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Clementi-Raimondi Effective Nuclear Charge Navigation

Aluminum to Gadolinium

Gallium to Neodymium

Neon to Selenium

Silicon to Zirconium

By Name

By Symbol

By Number

Clementi-Raimondi Effective Nuclear Charge

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Element

Orbital Exponent

( ζ )

Principle Quantum Number

( n )

Effective Nuclear Charge

( Zeff = ζ × n )

Silicon

1s

13.5745

1

13.5745

2s

 4.5100

2

 9.0200

2p

 4.9725

2

 9.9450

3s

 1.6344

3

 4.9032

3p

 1.4284

3

 4.2852

Silver

1s

46.0423

1

46.0423

2s

17.3171

2

34.6342

2p

21.4597

2

42.9194

3s

10.0104

3

30.0312

3p

 9.9362

3

29.809 

4s

 4.9662

4

19.865 

3d

10.8466

3

32.5398

4p

 4.6406

4

18.562 

5s

 1.3511

5

 6.7555

4d

 3.6907

4

14.763 

Sodium

1s

10.6259

1

10.6259

2s

 3.2857

2

 6.5714

2p

 3.4009

2

 6.8018

3s

 0.8358

3

 2.507 

Strontium

1s

37.1911

1

37.1911

2s

13.9509

2

27.9018

2p

17.0152

2

34.0304

3s

 7.5546

3

22.664 

3p

 7.3892

3

22.168 

4s

 3.3611

4

13.444 

3d

 7.5754

3

22.726 

4p

 2.9830

4

11.932 

5s

 1.2141

5

 6.0705

Sulfur

1s

15.5409

1

15.5409

2s

 5.3144

2

10.629 

2p

 5.9885

2

11.977 

3s

 2.1223

3

 6.3669

3p

 1.8273

3

 5.4819

Tantalum

1s

71.5837

1

71.5837

2s

26.9649

2

53.9298

2p

34.2932

2

68.5864

3s

17.0305

3

51.0915

3p

17.2668

3

51.8004

4s

 9.9397

4

39.759 

3d

19.8137

3

59.4411

4p

 9.6837

4

38.735 

5s

 4.5387

5

22.694 

4d

 9.0810

4

36.324 

5p

 4.0947

5

20.474 

6s

 1.5875

6

 9.5250

4f

 8.3676

4

33.470 

5d

 3.2736

5

16.368 

Technetium

1s

42.1090

1

42.1090

2s

15.8141

2

31.6282

2p

19.4704

2

38.9408

3s

 8.9304

3

26.791 

3p

 8.7947

3

26.384 

4s

 4.2996

4

17.198 

3d

 9.4510

3

28.353 

4p

 3.9528

4

15.811 

5s

 1.4453

5

 7.2265

4d

 3.2205

4

12.882 

Tellurium

1s

50.9568

1

50.9568

2s

19.1656

2

38.3312

2p

23.9300

2

47.8600

3s

11.3327

3

33.9981

3p

11.3363

3

34.0089

4s

 6.1021

4

24.408 

3d

12.6131

3

37.8393

4p

 5.7805

4

23.122 

5s

 2.5076

5

12.538 

4d

 4.9900

4

19.960 

5p

 2.1617

5

10.808 

Terbium

1s

63.7261

1

63.7261

2s

23.9861

2

47.9722

2p

30.3462

2

60.6924

3s

14.8505

3

44.5515

3p

15.0049

3

45.0147

4s

 8.5050

4

34.020 

3d

17.0995

3

51.2985

4p

 8.3497

4

33.399 

5s

 3.8341

5

19.170 

4d

 7.5775

4

30.310 

5p

 3.3922

5

16.961 

6s

 1.3834

6

 8.3004

4f

 6.4662

4

25.865 

Thallium

1s

79.4409

1

79.4409

2s

29.8421

2

59.6842

2p

38.2431

2

76.4862

3s

19.1397

3

57.4191

3p

19.4555

3

58.3665

4s

11.5197

4

46.0788

3d

22.5114

3

67.5342

4p

11.3042

4

45.2168

5s

 5.8244

5

29.122 

4d

10.8472

4

43.3888

5p

 5.4177

5

27.088 

6s

 2.1366

6

12.820 

4f

10.7169

4

42.8676

5d

 4.4050

5

22.025 

6p

 2.0423

6

12.254 

Thulium

1s

67.6563

1

67.6563

2s

25.4739

2

50.9478

2p

32.3206

2

64.6412

3s

15.9728

3

47.9184

3p

16.1587

3

48.4761

4s

 9.2844

4

37.138 

3d

18.4581

3

55.3743

4p

 8.9970

4

35.988 

5s

 4.0074

5

20.037 

4d

 8.2360

4

32.944 

5p

 3.5456

5

17.728 

6s

 1.4307

6

 8.5842

4f

 7.1585

4

28.634 

Tin

1s

48.9920

1

48.9920

2s

18.4297

2

36.8594

2p

22.9427

2

45.8854

3s

10.8066

3

32.4198

3p

10.7844

3

32.3532

4s

 5.6645

4

22.658 

3d

11.9139

3

35.7417

4p

 5.3163

4

21.265 

5s

 2.1257

5

10.628 

4d

 4.4925

4

17.970 

5p

 1.8204

5

 9.1020

Titanium

1s

21.4409

1

21.4409

2s

 7.6883

2

15.377 

2p

 9.0324

2

18.065 

3s

 3.6777

3

11.033 

3p

 3.3679

3

10.104 

4s

 1.2042

4

 4.8168

3d

 2.7138

3

 8.1414

Tungsten

1s

72.5657

1

72.5657

2s

27.3349

2

54.6698

2p

34.7871

2

69.5742

3s

17.2900

3

51.8700

3p

17.5392

3

52.6176

4s

10.1397

4

40.5588

3d

20.1508

3

60.4524

4p

 9.8871

4

39.548 

5s

 4.7083

5

23.542 

4d

 9.2933

4

37.173 

5p

 4.2651

5

21.326 

6s

 1.6424

6

 9.8544

4f

 8.6777

4

34.711 

5d

 3.3484

5

16.742 

Vanadium

1s

22.4256

1

22.4256

2s

 8.0907

2

16.181 

2p

 9.5364

2

19.073 

3s

 3.9031

3

11.709 

3p

 3.5950

3

10.785 

4s

 1.2453

4

 4.9812

3d

 2.9943

3

 8.9829

Xenon

1s

52.9215

1

52.9215

2s

19.9015

2

39.8030

2p

24.9173

2

49.8346

3s

11.8588

3

35.5764

3p

11.8892

3

35.6676

4s

 6.5432

4

26.173 

3d

13.3156

3

39.9468

4p

 6.2393

4

24.957 

5s

 2.8436

5

14.218 

4d

 5.4733

4

21.893 

5p

 2.4849

5

12.424 

Ytterbium

1s

68.6389

1

68.6389

2s

25.8470

2

51.6940

2p

32.8142

2

65.6284

3s

16.2534

3

48.7602

3p

16.4455

3

49.3365

4s

 9.3794

4

37.518 

3d

18.7989

3

56.3967

4p

 9.1005

4

36.402 

5s

 4.0300

5

20.150 

4d

 8.3974

4

33.590 

5p

 3.5663

5

17.832 

6s

 1.4322

6

 8.5932

4f

 7.3580

4

29.432 

Yttrium

1s

38.1756

1

38.1756

2s

14.3111

2

28.6222

2p

17.5016

2

35.0032

3s

 7.8505

3

23.552 

3p

 7.6975

3

23.092 

4s

 3.5659

4

14.264 

3d

 8.4657

3

25.397 

4p

 3.1864

4

12.746 

5s

 1.2512

5

 6.2560

4d

 3.9896

4

15.958 

Zinc

1s

29.3245

1

29.3245

2s

10.9140

2

21.8280

2p

13.0490

2

26.0980

3s

 5.4064

3

16.219 

3p

 5.1231

3

15.369 

4s

 1.4913

4

 5.9652

3d

 4.6261

3

13.878 

Zirconium

1s

39.1590

1

39.1590

2s

14.6869

2

29.3738

2p

17.9964

2

35.9928

3s

 8.1205

3

24.362 

3p

 7.9485

3

23.846 

4s

 3.7254

4

14.902 

3d

 8.5223

3

25.567 

4p

 3.3650

4

13.460 

5s

 1.2891

5

 6.4455

4d

 3.2679

4

13.072 

References    (Click the button next to a value above to see complete citation information for that entry)

Clementi, E., and D. L. Raimondi. "Atomic Screening Constants from SCF Functions." Journal of Chemical Physics, volume 38, number 11, 1963, pp. 2686–2689. doi:10.1063/1.1733573

Clementi, E., D. L. Raimondi, and W. P. Reinhardt. "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons." Journal of Chemical Physics, volume 47, number 4, 1967, pp. 1300–1307. doi:10.1063/1.1712084

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