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Research Article
Potential risk resulting from the influence of static magnetic field upon living organisms. Numerically simulated effects of the static magnetic field upon porphine
expand article infoWojciech Ciesielski, Tomasz Girek, Zdzisław Oszczęda§, Jacek A. Soroka|, Piotr Tomasik§
‡ Jan Długosz University, Częstochowa, Poland
§ Nantes Nanotechnological Systems, Bolesławiec, Poland
| Scientific Society of Szczecin, Szczecin, Poland
Open Access

Abstract

Background: Recognizing effects of static magnetic field (SMF) of varying flux density on flora and fauna is attempted. For this purpose the influence of SMF upon the porphine molecule is studied.

Methods: Computations of the effect of static magnetic field (SMF) of 0.0, 0.1, 1, 10 and 100 AFU (1 AFU > 1000 T) flux density were performed in silico for SMF changes distribution of the electron density in that molecule. HyperChem 8.0 software was used together with the AM1 method for optimization of the conformation of the molecule of porphine. The computations of polarizability, charge distribution, potential and dipole moment for molecules placed in SMF were performed for molecule situated subsequently in the x-y, y-z and x-z planes of the Cartesian system. The computations involved the DFT 3-21G method.

Results: Static magnetic field (SMF) decreased stability of the porphine molecule. This effect depended on the situating the molecule in respect to the direction of SMF of the Cartesian system. An increase in the value of heat of formation was accompanied by an increase in dipole moment.

Conclusions: Observed effects resulted from deformations of the molecule which involved pyrrole rings holding the hydrogen atoms at the ring nitrogen atoms and the length of the C–H and N–H bonds. In a consequence that macrocyclic ring lost its planarity.

Keywords

dipole moment, heat of formation, structure deformation

Introduction

Although porphine itself (Fig. 1) does not occur in nature, numerous porphine derivatives play an essential role in functioning in living organisms of flora and fauna.

Figure 1.

Structure of the porphine molecule with the system of numbering of the atoms followed throughout the discussion and situating axes of the Cartesian system.

Porphine is a macrocyclic compound of an aromatic character. It is formed of four pyrrole rings bound with four methine (-CH=) bridges. The macrocyclic ring is planar and only the N–H bonds are bent in opposite (trans) directions (Caughey and Ibers 1977; Kadish et al. 2000; Ortiz de Montellano 2008). Involving numerous biosynthetic ways (Elder 1994; Aylward and Bofinger 2005), many porphine derivatives are naturally formed from protoporhyrin IX, it being a precursor of several biologically important compounds. A biological activity of porphine derivatives is achieved when metal ions are coordinated within the macrocyclic ring (Caughey and Ibers 1977; Kadish et al. 2000; Ortiz de Montellano 2008). This course of study was developed as a consequence of considerable environmental pollution with magnetic fields generated by modern technologies and technical solutions in several areas of human everyday life (Hamza et al. 2002; Rankovic and Radulovic 2009; Committee to Assess the Current Status and Future Direction of High Magnetic Field Science in the United States 2013; Magnet Science and Technology 2021; Magnetism in real life 2021). This paper follows a series of three recent papers of ours in which the effect of static magnetic field (SMF) upon small inorganic molecules (Ciesielski et al. 2021), lower alkanols (Ciesielski et al. 2022a) and monosaccharides (Ciesielski et al. 2022b) was recognized. In order to recognize the effect of SMF upon biologically important metalloporphyrines, in the present study we focused on the effect of SMF upon their free ligand, i.e. porphine itself.

As in our former papers (Ciesielski et al. 2021; Ciesielski et al. 2022a, b) the effect of SMF of flux density varying from 0 to 100 AFU was simulated with advanced numerical computations involving the in silico approach.

Numerical computations

DFT Molecular structures were drawn using the Fujitsu Scigress 2.0 software (Marchand et al. 2014). Their principal symmetry axes were oriented along the x-, y and z-axes of the Cartesian system. The magnetic field was fixed in the same direction with the south pole from the left side. Z axis is directed perpendicularly to the porphine plane, the x and y axes are in the plane of the system, each of them along two nitrogen atoms. In the case of full mesomerism, because of the quaternary symmetry of z axis, the last two axes were undistinguished. When the nitrogen atoms differ from one another, the x axis crossed two nitrogen atoms substituted by hydrogen atoms and y axis crossed remained two unsubstituted nitrogen atoms. Thus, both x and y axes were distinguishable.

Subsequently, utilizing Gaussian 0.9 software equipped with the 6-31G** basis (Frisch et al. 2016), the molecules were optimized and all values of bond length, dipole moment, heath of formation, bond energy, HOMO/LUMO energy level for single molecules as well as HOMO/LUMO energy level and total energy for systems built of three molecules, were computed.

In the consecutive step, the influence of the static magnetic field (SMF) upon optimized molecules was computed with Amsterdam Modelling Suite software (Farberovich and Mazalova 2016; Charistos and Muñoz-Castro 2019) and the NR_LDOTB (non-relativistic orbital momentum L-dot-B) method (Glendening et al. 1987; Carpenter and Weinhold 1988). Following that step, using Gaussian 0.9 software equipped with the DFT with functional B3LYP 6-31G** basis (Frisch et al. 2016) the values of bond length, dipole moment, heath of formation equal to the energy of dissociation, bond energy HOMO/LUMO energy level for single molecules, were again computed using the single-point energy option key word.

Visualization of the HOMO/LUMO orbitals and changes of the electron density for particular molecules and their three molecule systems was performed involving the HyperChem 8.0 software (Froimowitz 1993; Mazurkiewicz and Tomasik 2013).

Results and discussion

Generally, SMF decreased stability of the poprhine molecule (Table 1). Heat of formation increased with an increase in applied flux density. This effect depended on the positioning of the molecule in respect to the direction of SMF defined in terms of the Cartesian system. The response of the molecule in the x-y, y-z and x-z planes did not parallel one another. An increase in the value of heat of formation was accompanied by an increase in dipole moment. Again, these changes did not parallel one another.

Table 1.

Heat of formation [kJ.mol-1] and dipole moment [D] of the porphine molecule depending on its positioning in the Cartesian system and applied SMF flux density [AFU].

Orientation along the axes of the Cartesian System Heat of formation [kJ·mol-1] at SMF flux density [AFU] Dipole moment [D] at SMF flux density [AFU]
0 0.1 1.0 10 100 0 0.1 1.0 10 100
x-y -792 -782 -758 -731 -704 2.01 2.12 2.48 2.88 3.09
y-z -792 -789 -765 -742 -711 2.01 2.03 2.11 2.16 2.63
x-z -792 -781 -763 -715 -697 2.01 2.06 2.34 2.74 2.89

Thus, SMF destabilized porphine, increasing interatomic distances and separating their charges.

Heat of formation and dipole moments regularly, although to a different extent, increased with an increase in the applied SMF flux density. This effect was common for porphine molecule, regardless whether it was located in either the x-y, y-z or x-z plane. However, in terms of dipole moment, the strongest reaction to an increase in flux density was noted for the molecule situated in the x-y plane.

These total effects resulted from the distribution of the charge density at particular atoms, bond lengths, the deformation of the molecules and changes of their initial position in selected plane of the Cartesian system. Table 2 shows that, usually, charge density at particular atoms changed irregularly against an increase in the SMF flux density. The irregularity in associated bond lengths is shown in Table 3.

Table 2.

Charge density [a.u] at particular atoms of the porphine molecule depending on SMF flux density [AFU] positioning in the Cartesian system.

Atom SMF along indicated Cartesian axis Tendency* Charge density [a.u] at SMF flux density [AFU]
0 0.1 1.0 10 100
N1 X RH -1.119 -1.045 -0.987 -0.985 -0.937
Z RH -1.025 -1.017 -1.012 -0.934
Y IH -1.004 -0.789 -0.940 -0.545
N2 X IL -0.817 -0.807 -0.795 -0.813 -0.855
Z RH -0.783 -0.779 -0.772 -0.756
Y V -0.750 -0.684 -0.425 -0.725
N3 X IH -1.089 -1.025 -0.993 -0.948 -0.985
Z IL -0.988 -0.986 -0.991 -0.995
Y IH -1.035 -0.938 -0.978 -0.789
N4 X RH -0.817 -0.816 -0.795 -0.762 -0.754
Z IH -0.785 -0.779 -0.785 -0.765
Y V -0.662 -0.759 -0.503 -0.454
C5 X IH 0.492 0.454 0.359 0.447 0.572
Z IL 0.450 0.457 0.431 0.391
Y RL 0.474 0.282 0.152 0.070
C6 X IH -0.355 -0.351 -0.312 -0.317 -0.283
Z NC -0.354 -0.362 -0.350 -0.348
Y IH -0.370 -0.148 -0.121 -0.094
C7 X IL 0.393 0.362 0.310 0.354 0.285
Z NC 0.384 0.380 0.385 0.383
Y RL 0.332 0.269 0.163 -0.283
C8 X IH -0.283 -0.251 -0.267 -0.244 -0.197
Z NC -0.274 -0.272 -0.278 -0.273
Y IH -0.219 -0.077 -0.007 -0.163
C9 X RL -0.213 -0.214 -0.233 -0.249 -0.257
Z NC -0.226 -0.223 -0.221 -0.222
Y V -0.150 -0.150 -0.232 -0.059
C10 X RH 0.282 0.285 0.286 0.305 0.353
Z IL 0.281 0.278 0.254 0.262
Y IL 0.220 0.105 0.185 -0.088
C11 X V -0.253 -0.273 -0.227 -0.301 -0.298
Z V -0.296 -0.291 -0.273 -0.268
Y V -0.116 -0.202 -0.235 -0.001
C12 X V 0.434 0.418 0.330 0.425 0.476
Z V 0.389 0.392 0.371 0.409
Y IL 0.339 0.255 0.260 0.226
C13 X V -0.292 -0.305 0.018 0.338 0.470
Z V -0.266 -0.269 -0.241 -0.272
Y V -0.353 -0.207 -0.152 0.356
C14 X IH -0.292 -0.249 -0.309 0.037 0.023
Z V -0.269 -0.269 -0.282 -0.268
Y V -0.291 -0.372 -0.184 -0.348
C15 X V 0.434 0.354 0.419 0.247 0.209
Z IL 0.397 0.392 0.418 0.385
Y RL 0.410 0.389 0.290 0.094
C16 X IH -0.253 -0.221 -0.322 -0.139 -0.189
Z IL -0.295 -0.291 -0.303 -0.311
Y V -0.311 -0.073 -0.103 -0.089
C17 X V 0.282 0.281 0.309 0.243 0.256
Z RL 0.278 0.278 0.277 0.257
Y RL 0.252 0.230 0.148 -0.051
C18 X NC -0.213 -0.201 -0.233 -0.206 -0.207
Z NC -0.224 -0.223 -0.224 -0.224
Y IH -0.197 -0.127 -0.095 -0.067
C19 X V -0.283 -0.272 -0.249 -0.274 -0.272
Z V -0.272 -0.272 -0.265 -0.274
Y IH -0.163 -0.183 -0.189 -0.124
C20 X RL 0.393 0.356 0.348 0.288 0.275
Z NC 0.388 0.379 0.393 0.400
Y V 0.235 0.243 0.263 0.113
C21 X V -0.355 -0.352 -0.360 -0.218 -0.095
Z NC -0.363 -0.359 -0.349 -0.375
Y IH -0.232 -0.238 -0.146 -0.123
C22 X RL 0.492 0.428 0.419 0.292 0.169
Z RL 0.470 0.456 0.456 0.442
Y IL 0.367 0.338 0.183 0.276
C23 X V -0.230 -0.210 -0.052 -0.175 -0.152
Z NC -0.241 -0.241 -0.242 -0.240
Y IH -0.133 -0.175 -0.129 -0.019
C24 X V -0.230 -0.160 -0.223 0.026 -0.032
Z NC -0.242 -0.241 -0.234 -0.232
Y V -0.288 -0.112 -0.140 -0.021
H25 X V 0.267 0.209 0.290 0.258 -0.071
Z NC 0.265 0.264 0.273 0.270
Y V 0.269 0.126 0.077 0.127
H26 X V 0.230 0.217 0.234 0.260 0.237
Z NC 0.239 0.235 0.232 0.233
Y IL 0.214 0.069 0.077 0.103
H27 X V 0.240 0.235 0.234 0.270 0.268
Z IL 0.239 0.241 0.235 0.232
Y V 0.179 0.175 0.179 0.151
H28 X NC 0.250 0.247 0.245 0.250 0.247
Z NC 0.246 0.246 0.249 0.251
Y IL 0.192 0.168 0.179 0.166
H29 X NC 0.254 0.248 0.259 0.260 0.258
Z NC 0.255 0.252 0.251 0.250
Y IL 0.170 0.197 0.151 0.075
H30 X V 0.237 0.247 0.018 0.234 0.188
Z NC 0.245 0.244 0.238 0.243
Y V 0.080 0.220 0.180 0.027
H31 X V 0.237 0.059 0.256 0.060 0.071
Z NC 0.243 0.244 0.237 0.238
Y IL 0.245 0.122 0.120 0.061
H32 X IL 0.254 0.242 0.253 0.218 0.206
Z NC 0.253 0.252 0.256 0.258
Y IL 0.261 0.149 0.114 0.099
H33 X V 0.250 0.237 0.250 0.233 0.189
Z NC 0.246 0.246 0.242 0.244
Y RL 0.216 0.174 0.167 0.132
H34 X V 0.240 0.233 0.252 0.238 0.218
Z NC 0.241 0.241 0.244 0.247
Y V 0.159 0.169 0.288 0.179
H35 X V 0.230 0.232 0.248 0.233 0.244
Z NC 0.236 0.236 0.227 0.234
Y IL 0.126 0.139 0.099 0.055
H36 X V 0.267 0.257 0.054 0.339 0.244
Z NC 0.264 0.264 0.256 0.253
Y V 0.177 0.207 0.165 0.035
H37 X NC 0.474 0.474 0.479 0.481 0.441
Z IL 0.452 0.446 0.447 0.434
Y V 0.585 0.402 0.091 0.378
H38 X RH 0.461 0.485 0.489 0.492 0.530
Z RL 0.454 0.447 0.445 0.442
Y V 0.484 0.508 0.048 0.594

Table 2 revealed that the highest number of irregular changes of the charge distribution against changes of flux density was met in the molecule situated in the x-y and y-z planes, whereas the number of such irregularities in the x-z plane was minute. It should also be noted that several cases of a lack of sensitivity of the charge density to an increase in the flux density were observed when the molecule was oriented in the x-z plane.

Table 3.

Bond lengths [Ǻ] between particular atoms of the porphine molecule depending on SMF flux density [AFU] positioning in the Cartesian system. See Table 2 for notation.

Bond SMF along indicated Cartesian axis Tendency* Bond length [Ǻ] at flux density [AFU]
0 0.1 1.0 10 100
N1-C5 X IL 1.326 1.352 1.409 1.373 1.387
Z IH 1.385 1.402 1.390 1.463
Y IH 1.358 1.451 1.640 1.502
N1-C22 X RH 1.340 1.354 1.381 1.434 1.438
Z V 1.407 1.402 1.405 1.425
Y IH 1.417 1.430 1.552 1.432
N1-H37 X NC 1.010 1.112 1.040 1.055 1.108
Z V 0.990 0.990 0.975 0.985
Y IH 1.052 1.480 1.732 1.727
N2-C7 X V 1.325 1.357 1.392 1.357 1.345
Z V 1.432 1.337 1.321 1.320
Y IH 1.422 1.349 1.448 1.552
N2-C10 X V 1.401 1.410 1.374 1.411 1.379
Z V 1.432 1.425 1.433 1.431
Y IH 1.458 1.593 1.579 1.676
N3-C12 X IH 1.328 1.358 1.367 1.389 1.370
Z V 1.384 1.391 1.375 1.368
Y V 1.303 1.416 1.484 1.226
N3-C15 X RH 1.328 1.347 1.389 1.404 1.435
Z V 1.394 1.391 1.392 1.395
Y V 1.359 1.270 1.358 1.277
N3-H38 X NC 1.010 1.104 1.024 1.023 1.101
Z NC 0.990 0.993 0.987 0.995
Y V 0.978 0.824 1.494 1.436
N4-C17 X IL 1.401 1.383 1.411 1.371 1.361
Z IH 1.427 1.425 1.434 1.500
Y IH 1.486 1.407 1.500 1.896
N4-C20 X IH 1.325 1.368 1.383 1.382 1.381
Z V 1.339 1.337 1.326 1.320
Y IH 1.480 1.476 1.365 1.772
C5-C6 X RH 1.340 1.336 1.370 1.440 1.480
Z V 1.364 1.365 1.361 1.344
Y IH 1.246 1.432 1.457 1.582
C5-C24 X V 1.458 1.472 1.473 1.350 1.375
Z IH 1.488 1.492 1.499 1.453
Y RH 1.478 1.597 1.656 1.671
C6-C7 X RL 1.460 1.442 1.412 1.412 1.379
Z V 1.428 1.435 1.410 1.450
Y V 1.416 1.546 1.559 1.596
C6-H26 X V 1.080 1.198 1.123 1.107 1.209
Z IH 1.098 1.100 1.171 1.113
Y RH 1.262 1.706 1.854 1.891
C7-C8 X V 1.462 1.453 1.425 1.450 1.514
Z IH 1.490 1.495 1.493 1.500
Y V 1.568 1.398 1.429 1.671
C8-C9 X V 1.326 1.307 1.398 1.388 1.396
Z V 1.366 1.365 1.359 1.395
Y IH 1.459 1.454 1.461 1.696
C8-H27 X V 1.080 1.172 1.098 1.077 1.223
Z RH 1.084 1.086 1.094 1.124
Y RH 1.382 1.657 1.730 1.776
C9-C10 X RL 1.456 1.445 1.428 1.424 1.441
Z IH 1.492 1.491 1.497 1.500
Y IH 1.562 1.532 1.547 1.802
C9-H28 X V 1.080 1.129 1.094 1.091 1.150
Z IH 1.082 1.094 1.104 1.085
Y IH 1.459 1.499 1.408 1.911
C10-C11 X IH 1.340 1.351 1.419 1.364 1.381
Z V 1.357 1.358 1.348 1.329
Y IH 1.418 1.418 1.383 1.587
C11-C12 X V 1.460 1.407 1.397 1.428 1.417
Z V 1.426 1.430 1.433 1.429
Y V 1.452 1.463 1.341 1.778
C11-H29 X V 1.080 1.160 1.141 1.076 1.179
Z V 1.104 1.105 1.097 1.103
Y IH 1.535 1.433 1.604 2.068
C12-C13 X RH 1.337 1.380 1.380 1.382 1.480
Z V 1.435 1.430 1.426 1.430
Y IH 1.410 1.464 1.614 1.599
C13-C14 X NC 1.450 1.400 1.395 1.425 1.431
Z IL 1.483 1.410 1.480 1.401
Y V 1.418 1.416 1.537 1.070
C13-H30 X V 1.080 1.138 2.265 1.179 1.109
Z V 1.082 1.085 1.085 1.007
Y V 1.817 1.338 1.496 2.060
C14-C15 X V 1.337 1.342 1.408 1.403 1.401
Z RH 1.430 1.430 1.442 1.453
Y IH 1.406 1.392 1.507 1.620
C14-H31 X IH 1.080 1.798 1.120 3.640 6.799
Z IH 1.083 1.086 1.127 1.079
Y IH 1.130 1.739 1.860 1.753
C15-C16 X V 1.460 1.414 1.382 1.436 1.452
Z V 1.434 1.430 1.428 1.442
Y IH 1.378 1.454 1.495 1.633
C16-C17 X RH 1.340 1.384 1.368 1.428 1.452
Z IH 1.355 1.358 1.362 1.329
Y V 1.316 1.428 1.518 1.497
C16-H32 X IH 1.080 1.225 1.084 1.298 1.359
Z NC 1.104 1.105 1.098 1.103
Y RH 1.104 1.595 1.778 1.891
C17-C18 X V 1.456 1.435 1.435 1.424 1.445
Z V 1.493 1.491 1.476 1.500
Y RH 1.504 1.508 1.560 1.671
C18-C19 X V 1.337 1.357 1.320 1.418 1.417
Z IH 1.367 1.365 1.374 1.395
Y IH 1.387 1.527 1.482 1.696
C18-H33 X V 1.080 1.198 1.085 1.200 1.232
Z RH 1.084 1.086 1.094 1.095
Y RH 1.276 1.547 1.568 1.776
C19-C20 X V 1.452 1.448 1.453 1.386 1.384
Z RH 1.485 1.496 1.499 1.516
Y V 1.517 1.378 1.417 1.802
C19-H34 X V 1.080 1.138 1.077 1.073 1.223
Z RH 1.083 1.086 1.094 1.971
Y V 1.521 1.494 1.407 1.911
C21-C22 X V 1.340 1.364 1.389 1.365 1.344
Z IH 1.354 1.362 1.368 1.344
Y IH 1.401 1.324 1.656 1.770
C20-C21 X V 1.460 1.418 1.402 1.451 1.472
Z IL 1.366 1.362 1.358 1.329
Y V 1.459 1.432 1.457 1.633
C21-H35 X V 1.080 1.997 1.088 1.157 1.056
Z V 1.102 1.100 1.095 1.113
Y IH 1.567 1.465 1.614 2.068
C22-C23 X V 1.458 1.441 1.428 1.520 1.584
Z V 1.485 1.492 1.475 1.453
Y RH 1.500 1.544 1.656 1.599
C23-C24 X V 1.333 1.277 1.280 1.355 1.329
Z RH 1.357 1.362 1.368 1.397
Y IH 1.403 1.484 1.593 1.070
C23-H36 X V 1.080 1.225 1.733 1.082 1.214
Z V 1.097 1.088 1.073 1.129
Y IH 1.528 1.445 1.623 2.060
C24-H25 X IH 1.080 1.354 1.064 3.183 6.835
Z NC 1.084 1.088 1.083 1.096
Y IH 1.1591 1.689 1.839 1.753

The highest number of irregular changes of the bond lengths against an increase in flux density was observed for the molecule situated in the x-y plane.

Fig. 2 presents deformation of this molecule situated in the x-y, y-z and x-z planes of the Cartesian system.

Figure 2.

Deformation of the porphine molecule in SMF of flux density increasing from 0 to 100 AFU. The molecule was situated either in the x-y (a), y-z (b) or x-z (c) planes of the Cartesian system. SMF was applied along the x-axis.

One might see that, first of all, regardless of the positioning of the molecule in the Cartesian system, the deformation involved pyrrole rings holding the hydrogen atoms at the ring nitrogen atoms and the length of the C–H and N–H bonds. The magnitudes of the deformation are well illustrated by a variation of the charge density at particular atoms (Table 2) and corresponding bond lengths (Table 3). Particularly, but not solely, structures of the molecule situated in the y-z plane show that the macrocyclic ring lost its planarity. Porphine treated with external electric field behaved similarly (Mazurkiewicz and Tomasik 2013).

Conclusions

The planar molecule of porphine deforms when placed in the static magnetic field. The deformation depends on the situating the molecule against the field. The deformation engages pyrrole rings holding the hydrogen atoms at the ring nitrogen atoms. The length of the C–H and N–H bonds is also an essential factor.

Data availability

All data underlying the results are available as part of the article and no additional source data are required.

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