Calculating the coordination numbers for different atomic sites¶
The Structure class of the strct sub-package can be used to determine the coordination number of periodic and non-periodic structures using different methods, all of them described here: doi:10.1021/acs.inorgchem.0c02996.
First, we create an object of the class and import a structure:
[1]:
from aim2dat.strct import Structure
strct = Structure.from_file("files/zif8_structure/ZIF-8.cif", label="ZIF-8")
Three different methods are implemented to calculate the coordination numbers:
"minimum_distance": The distance of the closest atom is taken as reference. All atoms inbetween that distance and a relative margin are considered as neighbours of the atomic site. The relative margin can be set via the attributeminimum_distance_delta, the default value is0.1."econ": The effective coordination number algorithm is an iterative method. Two parameters can be changed to tweak the method:econ_toleranceandecon_conv_thresholdwith the default values of0.5and0.001, respectively."okeeffe": The method developed by O’Keeffe is based on the Voronoi tessellation and thereby computationally a bit more demanding than the previous methods. The attributeokeeffe_weight_thresholdcan be set and acts as threshold for the solid angle of the Voronoi facets. Its default value is set to0.5.
The coordination numbers for each site can then be readily calculated using the methods calculate_coordination:
[2]:
strct.calculate_coordination()
[2]:
{'distance_avg': {('Zn', 'N'): 1.9651884952153824,
('C', 'N'): 1.3481992499546553,
('N', 'C'): 1.3734536168260307,
('C', 'H'): 0.9482500804509107,
('H', 'C'): 0.9482500804509109},
'distance_stdev': {('Zn', 'N'): 8.612455701839897e-06,
('C', 'N'): 6.170252041246332e-06,
('N', 'C'): 0.02552161688364479,
('C', 'H'): 0.01490735862562007,
('H', 'C'): 0.014907358625619952},
'distance_max': {('Zn', 'N'): 1.9652020658995912,
('C', 'N'): 1.3482095142807609,
('N', 'C'): 1.398712990170384,
('C', 'H'): 0.9612687439831057,
('H', 'C'): 0.9612687439831057},
'distance_min': {('Zn', 'N'): 1.9651805961901716,
('C', 'N'): 1.3481940221322792,
('N', 'C'): 1.3481940221322792,
('C', 'H'): 0.9301526896173402,
('H', 'C'): 0.9301526896173401},
'nrs_avg': {('Zn', 'Zn'): 0,
('Zn', 'C'): 0,
('Zn', 'N'): 4,
('Zn', 'H'): 0,
('C', 'Zn'): 0,
('C', 'C'): 0,
('C', 'N'): 0.5,
('C', 'H'): 1.25,
('N', 'Zn'): 0,
('N', 'C'): 2,
('N', 'N'): 0,
('N', 'H'): 0,
('H', 'Zn'): 0,
('H', 'C'): 1,
('H', 'N'): 0,
('H', 'H'): 0},
'nrs_stdev': {('Zn', 'Zn'): 0.0,
('Zn', 'C'): 0.0,
('Zn', 'N'): 0.0,
('Zn', 'H'): 0.0,
('C', 'Zn'): 0.0,
('C', 'C'): 0.0,
('C', 'N'): 0.8751899489873673,
('C', 'H'): 1.1012565357112796,
('N', 'Zn'): 0.0,
('N', 'C'): 0.0,
('N', 'N'): 0.0,
('N', 'H'): 0.0,
('H', 'Zn'): 0.0,
('H', 'C'): 0.0,
('H', 'N'): 0.0,
('H', 'H'): 0.0},
'nrs_max': {('Zn', 'Zn'): 0,
('Zn', 'C'): 0,
('Zn', 'N'): 4,
('Zn', 'H'): 0,
('C', 'Zn'): 0,
('C', 'C'): 0,
('C', 'N'): 2,
('C', 'H'): 3,
('N', 'Zn'): 0,
('N', 'C'): 2,
('N', 'N'): 0,
('N', 'H'): 0,
('H', 'Zn'): 0,
('H', 'C'): 1,
('H', 'N'): 0,
('H', 'H'): 0},
'nrs_min': {('Zn', 'Zn'): 0,
('Zn', 'C'): 0,
('Zn', 'N'): 4,
('Zn', 'H'): 0,
('C', 'Zn'): 0,
('C', 'C'): 0,
('C', 'N'): 0,
('C', 'H'): 0,
('N', 'Zn'): 0,
('N', 'C'): 2,
('N', 'N'): 0,
('N', 'H'): 0,
('H', 'Zn'): 0,
('H', 'C'): 1,
('H', 'N'): 0,
('H', 'H'): 0},
'sites': [{'Zn': 0,
'C': 0,
'N': 4,
'H': 0,
'element': 'Zn',
'kind': None,
'position': [7.296689736497134, 5.619566364689632e-05, 5.957730332583271],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 18,
'distance': 1.9651889528071236,
'position': [9.157826390914545, 0.07298329121481956, 6.58448356357103]},
{'element': 'N',
'kind': None,
'site_index': 19,
'distance': 1.9651805961901723,
'position': [6.745065666789741, 1.7790519935249622, 5.330977101595511]},
{'element': 'N',
'kind': None,
'site_index': 32,
'distance': 1.9651823659646426,
'position': [6.130206305553247, -0.5640371384649034, 7.435247455063922]},
{'element': 'N',
'kind': None,
'site_index': 33,
'distance': 1.9652020658995908,
'position': [7.153660582731001, -1.2877733636202902, 4.48021321010262]}],
'total_cn': 4,
'min_dist': 1.9651805961901723,
'max_dist': 1.9652020658995908,
'avg_dist': 1.9651884952153824},
{'Zn': 0,
'C': 0,
'N': 4,
'H': 0,
'element': 'Zn',
'kind': None,
'position': [-2.4321504391714384, 6.879413154848223, 5.957730332583271],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 20,
'distance': 1.9651823659646415,
'position': [-2.575159883634991, 5.591611468613456, 7.435247455063922]},
{'element': 'N',
'kind': None,
'site_index': 21,
'distance': 1.9652020658995908,
'position': [-3.5986535794179053, 6.315291947670503, 4.48021321010262]},
{'element': 'N',
'kind': None,
'site_index': 30,
'distance': 1.9651889528071242,
'position': [-2.983766148319832, 8.65842077627717, 6.58448356357103]},
{'element': 'N',
'kind': None,
'site_index': 31,
'distance': 1.9651805961901716,
'position': [-0.5710221453130249, 6.952328426831764, 5.330977101595511]}],
'total_cn': 4,
'min_dist': 1.9651805961901716,
'max_dist': 1.9652020658995908,
'avg_dist': 1.965188495215382},
{'Zn': 0,
'C': 0,
'N': 4,
'H': 0,
'element': 'Zn',
'kind': None,
'position': [2.4322696486628486, 8.599224296812542, 2.9788651662916354],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 22,
'distance': 1.9651889528071258,
'position': [2.289265226892534, 10.522696054166493, 3.3553937233108986]},
{'element': 'N',
'kind': None,
'site_index': 23,
'distance': 1.9651805961901718,
'position': [1.2657828798532025, 7.601729114037491, 4.206157614803789]},
{'element': 'N',
'kind': None,
'site_index': 40,
'distance': 1.9651823659646426,
'position': [4.293401280387023, 8.019984801067077, 3.229089840260133]},
{'element': 'N',
'kind': None,
'site_index': 41,
'distance': 1.9652020658995903,
'position': [1.8806292075186353, 8.252487217979114, 1.1248194867917216]}],
'total_cn': 4,
'min_dist': 1.9651805961901718,
'max_dist': 1.9652020658995903,
'avg_dist': 1.9651884952153826},
{'Zn': 0,
'C': 0,
'N': 4,
'H': 0,
'element': 'Zn',
'kind': None,
'position': [2.4322696486628486, -1.7197549463006727, 8.936595498874906],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 24,
'distance': 1.9651823659646437,
'position': [4.293401280387023, -1.2134378256706302, 8.560066941855643]},
{'element': 'N',
'kind': None,
'site_index': 25,
'distance': 1.9652020658995908,
'position': [1.8806292075186355, -3.1520486415096127, 7.709303050362752]},
{'element': 'N',
'kind': None,
'site_index': 38,
'distance': 1.9651889528071236,
'position': [2.289265226892534, -2.3553900412388, 10.79064117837482]},
{'element': 'N',
'kind': None,
'site_index': 39,
'distance': 1.9651805961901723,
'position': [1.265782879853203,
-0.15814327678364726,
8.686370824906408]}],
'total_cn': 4,
'min_dist': 1.9651805961901723,
'max_dist': 1.9652020658995908,
'avg_dist': 1.9651884952153824},
{'Zn': 0,
'C': 0,
'N': 4,
'H': 0,
'element': 'Zn',
'kind': None,
'position': [-2.4321504391714384, 1.7199235332916143, 8.936595498874906],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 26,
'distance': 1.9651889528071236,
'position': [-2.983766148319832, 1.3732214306392387, 10.79064117837482]},
{'element': 'N',
'kind': None,
'site_index': 27,
'distance': 1.9651805961901718,
'position': [-0.5710221453130249, 1.1406793171104, 8.686370824906408]},
{'element': 'N',
'kind': None,
'site_index': 36,
'distance': 1.9651823659646417,
'position': [-2.575159883634991, 3.643388187513678, 8.560066941855643]},
{'element': 'N',
'kind': None,
'site_index': 37,
'distance': 1.9652020658995912,
'position': [-3.5986535794179053,
0.7224051979031391,
7.709303050362752]}],
'total_cn': 4,
'min_dist': 1.9651805961901718,
'max_dist': 1.9652020658995912,
'avg_dist': 1.965188495215382},
{'Zn': 0,
'C': 0,
'N': 4,
'H': 0,
'element': 'Zn',
'kind': None,
'position': [7.296689736497135, 5.1595458172202555, 2.9788651662916354],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 28,
'distance': 1.9651823659646417,
'position': [6.130206305553249, 6.721162207173027, 3.229089840260133]},
{'element': 'N',
'kind': None,
'site_index': 29,
'distance': 1.9652020658995906,
'position': [7.1536605827310025, 4.523875746101074, 1.1248194867917216]},
{'element': 'N',
'kind': None,
'site_index': 34,
'distance': 1.9651889528071247,
'position': [9.157826390914547, 5.665870040982182, 3.3553937233108986]},
{'element': 'N',
'kind': None,
'site_index': 35,
'distance': 1.965180596190172,
'position': [6.745065666789744, 3.727275274624738, 4.206157614803789]}],
'total_cn': 4,
'min_dist': 1.965180596190172,
'max_dist': 1.9652020658995906,
'avg_dist': 1.9651884952153822},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [-4.915942783061324, 0.9170890105215702, 7.4983993965893045],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 18,
'distance': 1.3482095142807609,
'position': [-5.435473609085451, 0.0729832912148195, 6.58448356357103]},
{'element': 'N',
'kind': None,
'site_index': 37,
'distance': 1.3481961964440305,
'position': [-3.598653579417905, 0.7224051979031391, 7.709303050362752]}],
'total_cn': 2,
'min_dist': 1.3481961964440305,
'max_dist': 1.3482095142807609,
'avg_dist': 1.3482028553623957},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [7.367710007518636, 2.55021928823475, 4.417061268577236],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 19,
'distance': 1.34819402213228,
'position': [6.7450656667897455, 1.7790519935249627, 5.330977101595511]},
{'element': 'N',
'kind': None,
'site_index': 35,
'distance': 1.3481940221322792,
'position': [6.745065666789746, 3.7272752746247386, 4.206157614803789]}],
'total_cn': 2,
'min_dist': 1.3481940221322792,
'max_dist': 1.34819402213228,
'avg_dist': 1.3481940221322795},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [-2.40004584674459, 4.2563276871616935, 7.3720955135385395],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 20,
'distance': 1.348197266961551,
'position': [-2.5751598836349907, 5.591611468613456, 7.435247455063922]},
{'element': 'N',
'kind': None,
'site_index': 36,
'distance': 1.3481972669615494,
'position': [-2.5751598836349907, 3.643388187513678, 8.560066941855643]}],
'total_cn': 2,
'min_dist': 1.3481972669615494,
'max_dist': 1.348197266961551,
'avg_dist': 1.34819726696155},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [-4.915942783061324, 6.035302715105725, 4.543365151628002],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 21,
'distance': 1.3481961964440305,
'position': [-3.598653579417905, 6.315291947670503, 4.48021321010262]},
{'element': 'N',
'kind': None,
'site_index': 34,
'distance': 1.3482095142807602,
'position': [-5.435473609085451, 5.665870040982182, 3.3553937233108986]}],
'total_cn': 2,
'min_dist': 1.3481961964440305,
'max_dist': 1.3482095142807602,
'avg_dist': 1.3482028553623953},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [7.328775462035145, -2.6230559537239815, 4.543365151628002],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 22,
'distance': 1.3482095142807604,
'position': [7.153645578229685, -3.236017864202659, 3.3553937233108986]},
{'element': 'N',
'kind': None,
'site_index': 33,
'distance': 1.3481961964440308,
'position': [7.153660582731004, -1.2877733636202902, 4.48021321010262]}],
'total_cn': 2,
'min_dist': 1.3481961964440308,
'max_dist': 1.3482095142807604,
'avg_dist': 1.3482028553623957},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [-0.051503510446218856, 7.796416905308908, 4.417061268577236],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 23,
'distance': 1.3481940221322797,
'position': [1.2657828798532034, 7.601729114037492, 4.206157614803789]},
{'element': 'N',
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'distance': 1.3481940221322803,
'position': [-0.5710221453130243, 6.952328426831765, 5.330977101595511]}],
'total_cn': 2,
'min_dist': 1.3481940221322797,
'max_dist': 1.3481940221322803,
'avg_dist': 1.34819402213228},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [4.812916259496092, -0.8440275623777511, 7.3720955135385395],
'neighbours': [{'element': 'N',
'kind': None,
'site_index': 24,
'distance': 1.3481972669615487,
'position': [4.293401280387024, -1.213437825670631, 8.560066941855643]},
{'element': 'N',
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'distance': 1.34819726696155,
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'avg_dist': 1.3481972669615494},
{'Zn': 0,
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'H': 0,
'element': 'C',
'kind': None,
'position': [2.5032707349035297, -4.3291086065525874, 7.4983993965893045],
'neighbours': [{'element': 'N',
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{'element': 'N',
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'distance': 1.3482095142807602,
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'min_dist': 1.3481961964440305,
'max_dist': 1.3482095142807602,
'avg_dist': 1.3482028553623953},
{'Zn': 0,
'C': 0,
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'H': 0,
'element': 'C',
'kind': None,
'position': [2.5032707349035297, 8.658358668829706, 0.0],
'neighbours': [{'element': 'N',
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'distance': 1.3481961964440303,
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'min_dist': 1.3481961964440303,
'max_dist': 1.34820951428076,
'avg_dist': 1.3482028553623953},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [-0.05150351044621865, -0.07283666548923233, 8.96042642020524],
'neighbours': [{'element': 'N',
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8.686370824906408]}],
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'avg_dist': 1.3481940221322808},
{'Zn': 0,
'C': 0,
'N': 2,
'H': 0,
'element': 'C',
'kind': None,
'position': [4.812916259496092, 6.806463648466388, 2.955034244961302],
'neighbours': [{'element': 'N',
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{'element': 'N',
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'avg_dist': 1.3481972669615505},
{'Zn': 0,
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'kind': None,
'position': [7.328775462035145, 5.2461976170741575, 0.0],
'neighbours': [{'element': 'N',
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{'Zn': 0,
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'position': [9.157826390914549, 0.07298329121481943, 6.5844835635710295],
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Based on the coordination numbers and distances two atomic sites can be compared using the StructureOperations class:
[3]:
from aim2dat.strct import StructureCollection, StructureOperations
strct_op = StructureOperations(StructureCollection([strct]))
strct_op.compare_sites_via_coordination("ZIF-8", "ZIF-8", 0, 1)
[3]:
True