-0.0051820.0384480.012584-0.0078770.0019270.0060930.0119210.007100-0.1692680.000380

-0.0119220.135742-0.0502370.050238-0.044098-0.0200270.009608-0.0244000.0064300.0034900.001990-0.008865-0.0072210.008729-0.0682460.000000

0.0000400.014311-0.015012-0.007141-0.008230-0.013600-0.0031220.0638770.0171990.032708-0.1193460.0580800.059220-0.935046-0.052116-0.018286

0.0000170.011408-0.017190-0.0068460.0189800.0044050.0036000.0044290.018321-0.007169-0.099343-0.082461-0.1520440.229346-0.0408250.000000

wave function 6 wave function 7 wave function 8 wave function 9 wave function 10-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2

-0.0168430.063899-0.7719680.0046500.0213910.1486070.027335-0.0229750.0605610.001474-0.0108120.000191-0.0092430.0205200.017623-0.000044

-0.007120-0.017312-0.575306-0.1631030.098568-0.0450370.0193380.0101790.0207910.004532-0.0093520.0206870.003525-0.009989-0.0049360.000000

-0.005219-0.0122010.009863-0.0076370.0562180.015103-0.0532780.001772-0.0675070.106333-0.103145-0.1689460.8549880.0197330.0225960.116748

0.007829-0.0064070.003293-0.1113240.0008330.017742-0.080702-0.033833-0.0002260.2118150.0417450.1342600.2897260.1335650.0772290.000000

0.0647550.051728-0.100192-0.233146-0.2054220.091945-0.1172690.0372550.029134-0.037600-0.006386-0.0304890.088394-0.002731-0.0014360.009409

-0.0971440.061637-0.0905020.8721170.066109-0.062671-0.205961-0.0562960.017291-0.089094-0.0224070.0472400.0681010.0100330.0137060.000000

0.000193-0.000064-0.0408150.061817-0.2630790.193568-0.0021650.106315-0.2128370.0776060.146490-0.775375-0.068627-0.022836-0.0259270.009102

-0.000530-0.0286560.081526-0.0440850.0557810.1425300.134194-0.116110-0.131732-0.055664-0.2810060.066059-0.154238-0.034342-0.0589630.000000

0.003110-0.0465580.024475-0.121513-0.326979-0.3141440.078828-0.0510940.1454450.126860-0.0678250.1423020.0625520.0905650.026910-0.000564

-0.008555-0.0445110.033194-0.1171910.7061550.041675-0.053920-0.245036-0.0602510.043811-0.230615-0.228193-0.043037-0.0105070.009850-0.000000


-0.0001770.0225670.0187780.052401-0.056177-0.4393280.103641-0.0099840.1809670.068969-0.503922-0.361758-0.0431060.0154650.0204660.005739

0.000105-0.003423-0.110080-0.024496-0.208492-0.441623-0.1899720.002476-0.134358-0.1459890.135878-0.031791-0.068540-0.113853-0.0264720.000000

-0.0049290.031135-0.071589-0.0019240.294439-0.502412-0.1340030.2242430.0098430.1863070.1511830.058521-0.0575530.072502-0.021137-0.000206

0.0029390.012256-0.0898710.080946-0.2125680.141360-0.0900720.022726-0.0029860.110093-0.6043050.2078460.0057960.0849330.0086170.000000

-0.0005240.0015600.043469-0.0660700.0728720.105900-0.1823900.2673550.179925-0.783835-0.0647630.0012920.1215910.0504420.016955-0.011560

0.0014240.0028560.002147-0.1588600.009540-0.001580-0.248711-0.145317-0.158331-0.070342-0.188252-0.002171-0.172792-0.0108480.0014500.000000

-0.003992-0.0044940.027600-0.2041510.002484-0.154308-0.204662-0.2107240.228701-0.1704270.038052-0.0162120.126272-0.012996-0.0021410.001517

0.0108490.016413-0.0435930.054442-0.000463-0.1257870.7599070.114181-0.200727-0.257056-0.0988400.0716830.1168640.041537-0.0024500.000000

-0.0064310.0174210.008897-0.0814640.101446-0.045363-0.2010920.707404-0.4311190.071731-0.1749630.062187-0.0169390.051112-0.006761-0.000000

0.0004650.029188-0.038080-0.0078310.214988-0.1792710.2461230.0621990.093311-0.1061730.166562-0.1178500.044455-0.0481070.0151540.000000

wave function 16


-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2

-0.000000 0.007837 0.054451 0.020104 0.070532 0.186530 0.079208 0.436730 0.701069 0.218334-0.032304-0.085662-0.080686-0.011623 0.015269 0.006448

-0.000000 0.014627 0.044292 0.043116 0.113053 0.153498 0.100718 0.061947 -0.113101 0.230965 0.182078 0.221750 0.013691 -0.037339 -0.030369 0.000000


Table S4. SINGLE_ANISO computed composition of wave functions of the ground J=15/2 of Er(III) for complex 1a + 4 layers of point charges, @BS1 level of theory

wave function 1 wave function 2 wave function 3 wave function 4 wave function 5mJ real imag real imag real imag real imag real imag

-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2

0.000067-0.000829 0.000028 0.002676 0.000580-0.001658-0.006112 0.002228-0.003989-0.026788-0.001893 0.020945 0.091985-0.025750-0.004468 0.994407

-0.000007 0.000608-0.000098 0.000088-0.000752 0.000490-0.001443 0.000980 0.000836-0.008628 0.007782-0.017634 0.017925 0.001866-0.002358 0.000000

0.989014 0.004198-0.025805-0.089622 0.022665 0.002692-0.025745 0.004054 0.002114 0.005929-0.001700-0.000655 0.002652-0.000038-0.000887-0.000068

-0.103423-0.002810 0.000823 0.027394 0.015361 0.007543 0.011367 0.000416-0.001206-0.002071-0.000315-0.000688-0.000366-0.000094-0.000519 0.000000

0.012647-0.659336 0.092556 0.067297 0.024623-0.011582 0.004229 0.029788-0.011531-0.005201-0.001573 0.004285-0.008883 0.003666 0.117396-0.000002

-0.000303 0.725667 0.004632 0.005605 0.026033-0.007654-0.009723-0.026757-0.002538 0.002323-0.000347-0.005919 0.004064 0.004904 0.089666 0.000000

-0.000002 -0.115212 0.003547 0.008977 0.004426 0.001564 -0.005255 0.011467 0.030421 -0.004461 -0.011395 -0.023991 0.067143 -0.092418 -0.676549 -0.012650

0.000000 0.092456-0.004990 0.003850 0.005814-0.000385-0.002197-0.002813 0.026035-0.009619 0.007929 0.026616-0.007218 0.006851-0.709646 0.000000

-0.013448 -0.064497 0.003147 -0.119850 -0.060320 -0.086914 -0.003066 0.009552 -0.013646 0.004272 0.004724 0.012360 0.004017 0.027187 -0.004027 0.000499

-0.019088-0.044892-0.966836 0.106372 0.051216-0.113392 0.026659 0.019165 0.058303-0.006139-0.012828 0.004107-0.006302-0.002739 0.012264 0.000000


-0.000288 0.007707-0.013419-0.002839-0.010476-0.007766 0.002558 0.039803-0.021168 0.020028 0.142754 0.007128-0.017933-0.788569 0.073845-0.023350

-0.000408-0.010356-0.023803 0.006913-0.007739 0.011250-0.007028-0.044734 0.003229-0.017860 0.005745-0.078809 0.159240 0.559411 0.026871-0.000000

-0.003405 0.002534 0.000570 0.014185 0.030934 -0.024517 -0.112606 0.026301 -0.048330 -0.171297 -0.063176 0.152089 0.914215 -0.066226 0.024804 -0.101172

-0.001385-0.003559 0.000457-0.012945-0.010807 0.006170-0.022713 0.028913 0.014764-0.133005 0.060029-0.139146 0.123070-0.114922 0.064088 0.000000

-0.093714-0.047126-0.104650-0.893198 0.088443 0.035898-0.208790 0.039204 0.035257 0.112864-0.020385-0.024582 0.008262-0.000700 0.001007 0.003676

-0.038125 0.050016 0.081495-0.230506 0.186200 0.079410 0.058650 0.031888-0.016870 0.021394-0.014954-0.021667 0.017336 0.000208 0.004251 0.000000

0.000979-0.030048-0.011732-0.133163-0.223411-0.294362 0.019847-0.136502-0.225355 0.075816 0.131140 0.555610-0.108489 0.083683-0.031537-0.003721

0.004317 0.011490 0.024185 0.006212-0.490042 0.196245 0.090371-0.086625 0.064460 0.057569 0.003628-0.345314-0.011162 0.009907-0.037131 0.000000

-0.000823 0.043188 0.028175 0.034887-0.213839-0.032550 0.072915-0.013008-0.114677-0.092523 0.126260 0.527325-0.023402-0.020990 0.004558-0.004427

-0.003629 0.022541 0.079418 0.103331 0.618237-0.127088 0.061202 0.234032-0.113955 0.000638-0.330484 0.109462-0.131238 0.016792-0.031845 0.000000


-0.001966-0.029122-0.089315 0.004162 0.237745 0.426724-0.161072-0.224587 0.010088-0.110761 0.322315-0.008244-0.028895-0.026176-0.016157 0.000661

0.003471 0.002421 -0.039298 -0.077287 -0.271660 -0.266712 -0.028891 -0.006011 -0.021980 -0.141242 -0.588141 -0.164408 -0.014788 -0.105406 0.002328 0.000000

-0.000326 -0.009989 -0.078813 -0.001374 -0.138989 0.670603 -0.068305 0.024097 0.105461 -0.054249 -0.442385 0.353549 -0.069299 -0.009827 0.016460 -0.003990

0.000575 0.012911 -0.074727 0.032431 -0.088204 0.009427 -0.165987 0.002056 -0.198377 0.154389 0.239842 -0.072971 -0.034471 0.097082 -0.024146 0.000000

0.009621 -0.011236 -0.016678 0.064538 0.025813 0.167456 0.402203 0.043554 0.052944 0.290896 -0.040392 -0.011996 0.132626 -0.005588 -0.000605 -0.000701

0.005438-0.010687-0.050041-0.198977 0.025113 0.033755 0.707726-0.217210-0.279804 0.092099-0.096964-0.049952 0.065980-0.032388-0.002544 0.000000

0.000610-0.001778 0.020803 0.147925 0.035024-0.082878-0.298558-0.091600 0.068973 0.698402-0.162388 0.034829 0.041732-0.039144 0.015041 0.011052

0.000345 0.001917 -0.025445 0.007826 -0.037582 0.064535 -0.062972 0.269635 -0.210523 -0.418184 -0.053019 -0.009159 -0.204977 0.035355 -0.003774 0.000000

-0.000000-0.014918 0.052232-0.042167 0.150824-0.211679 0.142108-0.400837 0.538578-0.290388 0.078884 0.013123-0.055179 0.011767 0.013617-0.005222

0.000000 0.006417-0.023562-0.008487-0.002446 0.028403 0.024376 0.318286-0.419236-0.023218 0.182910-0.213623 0.047012 0.034083-0.022945 0.000000

wave function 16


-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2

-0.003761-0.025726-0.015174 0.072355 0.157668 0.070100-0.193012-0.678730-0.509495-0.085425-0.172145-0.110313-0.024478-0.053962-0.015195 0.000000

0.003623-0.007076-0.032709-0.004429 0.144733 0.186453 0.218198 0.071770 0.048899 0.116153 0.126414 0.102884 0.035368 0.019272 0.005730 0.000000


Table S5. CASSCF+RASSI computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1a with experimental geometry + 4 layers of point charges@BS1 level of theory.

J multiplet Energies of KDs gXX gyy gzz

4I15/2

0.0043.48987.625

140.706194.393286.802337.393374.963

0.0120940.1697970.1309570.74469

6.6633295.9906325.3007630.862937

0.0156220.1856780.2088020.8293856.1467185.8256274.0924234.759339

17.8315515.4705112.8733

10.172235.1344953.7816282.53549

13.62414

-3.85.15.8

107.67.4

29.287.3


Table S6. SINGLE_ANISO computed crystal field parameters of complex 1a and 1 along with experimental geometry + 4 layers of point charges on complex 1a@ BS1 level of theory.

It is important to note here that charges on complex 1a are computed in presence of all the solvent and counter ions.

Complex 1a@BS1level Complex 1@BS1level Complex 1a + 4 layers of point charges@ BS1level

k q 𝐵𝑘𝑞 𝐵𝑘

𝑞

2

-2 -1 0 1 2

0.1393E+00-0.6100E+

00-0.1861E+01-0.3198E+00 0.2322E+00

0.2548E+00-0.4451E+00-0.2025E+01-0.7480E+00 0.8028E-01

0.1662E+00 0.5757E+00-0.2086E+01 0.3969E+00 0.2434E+00

4

-4-3-2-1 0 1 2 3 4

0.2129E-02-0.3783E-01 0.2220E-02 0.4983E-02 0.2427E-02 0.1747E-02 0.8557E-03 0.2971E-01 0.1889E-02

0.1015E-02-0.5741E-02 0.2361E-02 0.2920E-02 0.2708E-02 0.4812E-02-0.1771E-02 0.4772E-01 0.3092E-03

0.2001E-02 0.2874E-01 0.2169E-02-0.4196E-02 0.2546E-02-0.2391E-02 0.5322E-04-0.3736E-01 0.6654E-03

6

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-0.1241E-03 0.9443E-04-0.3122E-04 0.2291E-03-0.4617E-04-0.1482E-04-0.5076E-05 0.5294E-05-0.1717E-04-0.2707E-03-0.4299E-04 0.9535E-04 0.1929E-03

0.2125E-03 -0.1424E-04 -0.4003E-04 -0.3595E-04 -0.2798E-04 0.2628E-05 -0.4135E-05 -0.3985E-05 0.4374E-04 -0.3550E-03 -0.2761E-04 -0.5276E-04 0.5941E-04

-0.2258E-05-0.8952E-04-0.3158E-04-0.1647E-03-0.4172E-04 0.4486E-05-0.4636E-05-0.1692E-05-0.5501E-06 0.3231E-03-0.2960E-04-0.7555E-05 0.2276E-03


Table S7. CASSCF+RASSI computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1a @BS2 level of theory.

Table S8. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 2 @BS1 level of theory.

Table S9. CASSCF+RASSI computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1m@BS1 level of theory


4I15/2

0.00030.765.4113.0162.8254.7304.5339.7

0.024850.186460.079370.744066.869113.698932.144210.92027

0.030620.198760.311950.945976.098845.121693.577835.37676

17.7917515.4185412.8083810.197075.119136.916755.1974513.12406

-5.46.5

8.538114.49487.51865.41486.142


4I15/2

0.027.9 43.6 76.2 113.4 170.9 226.6268.6

0.023890.092060.252222.329954.248160.211880.727660.139209

0.068550.203780.577032.768254.990531.872511.202890.42886

17.6389716.8606913.178979.513938.68748

14.73415013.5682516.44025

-33.226.619.787.363.887.282.1


4I15/2

0161.426261.512350.14439.757557.428639.055693.349

0.001420.055810.0147650.3101124.1886735.0557012.7935240.971017

0.0016680.0581840.0868320.3814184.7911674.7090032.8614615.731619

17.8767915.4777113.0014810.424947.0864563.8710314.8081712.90281

-0.9660.132.0263.62291.90457.8989.765


Table S10. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1TP.

Table S11. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1TD.

Table S12. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Dy{N(SiMe3)2}3Cl]–


4I15/2

051.42385.907

135.075198.806285.643349.839388.713

0.00190.1990360.1573480.0661754.0546214.1081860.8388610.4111

0.002170.2000860.2155670.1263054.2184594.2238950.9552218.612665

17.870715.5108313.0471510.5707

7.3812265.0079523.5190311.130831

-1.45

1.1610.8381.5153.6133.3640.391


4I15/2

015.49235.82955.91562.078147.307161.036172.334

0.5210270.3836630.4712031.2275293.2481599.3757794.93665511.27383

0.6009910.6586840.6706061.5693725.8941586.4843333.078256.934004

15.0997312.1293211.6155714.539619.853561.4796790.2398510.950846

-4.6099.0815.40393.5616.81683.7793.106


6H15/2

054.226123.096233.874377.023544.323689.929773.974

0.6646313.2628790.5599391.6176580.1426170.0042360.0158240.00136

2.472766.1104363.0653251.8374470.179940.0318980.0186220.001667

17.569889.0453046.6031979.42195512.205114.6506117.2419619.78676

-65.44590.52190.16889.95690.16590.3287.518


Table S13. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Er{N(SiMe3)2}3F]–

Table S14. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Er{N(SiMe3)2}3Br]–

Table S15. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Er{N(SiMe3)2}3I]–


4I15/2

016.38345.28989.167112.052174.819210.499240.277

0.1211080.0804330.7998085.2326430.0676187.6646346.5555380.716746

0.5790420.4023551.2012715.7497

0.0832865.7096634.5943373.798668

15.983814.4376710.089057.72094117.621663.0234342.16594414.2454

-45.32831.79572.38334.53527.81428.55478.523


4I15/2

057.71199.813146.593195.211289.116339.438376.757

0.010220.188980.1035830.7507855.2522196.1808795.1297950.886134

0.0114430.2040220.2741520.8809736.0374086.0641813.946124.974724

17.8332515.4441412.8194810.115156.9229333.6569122.49378313.43618

-0.5832.094.29595.9194.82632.50588.43


4I15/2

075.558126.829178.584230.973326.11378.756417.494

0.0059960.153720.0780980.7126076.7281716.1366285.0320030.891076

0.0063110.1629510.2225110.8226986.1230335.8362043.9895195.005495

17.8514315.4616512.8500410.126195.203453.7530612.50210113.41989

-1.1961.4652.209

109.1786.12434.40688.808


Table S16. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3F]–.

CASSCF computed spin-free states

NEVPT2 computed spin-free states

NEVPT2 computed energies of low-lying eight

KDs.00

15.649115.649142.645242.645283.157783.1577108.7098108.7098219.4431219.4431291.8797291.8797345.6315345.6315

Main value of g-tensor (NEVPT2)

0.832.737.872.9136139.5156.6186.8193.2229.5242255.513075.213095.213099.91312813132.713196.113199.713230.613239.913257.413257.922114.222138.822155.322226.822234.122287.522291.622321.822327.922596.322608.722662.52268022714.522715.722845.822922.1

24327.524410.124415.524460.124503.824511.429350.429353.129371.829445.229452.329467.429506.529513.335467.235475.535476.935644.235651.535717.735731.635744.635793.9416254162541799.841799.841925.641925.842040.842041.942144.54215142225.742245.142282.842321.842331.842398.942399.7

4345743473.743495.143501.547528.947531.247568.347582.547595.747615.847627.347634.847649.847665.547677.450852.750873.65088050890.550934.550944.950957.451349.451384.35143551503.351539.557943.257985.258262.858422.95850782098.282100.482169.982214.982298.182304.382347.582359.5

216.423.136.999.4104.2139.5226.7238332.1347.738112671.312693.812699.912765.51277012817.512818.312839.712847.8128841288421313.921349.521365.921459.92147121479.621490.821544.321564.421596.121637.321637.421646.821655.321784.221863.621923.5

23717.323874.523893.824066.82416824198.42800228010.728117.728135.928176.628183.328348.228370.833415.833432.633435.833662.233676.833728.233755.33381533904.739619.839619.839964.239964.240231.84023240492.740493.140735.340739.240966.440993.741002.941006.241008.241157.741162.8

42044.242067.542079.242098.445632.545633.745730.845738.345751.145796.345808.745810.145849.345868.745883.94793047946.24794747981.148063.148077.34808148928.44894149092.349103.949143.854651.354690.955510.555646.955657.578400.578400.878605.578660.578852.978862.778953.679009.3

gzz = 16.468435gyy = 0.597440gxx = 0.156503


24019.124019.52409824098.724129.724130.124210.32421224310.2

43162.743162.743325.943335.743341.243346.843371.243413.743416.1

82372.8111260.3111390.1111781.1111867.3111913.3112034.4112066.9

23109.323109.523210.723211.123231.723232.623482.923485.523693.5

41522.441522.541854.541870.241909.441926.341928.641974.541988.4

79010.4105840105983.1106882.8106915.9107085.5107217.8107285.5


Table S17. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3Cl]–.




KDs.00

55.448655.448674.73674.736

104.2855104.2855162.6404162.6404265.9998265.9998342.8371342.8371399.1787


144.645.189.293.5136.1205.5257.8261.4318.5336.8355.913084.513103.213108.913161.713168.813244.813252.713277.213277.613298.613299.222064.82210122120.422226.522232.72237622380.122490.622490.82260922613.422638.422666.722683.42275522979.823029.6

24487.524606.22461124671.924720.524731.129313.629325.629329.729439.729500.329508.429647.829653.935560.335561.8355743570335705.935737.835744.735769.935821.540995.740995.74142441424.141768.341768.542053.142053.64228442288.642457.242477.34257842610.342648.442727.942732.4

43614.94363243664.243666.84752847528.64761547618.647660.947700.847729.747732.747754.647771.447777.450733.650735.150847.650877.850967.650987.351056.651485.651505.851627.651661.95170157709.657734.658588.658659.958717.581941.881943.28216382211.682404.982406.482527.982560.9

3.659.460.462.466.177.3163.7245.5254.5359.6381.342012714.712728.812733.212778.312784.612855.112863.712884.412885.112906.41290721380.321413.621432.421532.12153721619.821638.321663.82167021673.121678.221683.421793.121793.321952.222008.122070.8

23812.523936.723943.424007.524056.824067.528174.328181.528255.628260.128319.128329.328543.628560.433686.233690.33374933872.833875.333938.333946.133972.734062.239678.639678.640069.240069.240400.340400.640676.140677.140903.140911.741072.841106.841205.641237.441277.341359.941363.7

42286.942298.542335.142339.245861.645862.745934.245937.345993.546031.346061.146064.146083.346098.646102.748165.948224.748253.148258.748338.5483514841049120.749136.349389.949411.249424.354929.654963.655837.255901.75590978794.278795.879020.879072.579249.379250.479375.279408.5

gzz = 17.884149gyy = 0.004298gxx = 0.002807


23741.823741.92390423904.524100.824100.924300.624302.724467.1

4307443074.243287.843287.943444.443445.943536.84355243596.8

82590.1110787.8110920.4111859.9111888.6112340112444.4112543.1

23097.523097.523226.823227.42341123411.223615.92361823790.9

41738.341738.341959.941960.14213342136.242210.242239.142262.3

79439.6106392.2106531.6107452.5107487.1107918.9108025.2108072.2


Table S18. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3Br]–.




KDs.00

93.471193.4711122.9477122.9477150.4914150.4914213.9123213.9123327.8859327.8859421.9603421.9603


167.367.6115.4119.8162.6235289.2292.7353.1371.9392.313105.213123.613129.213182.713189.913266.313273.713313.513313.913325.113325.822076.122114.222133.822245.722251.82240722410.522541.82254222619.222623.922651.822692.722707.122781.123019.523070.3

24534.624659.524664.32472824776.824788.129324.529339.929344.429459.429526.829534.629692.429698.435592.435593.735608.735727.435732.835770.735776.135798.335851.840913.240913.241382.441382.441763.341763.542074.142074.64232342327.842507.942529.342637.242668.44271042789.742794.8

43675.843702.943734.443738.847550.647551.14764347646.647699.147739.147770.847773.647794.847811.547816.450728.550729.550866.75089950989.751010.151097.951535.151554.151682.25171651755.157692.1577165864158712.158809.88193981940.482184.882234.782444.682446.182581.882615.6

3.1106.2106.3107.7112.7121.4192.6301.2313.6441.6467.2512.41255112564.112568.112614.612621.112692.812702.91274512745.612754.112754.820688.120728.820761.120771.520789.920944.820983.720994.321003.521115.821120.121176.621229.82128321287.721447.621447.9

23377.623526.32353423613.423672.223678.927041.527051.927111.727140.227190.827201.927476.227498.332193.132197.532265.732385.93239332465.532469.432517.832608.438172.538172.538594.238594.238977.838978.239298.739299.539566.339573.339768.839800.439936.639954.340009.240122.140128.5

40989.941015.341059.141061.744144.34414544235.844238.844324.444359.244397.944400.444419.444437.444438.946258.246311.946319.246324.646432.946448.146542.447247.447260.147517.347546.447555.35237452408.853452.753530.453580.875516.375517.675803.875855.976074.476074.67623676274.2

gzz = 17.883549gyy = 0.002194gxx = 0.001815


23704.123704.12389823898.524119.624119.824336.624338.624513.9

4308043080.143297.743297.843473.143474.143586.143598.543662

82650.9110734.3110868.4111892.9111918.7112436.4112538.2112650.5

22506.322506.42267322673.522899.522899.823145.923148.123354.7

40269.240269.240515.740515.940753.540755.440889.540906.140972.1

76313101847.8101984.7103059.7103091.1103711.9103825.5103871


Table S19. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3I]–.




KDs.00

122.3681122.3681158.3934158.3934187.8547187.8547254.1653254.1653373.1904373.1904472.1602472.1602543.3232543.3232


0.990.490.6147.1151.4198.3271.1328.5332395.5414.7436.213127.213145.713151.313206.213213.413291.513298.313353.113353.113361.313361.822085.222126.222146.122266.622272.522443.922446.822604.322604.422624.422636.422663.322719.722732.522810.623068.523118.8

24591.224725.624730.524798.924848.624860.929333.229352.229357.129480.929555.829563.329745.629751.63562835628.935644.13575735763.835807.235811.93583335887.340796.940796.941321.441321.441748.641748.842092.842093.24236542369.642565.24258742704.342734.842780.84286142866.8

43753.243794.8438264383447574.247574.647676.147679.647743.247782.847817.647820.347840.947857.647861.650712.850713.550885.550918.151012.251033.451143.751594.551612.551746.351782.351821.957659.957682.858704.658775.358921.881925.481926.782202.682253.582487.782489.28264382677.9

2.6139.9140.3141.3146.1154230.4342.5355.5489.9516.6564.312715.712727.912731.81277812784.212856.61286612918.71291912928.312928.521221.321235.921271.421277.321297.62130321322.521340.321417.221421.121534.421598.521603.621753.521791.621791.921810.6

23794.323951.523958.924042.124101.424109.127705.727710.527737.827795.627908.627919.428146.728162.933095.533099.633172.333277.333287.43336533367.533419.233510.538942.238942.239429.239429.239863.539863.940213.340214.240498.140505.340709.740743.640881.840902.24095941067.241073.4

41934.641970.64201342016.445235.545236.145330.645333.345435.2454724551645518.145536.445553.845554.747367.147397.847422.847549.447566.447678.248384.248396.748666.548706.54871253753.153789.254933.355010.955098.177398.677399.977713.977768.578012.178012.878197.178236.378285

gzz = 17.885379gyy = 0.001238gxx = 0.001132


23651.323651.323884.123884.624137.424137.524377.324379.324569.9

43080.243080.343306.443306.643505.743506.543644.843655.643743.1

82720.1110650.6110785.5111925.8111949.3112548112648.7112780.6

22808.722808.723018.423018.923278.123278.323547.523549.723771.2

41118.741118.74138241382.341654.441655.941820.941832.241921.1

104294.6104435.9105631.7105663.1106353.1106464.7106523.7


Table S20. Reduced LOEWDIN POPULATION ANALYSIS on model complexes [Er{N(SiMe3)2}3X]– (where X = F, Cl, Br and I). The Er is considered in +III oxidation state, while halide is considered as X– ion. The numbers provided here are net gain/loss of electron compared to reference (electronic structure of ions). The negative and positive sign here are the loss and gain of the electrons from reference electronic structure.

[Er{N(SiMe3)2}3F]– [Er{N(SiMe3)2}3Cl]– [Er{N(SiMe3)2}3Br]– [Er{N(SiMe3)2}3I]–

Er(III)(4f) 0.74 0.75 0.74 0.70Er(III)(5d) 0.76 0.93 0.99 1.08Er(III)(6s) 0.21 0.25 0.26 0.28Er(III)(6p) 0.61 0.73 0.77 0.84

X– (ns) -0.33 -0.47 -0.48 -0.48X– (np) -0.57 -0.81 -0.85 -0.93


Figure S3. Experimental and ab initio computed molar magnetic susceptibility plots for complex 1. The black hollow circle represents the experimental magnetic susceptibility extracted from the

[Er{N(SiMe3)2}3F]– [Er{N(SiMe3)2}3Cl]–

[Er{N(SiMe3)2}3Br]– [Er{N(SiMe3)2}3I]–


experimental data. The coloured lines represent computed magnetic susceptibility at BS1 level of theory.


Energy Decomposition Analysis (EDA)

Table S21. Energy decomposition analysis (in kcal mol-1) of complex 1a at the B3LYP/TZ2P level. The values in the parentheses give the percentage contribution to the total attractive interactions (ΔEelstat + ΔEorb)

Fragment Pair Complex 1aPauli

repulsion∆Epauli

Electrostatic interaction

∆Eelstat

Total steric interaction

Orbital interactions

∆Eorb

Total interaction

∆Eint

Total bonding energy

Fragment Pair A [Er{N(SiMe3)2}3

….Cl]– 1179.11 -214.51 (20.34) 964.59 -840.04

(79.65) 124.56 124.54

Fragment Pair B {Cl}….{Er….{(NSiMe)3} 397.58 -1250.70

(66.50) -853.12 -630.07(33.50) -1483.19 -

1483.19


Table S22. Structure of model complex 1TP generated from SHAPE code.

Er 8.845700000 4.215200000 12.419500000C 5.866944889 0.795726621 9.939975795H 5.569607889 1.278330621 9.166005795H 5.183693889 0.182646621 10.216070795H 6.666496889 0.308406621 9.724983795Si 7.653131715 3.872741035 9.377930198C 6.793668889 0.951354621 12.748447795H 6.080887889 0.364998621 13.015489795H 7.039202889 1.510986621 13.488471795H 7.551048889 0.429450621 12.476878795Cl 7.217900000 4.289600000 14.095500000C 4.582521889 2.765442621 11.793431795H 4.264204889 3.303066621 11.064722795H 4.689928889 3.312498621 12.574190795H 3.948905889 2.067474621 11.976739795Si 10.461818185 2.998557240 15.429178156C 6.009723715 4.488965035 8.700367198H 6.159171715 4.963709035 7.878872198H 5.600848715 5.078465035 9.338553198H 5.430011715 3.742265035 8.537426198Si 6.227484889 2.006638621 11.332669795C 8.290708715 2.608853035 8.145914198H 8.404631715 3.025433035 7.288210198H 7.658571715 1.888877035 8.068970198H 9.133621715 2.263013035 8.446903198Si 7.782688942 7.631468344 12.598593410C 8.877448715 5.274965035 9.238978198H 8.964546715 5.535917035 8.320171198H 9.731657715 4.988861035 9.571649198H 8.567274715 6.023237035 9.757221198Si 10.980073027 1.728771179 12.724484917Si 10.725344379 6.893955189 12.189232330N 7.284500000 3.293400000 10.944000000N 10.158100000 2.816900000 13.756200000N 9.094600000 6.535400000 12.558300000C 7.476981942 8.073200344 14.384157410H 6.669544942 8.587244344 14.454312410H 8.214183942 8.590388344 14.716828410H 7.390499942 7.269908344 14.902400410C 10.698567027 0.001143179 13.389148917H 9.756584027 -0.146624821 13.504565917H 11.142664027 -0.091604821 14.235537917H 11.051215027 -0.641804821 12.769066917C 11.870889379 5.424135189 12.121566330H 11.610424379 4.848783189 11.399646330


H 11.820590379 4.939959189 12.949850330H 12.771673379 5.725959189 11.981256330C 11.333631379 7.981779189 13.594825330H 12.222424379 8.288319189 13.400201330H 11.341419379 7.477167189 14.409531330H 10.749788379 8.737911189 13.689874330C 11.020943379 7.871739189 10.609834330H 11.963356379 7.903179189 10.424262330H 10.687019379 8.766207189 10.718462330H 10.565762379 7.447299189 9.878862330C 10.444214027 1.720911179 10.931452917H 10.522582027 2.605947179 10.569361917H 9.530438027 1.431663179 10.872612917H 11.001933027 1.120407179 10.433577917C 12.829972027 1.923699179 12.642334917H 13.173847027 1.415943179 11.904573917H 13.222406027 1.606155179 13.459303917H 13.048332027 2.851179179 12.524655917C 8.077520942 9.283640344 11.720522410H 8.481450942 9.123296344 10.865081410H 8.660807942 9.829124344 12.252344410H 7.239231942 9.734804344 11.598316410C 6.204957942 6.975944344 11.874411410H 6.320613942 6.826604344 10.932973410H 5.499404942 7.612604344 12.012458410H 5.975530942 6.147500344 12.304394410C 12.158379185 2.450243240 16.058538156H 12.380730185 1.596647240 15.678342156H 12.136987185 2.377931240 17.015817156H 12.819025185 3.096335240 15.802811156C 10.315425185 4.748507240 15.999698156H 11.060675185 5.256263240 15.669290156H 10.310449185 4.773659240 16.959240156H 9.497350185 5.125787240 15.667027156C 9.209799185 1.972355240 16.361790156H 8.326827185 2.308763240 16.185270156H 9.390103185 2.024231240 17.303227156H 9.268019185 1.059023240 16.072116156


Table S23. Structure of model complex 1TD generated from SHAPE code.

Er 8.520200000 4.230100000 12.754700000C 6.041298892 0.999597997 9.876194671H 5.743961892 1.482201997 9.102224671H 5.358047892 0.386517997 10.152289671H 6.840850892 0.512277997 9.661202671Si 7.682015382 3.926362636 9.232058331C 6.968022892 1.155225997 12.684666671H 6.255241892 0.568869997 12.951708671H 7.213556892 1.714857997 13.424690671H 7.725402892 0.633321997 12.413097671Cl 6.922400000 4.306600000 14.405100000C 4.756875892 2.969313997 11.729650671H 4.438558892 3.506937997 11.000941671H 4.864282892 3.516369997 12.510409671H 4.123259892 2.271345997 11.912958671Si 10.417088306 2.972791644 15.145536289C 6.038607382 4.542586636 8.554495331H 6.188055382 5.017330636 7.733000331H 5.629732382 5.132086636 9.192681331H 5.458895382 3.795886636 8.391554331Si 6.401838892 2.210509997 11.268888671C 8.319592382 2.662474636 8.000042331H 8.433515382 3.079054636 7.142338331H 7.687455382 1.942498636 7.923098331H 9.162505382 2.316634636 8.301031331Si 7.997394698 7.451110320 12.581368422C 8.906332382 5.328586636 9.093106331H 8.993430382 5.589538636 8.174299331H 9.760541382 5.042482636 9.425777331H 8.596158382 6.076858636 9.611349331Si 11.056169328 1.625344722 12.630911783Si 10.883986214 6.939963113 12.162555561N 7.602400000 3.350200000 10.840100000N 10.269900000 2.908400000 13.443100000N 9.285900000 6.355200000 12.330700000C 7.691687698 7.892842320 14.366932422H 6.884250698 8.406886320 14.437087422H 8.428889698 8.410030320 14.699603422H 7.605205698 7.089550320 14.885175422C 10.774663328 -0.102283278 13.295575783H 9.832680328 -0.250051278 13.410992783H 11.218760328 -0.195031278 14.141964783H 11.127311328 -0.745231278 12.675493783C 12.029531214 5.470143113 12.094889561H 11.769066214 4.894791113 11.372969561


H 11.979232214 4.985967113 12.923173561H 12.930315214 5.771967113 11.954579561C 11.492273214 8.027787113 13.568148561H 12.381066214 8.334327113 13.373524561H 11.500061214 7.523175113 14.382854561H 10.908430214 8.783919113 13.663197561C 11.179585214 7.917747113 10.583157561H 12.121998214 7.949187113 10.397585561H 10.845661214 8.812215113 10.691785561H 10.724404214 7.493307113 9.852185561C 10.520310328 1.617484722 10.837879783H 10.598678328 2.502520722 10.475788783H 9.606534328 1.328236722 10.779039783H 11.078029328 1.016980722 10.340004783C 12.906068328 1.820272722 12.548761783H 13.249943328 1.312516722 11.811000783H 13.298502328 1.502728722 13.365730783H 13.124428328 2.747752722 12.431082783C 8.292226698 9.103282320 11.703297422H 8.696156698 8.942938320 10.847856422H 8.875513698 9.648766320 12.235119422H 7.453937698 9.554446320 11.581091422C 6.419663698 6.795586320 11.857186422H 6.535319698 6.646246320 10.915748422H 5.714110698 7.432246320 11.995233422H 6.190236698 5.967142320 12.287169422C 12.113649306 2.424477644 15.774896289H 12.336000306 1.570881644 15.394700289H 12.092257306 2.352165644 16.732175289H 12.774295306 3.070569644 15.519169289C 10.270695306 4.722741644 15.716056289H 11.015945306 5.230497644 15.385648289H 10.265719306 4.747893644 16.675598289H 9.452620306 5.100021644 15.383385289C 9.165069306 1.946589644 16.078148289H 8.282097306 2.282997644 15.901628289H 9.345373306 1.998465644 17.019585289H 9.223289306 1.033257644 15.788474289

Table S24. Er-X bond lengths in the model [Er{N(SiMe3)2}3X]– model complexes.

Er-X bonds Bond lengths (Å)Er—F 2.053Er—Br 2.67Er—I 2.88


Figure S4. Ab initio blockade barrier for complex 1m. The thick black line indicates the Kramer’s doublets (KDs) as a function of magnetic moment. The green lines show the possible pathway of the Orbach process. The blue lines show the most probable relaxation pathways for magnetization reversal. The dotted red lines represent the presence of QTM/TA-QTM between the connecting pairs. The numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the transition magnetic moment.

-10 -8 -6 -4 -2 0 2 4 6 8 10-100

0

100

200

300

400

500

600

700En

ergy

(cm

-1)

M(B)

0.51E-03

1.54

2.10

0.19E-01

0.19E-01

0.11

1.54

2.50

2.75

-1

-2

-4

-5

-3

+1

+2

+4

+5

+3


Figure S5. Ab initio blockade barrier for complex 3. The thick black line indicates the Kramer’s doublets (KDs) as a function of magnetic moment. The green lines show the possible pathway of the Orbach process. The blue lines show the most probable relaxation pathways for magnetization reversal. The dotted red lines represent the presence of QTM/TA-QTM between the connecting pairs. The numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the transition magnetic moment.

-10 -8 -6 -4 -2 0 2 4 6 8 10-50

0

50

100

150

200

250

300

350

400En

ergy

(cm

-1)

M(B)

0.70E-02

1.53

-1

-2-3

-4

0.76E-01

0.41

0.76E-012.10

2.54

+1

+2

+3

+4


-out of plane shift parameter

Figure S6. CASSF+RASSI computed Ucal value plotted against parameter extracted from the experimental geometry of the complexes of 1-3.


Figure S7. SINGLE_ANISO computed principal magnetization orientation of each KDs of complex 1TD.

Figure S8. SINGLE_ANISO computed principal magnetization orientation of each KDs of complex 1TD.

123 6

47

8 5

1,2,3,4,5,6,7,8


Figure S9. Ab initio blockade barrier for complexes [Er{N(SiMe3)2}3X]– a) X=F, b) X=Cl, c) X=Br, d) X=I. The thick black line indicates the Kramer’s doublets (KDs) as a function of magnetic moment. The green lines show the possible pathway of the Orbach process. The blue lines show the most probable relaxation pathways for magnetization reversal. The dotted red lines represent the presence of QTM/TA-QTM between the connecting pairs. The numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the transition magnetic moment.


1. L. Ungur, M. Thewissen, J. P. Costes, W. Wernsdorfer and L. F. Chibotaru, Inorg. Chem., 2013, 52, 6328-6337.

2. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, N. J. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Journal, 2009.

3. A. D. Becke, J. Chem. Phys., 1993, 98, 5648-5652.4. T. R. Cundari and W. J. Stevens, J. Chem. Phys., 1993, 98, 5555-5565.5. A. Schafer, C. Huber and R. Ahlrichs, J. Chem. Phys., 1994, 100, 5829-5835.6. F. Biegler‐König and J. Schönbohm, J. Comput. Chem., 2002, 23, 1489-1494.7. T. Lu and F. Chen, J. Comput. Chem., 2012, 33, 580-592.8. G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fonseca Guerra, S. J. A. van

Gisbergen, J. G. Snijders and T. Ziegler, J. Comput. Chem., 2001, 22, 931-967.9. K. Morokuma, J. Chem. Phys., 1971, 55, 1236-1244.10. T. Ziegler and A. Rauk, Theor. Chim. Acta., 1977, 46, 1-10.

Er(III) Complexes ** Supplementary Information Field Design ...Supplementary Information Table S1. Selected structural-parameters of complex 1, 2, and 3.Selected structural parameters

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