ar-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibo+-mpn_Rfcic2-mpn_Rfcicn+-mpn_Rfcin2-mpn_Rfcihf-mpn_Rfcihf-mpn_Rfcihcl-mpn_Rfcihcl-mpn_Rfcif--mpn_Rfcicl--mpn_Rfcicl--mpn_Rfcine-mpn_Rfcioh--mpn_Rfcish--mpn_Rfci

Moller-Plesset perturbation theory: example "c2-mpn_Rfci"

System c2-mpn_Rfci

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-75.3864565-75.38646
2-0.3129603-75.69942
30.0346582-75.66476
4-0.0731568-75.73792
50.040188-75.69773
6-0.0424546-75.74018
70.0281678-75.71201
8-0.0254155-75.73743
90.0160167-75.72141
10-0.0118944-75.73331
110.0055285-75.72778
12-0.0018493-75.72963
13-0.001938-75.73157
140.0042006-75.72737
15-0.0057493-75.73311
160.0063768-75.72674
17-0.0062089-75.73295
180.0055382-75.72741
19-0.0043467-75.73176
200.0030044-75.72875
21-0.0015121-75.73026
220.0001507-75.73011
230.001056-75.72906
24-0.0019595-75.73102
250.0025488-75.72847
26-0.0027947-75.73126
270.0027222-75.72854
28-0.0023837-75.73092
290.0018377-75.72909
30-0.0011733-75.73026
310.0004608-75.72980
320.0002146-75.72958
33-0.0007963-75.73038
340.0012308-75.72915
35-0.0014938-75.73064
360.0015741-75.72907
37-0.0014836-75.73055
380.001248-75.72930
39-0.0009053-75.73021
400.0005011-75.72971
41-0.0000819-75.72979
42-0.0003074-75.73010
430.0006302-75.72947
44-0.0008587-75.73033
450.0009781-75.72935
46-0.0009852-75.73033
470.0008887-75.72944
48-0.0007072-75.73015
490.0004664-75.72969
50-0.0001959-75.72988
51-0.000074-75.72996
520.0003152-75.72964
53-0.0005051-75.73015
540.0006277-75.72952
55-0.0006754-75.73019
560.0006487-75.72954
57-0.0005558-75.73010
580.0004111-75.72969
59-0.0002333-75.72992
600.0000434-75.72988
610.000138-75.72974
62-0.0002926-75.73003
630.000406-75.72963
64-0.0004691-75.73010
650.0004787-75.72962
66-0.0004372-75.73006
670.0003523-75.72970
68-0.0002356-75.72994
690.0001015-75.72984
700.000035-75.72980
71-0.0001593-75.72996
720.0002593-75.72970
73-0.0003258-75.73003
740.0003538-75.72967
75-0.0003429-75.73002
760.0002964-75.72972
77-0.0002212-75.72994
780.0001271-75.72981
79-0.0000249-75.72984
80-0.000074-75.72991
810.0001596-75.72975
82-0.0002234-75.72998
830.0002601-75.72972
84-0.0002672-75.72998
850.0002456-75.72974
86-0.0001992-75.72994
870.0001343-75.72980
88-0.0000586-75.72986
89-0.0000193-75.72988
900.000091-75.72979
91-0.0001493-75.72994
920.0001887-75.72975
93-0.0002061-75.72996
940.0002007-75.72976
95-0.0001744-75.72993
960.0001308-75.72980
97-0.0000757-75.72988
980.0000152-75.72986
990.0000438-75.72982
100-0.0000952-75.72991
1010.000134-75.72978
102-0.0001567-75.72993
1030.0001617-75.72977
104-0.0001492-75.72992
1050.0001215-75.72980
106-0.0000823-75.72988
1070.0000361-75.72985
1080.0000116-75.72984
109-0.0000559-75.72989
1100.0000922-75.72980
111-0.0001169-75.72992
1120.0001282-75.72979
113-0.0001252-75.72991
1140.0001091-75.72980
115-0.0000822-75.72989
1160.0000477-75.72984
117-9.7e-6-75.72985
118-0.0000275-75.72988
1190.0000602-75.72982
120-0.000085-75.72990
1210.0000997-75.72980
122-0.0001031-75.72990
1230.0000955-75.72981
124-0.0000779-75.72989
1250.0000529-75.72983
126-0.0000233-75.72986
127-7.4e-6-75.72986
1280.0000361-75.72983
129-0.0000597-75.72989
1300.0000759-75.72981
131-0.0000833-75.72990
1320.0000816-75.72981
133-0.0000713-75.72989
1340.0000538-75.72983
135-0.0000313-75.72986
1366.4e-6-75.72986
1370.0000181-75.72984
138-0.0000397-75.72988
1390.0000561-75.72982
140-0.0000659-75.72989
1410.0000683-75.72982
142-0.0000633-75.72988
1430.0000518-75.72983
144-0.0000352-75.72987
1450.0000156-75.72985
1464.9e-6-75.72985
147-0.0000241-75.72987
1480.00004-75.72983
149-0.0000509-75.72988
1500.000056-75.72982
151-0.0000549-75.72988
1520.000048-75.72983
153-0.0000363-75.72987
1540.0000212-75.72985
155-4.4e-6-75.72985
Exact energy-75.72985
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Coefficients of Moller-Plesset perturbation theory, semilogarithmic plot.
Red/blue dots correspond to positive/negative coefficients
Plot of MP coefficients
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Scaled coefficients of Moller-Plesset perturbation theory.
Parameters a =  1.0073, b = -2.8132 and c =  18.8542
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -75.39 is not shown because it is too small and out of scale
Plot of MP coefficients
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Convergence of summation approximants for the Moller - Plesset series
measured in growth of number of accurate decimal digits of summation results
with increase of n, number of used coefficients.
The summation methods are partial sums (red connected disks),
Pade approximants (blue circles),
quadratic approximants (green boxes),
cubic, quartic, fifth and sixth degree approximants
(triangles, diamonds, pentagonal and hexagonal stars respectively).
Plot of number of accurate digits
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Location of singularities in the complex plane of the parameter z.
Left panel refers to quadratic approximants,
right panel to differential approximants.
To view an individual approximant, click on the right bar.
Location of singularities in the  complex plane
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ar-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibh-mpn_Rfcibo+-mpn_Rfcic2-mpn_Rfcicn+-mpn_Rfcin2-mpn_Rfcihf-mpn_Rfcihf-mpn_Rfcihcl-mpn_Rfcihcl-mpn_Rfcif--mpn_Rfcicl--mpn_Rfcicl--mpn_Rfcine-mpn_Rfcioh--mpn_Rfcish--mpn_Rfci
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Designed by A. Sergeev.