CN111681713B - Model construction method for polymer molecule electrical property containing decoherence and application thereof - Google Patents
Model construction method for polymer molecule electrical property containing decoherence and application thereof Download PDFInfo
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Abstract
The invention relates to a model construction method of polymer molecule electrical properties with a decoherence effect and application thereof, belonging to the field of electrochemical detection. The model constructed by the invention is that the molecular structure of the molecule to be detected is firstly obtained, and then DFT calculation is carried out on the nucleic acid structure with minimized energy so as to obtain the electronic Hamilton quantity; then, based on a double-helix decoherence transport model developed by a Landauer-B ü ttiker framework, quantum transport calculation is carried out by using the Landauer-B ü ttiker framework. Compared with the model in the prior art, the invention uses the Green function formula and the Huttiker probe to realize the consideration of the coupling effect of two electric levels and the external environment, and the model is used for explaining the experimental result. The model constructed by the invention is suitable for detecting and analyzing the electrical properties such as the conductivity, the effective charge transfer rate and the like of polymers such as nucleic acid molecules, biological macromolecules, natural macromolecules, synthetic macromolecules and the like.
Description
Technical Field
The invention belongs to the field of electrochemistry, and particularly relates to a model construction method of polymer molecule electrical properties with a decoherence effect and application thereof.
Background
Nucleic acids play a crucial role in many biological systems and activities. In recent years engineers and scientists have been interested in studying their electrical properties, the motivation for these studies stems from the fact that: (1) The bases constituting the nucleic acid building block have unique ionization potentials, and furthermore nucleic acids are one of a few nanomaterials that can be reproducibly produced with high accuracy. Thus, a design chain with a specific sequence may provide unique device characteristics; (2) Electrical methods offer the potential for single molecule-based nucleic acid sequencing; (3) An electrical method for disease detection based on the current flowing through the nucleic acid was demonstrated.
Although experimentation in the above field is promising, there is a need to develop a more thorough understanding of the current through nucleic acids. The modeling of the currents to flow in these molecules is complicated by the following: (1) They are based on atomic-scale contact between nucleic acids and metals and cannot be established in a reproducible manner; (2) The conductivity of nucleic acid is easily affected by the environment, which is constantly changing; (3) the nucleic acid itself has softness.
Therefore, in order to overcome the defects in the prior art in the process of researching the electrical properties of macromolecules such as nucleic acid, a new model construction method for the electrical properties of polymer molecules containing the decoherence effect needs to be developed.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a method for modeling electrical properties of polymer molecules including decoherence; the invention also aims to provide an application of the model of the electrical property of the polymer molecule containing the decoherence in detecting the conductivity of the polymer molecule.
In order to achieve the purpose, the invention provides the following technical scheme:
1. a method of modeling electrical properties of polymer molecules comprising decoherence, said method comprising the steps of:
(1) Obtaining structural information of a molecule to be detected;
(2) In the model, the molecule to be measured is placed between two nanoscale metal electrodes for analog electrical measurement;
(3) The structural information is used for completing Density Functional Theory (DFT) calculation in Gaussian calculation to obtain a Hamilton quantity H;
(4) Taking the interaction between electrons in the molecules to be detected, the lattice vibration of the molecules and the surrounding electromagnetic field into consideration by using a phenomenological Britt iker probe, constructing a model containing decoherence action, and obtaining a delay Green function G at the Fermi energy E r M ，
Wherein E is Fermi energy, the unit is eV, H is the Hamiltonian in the step (3), the unit is eV, I is a unit matrix with the same size as H, and the unit is 1 and sigma L r Is the leading self-energy of the left electrode and has the units of eV and Sigma R r Is the leading self-energy of the right electrode and has the units of eV and Sigma B Is the self-energy produced by the Buttiker probe in eV;
(5) A coherent transmission rate T (E) is calculated,
T(E)＝Trace(Γ L G r M Γ R G a M ) (2)，
wherein gamma is L And Γ R Represents the expansion of the molecular energy level in eV, G when the molecule to be measured is placed near the left electrode or the right electrode a M Is a leading Green function with the unit of eV;
(6) The relationship between the conductance G of the polymer to be tested and the fermi energy E is:
wherein G 0 In order to be a quantum conductance,
E f is the fermi level in eV;
or the effective charge transport rate T of the polymer to be tested eff The relationship to the fermi energy E is:
wherein T is LR Representing the rate of coherent charge transfer, T, between the left and right electrodes LR = T (E), nb number of probes, i =1,2, 3., (Nb + 2), j =1,2, 3., nb, T L,i Is the charge transfer rate, W, from the left electrode to site i ij -1 Is W ij Inverse matrix of, T j,R Is the charge transfer rate, T, from the right electrode to site j ij The charge transport rate from site i to site j.
Preferably, the structural information in step (1) includes spatial coordinates of atoms in the polymer molecule to be detected.
Preferably, the nanoscale metal electrode in step (2) is a gold electrode.
Preferably, the hamiltonian H in step (3) is calculated as follows:
wherein H 0 Is an initial Hamiltonian matrix with the units of eV,
S 0 Is a superposition matrix with the units of eV,
H 0 And S 0 Are all calculated by the Density Functional Theory (DFT).
Preferably, the self-energy generated by the B ü ttiker probe in step (4) is calculated as follows:
∑B＝∑∑i (7)，
where Σ i denotes the decoherence of the ith probe, by the probe and the coherent system Γ i The coupling strength between them, i.e., Σ i = - Γ i ，Γ i The coupling strength generated by the probe and the system is expressed in eV.
Preferably, said Γ in step (5) L And gamma R The calculation is performed according to the following formula:
wherein
Is the leading self-energy of the left and right electrodes in eV, i.e. < >>
G a M Is a look-ahead Green function, in eV, i.e
i represents a complex number.
Preferably, the
Is delayed self-energy of left and right electrodes at energy E
Calculated as follows: />
Wherein H ML(R) The sub-Hamilton quantity of the coupling between the molecule to be detected and the right electrode or the left electrode is determined in eV and H L(R)M The sub-Hamilton quantity of the coupling between the right electrode or the left electrode and the molecule to be detected is expressed in eV,
g L(R) (E) Is the green function of the retardation surface of the left or right half infinite electrode.
Preferably, said g is L(R) (E) The calculation is as follows:
wherein H LL And H RR Submatrix of Hamiltonian H, H LL The sub-Hamiltonian of the coupling between the left electrode and the left electrode in eV and H RR The sub-Hamiltonian of the coupling between the right electrode and the right electrode in eV,
I LL(RR) Is a reaction with H LL(RR) The unit matrix has the same size and the unit is 1.
Preferably, said W ij Calculated according to the following formula:
W ij ＝[(1-R ii )δ ij -T ij (1-δ ij )] (11)，
wherein delta ij Is a function of Crohn's function, T ij Is the charge transport rate, R, from site i to site j ii Is the reflectivity at the location of the probe i,
where N = Nb +2.
Preferably, the molecule to be detected is any one of a biomolecule, a natural polymer or a synthetic polymer.
Preferably, the biomolecule is a nucleic acid molecule.
2. The model constructed by the method is applied to detecting the electrical property of the polymer molecule.
Preferably, the electrical property is conductivity or effective charge transport efficiency.
The invention has the beneficial effects that:
the invention discloses a model construction method of polymer molecule electrical properties with a decoherence effect, which focuses on the model construction of electric transmission of molecules to be detected connected with two nanoscale metal electrodes. The constructed model is that firstly, the molecular structure of the molecule to be detected is obtained, and then the Density Functional Theory (DFT) calculation is carried out on the nucleic acid structure with minimized energy so as to obtain the electronic Hamilton quantity; then, based on a double-helix decoherence transport model developed by a Landauer-B ü ttiker framework, quantum transport calculation is carried out by using the Landauer-B ü ttiker framework. Compared with the model in the prior art, the invention uses the Green function formula and the Bttiker probe to realize the consideration of the coupling action of the two electric levels and the external environment, and further can use the model to explain the experimental result. Further developments from the recalculation method, including the effects of environmental shock, are also disclosed without unduly simplifying assumptions. The model constructed by the invention is suitable for detecting and analyzing the electrical properties such as the conductivity of polymers such as nucleic acid molecules, biological macromolecules, natural macromolecules, synthetic macromolecules and the like.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flowchart of the construction of a model in example 1;
FIG. 2 shows the molecule to be detected in example 1-GCGCGCGC- (GC) 8 ) The structure of (1);
FIG. 3 shows the molecule G to be detected in example 1 8 Schematic diagram after connecting with two nanometer metal gold electrodes;
FIG. 4 shows a GC of a molecule to be detected obtained by the model constructed in example 1 8 The conductance G of (a) at different fermi energies;
FIG. 5 shows GC of the molecule to be detected 8 Effective charge transfer rate of (T) eff Curves at different fermi energies.
Detailed Description
The following embodiments of the present invention are provided by way of specific examples, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure herein. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the features in the following embodiments and examples may be combined with each other without conflict.
Example 1:
the purpose of detecting the electrochemical properties of oligonucleotide molecule DNA is achieved by adopting a model construction method of polymer molecule electrical properties including the decoherence effect to construct a model, the specific model construction process is shown in figure 1, and the main method is as follows:
1. selecting a DNA molecule with an eight base pair sequence (the sequence is SEQ ID NO: 1), and detecting GC in the molecule to be detected 8 To the 3' end of (A) a thiol group (-CH) 2 -SH-); then, acquiring coordinate information of the molecule to be detected by using a Nucleic Acid Builder (NAB) software package; the results of the monitoring were then opened using GaussView5.0 software, and the structural diagram of the molecule was observed as shown in FIG. 2; then utilizing the structure chart to obtain the GC of the molecule to be detected 8 The spatial coordinates of each atom in (a).
2. GC of the molecule to be detected 8 Thiol group of (2)Respectively connected with two nanoscale metal gold electrodes to obtain the structure shown in figure 3 for analog detection.
3. Subjecting the obtained molecule to GC analysis 8 The space coordinates of the atoms are used for Gaussian calculation to complete the calculation of the Density Functional Theory (DFT) to obtain an initial Hamiltonian matrix H 0 A matrix of 5706 × 5706, an overlap matrix S 0 Is a matrix of 5706 × 5706, and then passes
Orthogonal transformation obtains the real Hamiltonian H of the system, wherein H is obtained by calculating formulas (5) and (6):
by mixing H 1 Diagonalizing each diagonal sub-block, and arranging the eigenvectors according to the sequence of the bases in the nucleic acid sequence to obtain U, wherein U is H 1 And the matrix is a block diagonal matrix with equal row number and column number.
4. Using a phenomenological Britt probe, considering the interaction between electrons and the lattice vibration of molecules and the surrounding electromagnetic field, constructing a model containing decoherence action, and obtaining a delay Green function G r M ，G r M The calculation formula of (a) is as follows:
where E is Fermi energy, the unit is eV, H is Hamiltonian obtained by the calculation, I is unit matrix with the same size as H, and sigma L r For the leading self-energy of the left electrode R r Is the leading self-energy of the right electrode B Is the self energy generated by the Btuttiker probe；
Sigma above B Calculated according to the following formula:
∑B＝∑∑i (7)，
represents the decoherence sigma of the ith probe i ＝iΓ i From a probe and a coherent system Γ i (coupling strength between probe and system in eV), and Γ is set in this embodiment i Is 0.01eV.
5. Calculation of GC of the molecule to be detected 8 The coherent transmission rate T (E), i.e. the charge transmission rate between the left and right electrodes, considering only the coherent interaction, is calculated as follows:
T(E)＝T LR ＝Trace(Γ L G r M Γ R G a M ) (2)，
wherein G is a M As a function of lead Green
Γ L And Γ R Respectively show the GC of the molecules to be detected 8 The gamma is set by the expansion of the molecular energy level when the nano-gold electrode is placed near the left nano-gold electrode or the right nano-gold electrode L ＝0.1eV，Γ R =0.1eV, calculated as follows:
and the delayed self-energy of the left (right) electrode at the energy E is
The calculation method is as follows:
wherein H ML(R) GC for the molecule to be detected 8 sub-Hamilton of coupling with left or right electrode, H L(R)M The sub-Hamilton quantity of the coupling between the right electrode or the left electrode and the molecule to be detected,
g L (E) Green function of the retardation surface for the right half infinite electrode, g R (E) The green function of the retardation surface for the right half infinite electrode is calculated as follows:
wherein H LL And H RR Submatrix of Hamiltonian H, H LL The sub-Hamiltonian of the coupling between the left electrode and the left electrode in eV and H RR The sub-Hamiltonian of the coupling between the right and left electrodes in eV, I LL(RR) Is a reaction with H LL(RR) The unit matrix of the same size is 1.
6. Obtaining the molecule GC to be detected 8 The relationship between conductance G and energy E of (a) is:
wherein the quantum conductance
Fermi level E f Around HOMO = -5.06eV of the molecule.
Obtaining the GC of the molecule to be detected by the constructed model 8 The conductance G of (a) at different fermi energies is plotted in fig. 4.
7. According to the formula
Calculating the charge transfer rate R from probe i to probe j ii Then according to the formula W ij ＝[(1-R ii )δ ij -T ij (1-δ ij )]Calculating W ij Wherein N is the GC of the molecule to be detected 8 Total number of medium bases, i =1,2,3 ij Is the charge transport rate, delta, from site i to site j ij Is the kronecker function.
8. Obtaining the molecule GC to be detected 8 Effective charge transfer rate of (T) eff The relationship to the fermi energy E is:
in the formula T LR Denotes the coherent charge transfer rate, Γ, between the left and right electrodes L(R) Representing the expansion of the energy level when the molecule to be measured is placed near the left or right electrode, set Γ L ＝0.1eV，Γ R ＝0.1eV、G a As a function of lead Green, G a M Is a delayed Green function in eV, nb is the number of probes, T L,i Is the charge transfer rate, T, from the left electrode to site i j,R The charge transport rate between site j and the right electrode.
Obtaining the GC of the molecule to be detected by constructing the obtained model 8 Effective charge transfer rate of (T) eff The curves at different fermi energies are shown in figure 5.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.
Sequence listing
<110> Chongqing post and telecommunications university
<120> method for constructing model of polymer molecule electrical property comprising decoherence and application thereof
<160> 1
<170> SIPOSequenceListing 1.0
<210> 1
<211> 8
<212> DNA
<213> Artificial Sequence (Artificial Sequence)
<400> 1
gcgcgcgc 8
Claims (3)
1. A method of modeling an electrical property of a polymer molecule comprising decoherence, the method comprising the steps of:
(1) Obtaining structural information of a molecule to be detected, wherein the molecule to be detected is a DNA molecule with an eight base pair sequence, and the sequence of the molecule to be detected is SEQ ID NO:1 is shown in the specification;
(2) In the model, the molecule to be measured is placed between two nanoscale metal electrodes for analog electrical measurement;
(3) The structural information is used for completing Density Functional Theory (DFT) calculation in Gaussian calculation to obtain a Hamilton quantity H;
(4) Taking the interaction between electrons in the molecules to be detected, the lattice vibration of the molecules and the surrounding electromagnetic field into consideration by using a phenomenological Britt iker probe, constructing a model containing decoherence action, and obtaining a delay Green function G at the Fermi energy E r M ，
Wherein E is Fermi energy, the unit is eV, H is the Hamiltonian in the step (3), the unit is eV, I is a unit matrix with the same size as H, and the unit is 1 and sigma L r Is the leading self-energy of the left electrode and has the units of eV and Sigma R r Is the leading self-energy of the right electrode with the units of eV and Sigma B Is the self energy produced by the Buttiker probe in eV;
(5) Calculating a coherent transmission rate T LR ＝T(E)，
T LR ＝T(E)＝Trace(Γ L G r M Γ R G a M ) (2)，
Wherein gamma is L And Γ R Represents the expansion of the molecular energy level in eV, G when the molecule to be measured is placed near the left electrode or the right electrode a M Is a look-ahead Green function with units of eV;
(6) The relationship between the conductance G of the polymer to be measured and the fermi energy E is:
wherein G is 0 Is the quantum conductance in omega -1 、E f Is the fermi level in eV;
or the effective charge transport rate T of the polymer to be tested eff The relationship to the fermi energy E is:
wherein T is LR Representing the rate of coherent charge transfer, T, between the left and right electrodes LR = T (E), nb number of probes, i =1,2, 3., (Nb + 2), j =1,2, 3., nb, T L,i Is the charge transfer rate, W, from the left electrode to site i ij Is site T eff Between i and j, reflection matrix of the probe, W ij -1 Is W ij Inverse matrix of, T j,R Is the charge transfer rate, T, of the right electrode to site j ij The charge transport rate from site i to site j;
in the step (3), the Hamiltonian H is calculated according to the following mode:
wherein H 0 Is an initial Hamiltonian matrix with the unit of eV and S 0 Is an overlapping matrix with units of eV and H 0 And S 0 Are all obtained by the calculation of the Density Functional Theory (DFT);
the self-energy generated by the B ü ttiker probe in step (4) is calculated as follows:
∑B＝∑∑i (7)，
where Σ i denotes the decoherence of the ith probe, by the probe and the coherent system Γ i The coupling strength between them, i.e., Σ i = - Γ i ，Γ i Coupling strength generated by the probe and the system is expressed in eV;
the gamma is obtained in the step (5) L And gamma R The calculation is performed according to the following formula:
wherein
Is the leading self-energy of the left and right electrodes in eV, i.e. < >>
G a M Is a look-ahead Green function, in eV, i.e
i represents a plurality;
the described
Is delayed self-energy of left and right electrodes, wherein the delayed self-energy of the left and right electrodes at energy E->
Calculated as follows:
wherein H ML(R) The sub-Hamiltonian of the coupling between the molecule to be measured and the right or left electrode is expressed in eV,
H L(R)M The sub-Hamilton quantity of the coupling between the right electrode or the left electrode and the molecule to be detected is expressed in eV,
g L(R) (E) A green's function of the retardation surface for the left or right half infinite electrode;
said g is L(R) (E) The calculation is as follows:
wherein H LL And H RR Submatrix of Hamiltonian H, H LL The sub-Hamiltonian of the coupling between the left electrode and the left electrode in eV and H RR The sub-Hamiltonian of the coupling between the right electrode and the right electrode in eV,
I LL(RR) Is a reaction with H LL(RR) The unit matrixes with the same size have the unit of 1;
w is ij Calculated according to the following formula:
W ij ＝[(1-R ii )δ ij -T ij (1-δ ij )] (11)，
wherein delta ij Is a function of Crohn's function, T ij Is the charge transport rate, R, from site i to site j ii To be the reflectivity at the probe i,
where N = Nb +2.
2. The model building method according to claim 1, wherein the structural information includes spatial coordinates of atoms in the polymer molecule to be tested; the nanoscale metal electrode is a gold electrode.
3. Use of a model constructed by the model construction method of any one of claims 1 to 2 for detecting electrical properties of polymer molecules.
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