Contents

水素原子の電子軌道

波動関数は球面調和関数と動径関数の積です。

close all;clear;
figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,700,400]);
st1='$$\psi(r,\theta,\phi)=R(r)\Theta(\theta)\Phi(\phi)$$';
st2='$$\Phi(\phi)=\frac{1}{\sqrt{2\pi}}\exp(im\phi)$$';
st3='$$\Theta(\theta)=(-1)^{(m+|m|)/2}\sqrt{l+\frac{1}{2}}\sqrt{\frac{(l-|m|)!}{(l+|m|)!}}P_l^m(\cos\theta)$$';
st4='$$R(r)=-\left(\frac{2}{na_0}\right)^{3/2}\sqrt{\frac{(n-l-1)!}{2n(n+l)!}}\exp\left(-\frac{r}{na_0}\right)r^lL_{n+l}^{2l+1}\left(\frac{2r}{na_0}\right)$$';
st5='$$L_n^k(x)=\frac{d^k}{dx^k}\left(exp(x)\frac{d^n}{dx^n}x^n\left(exp(-x)\right)\right)$$';
text(-0.1,0.9,st1,'interpreter','latex','FontSize',18);
text(-0.1,0.65,st2,'interpreter','latex','FontSize',18);
text(-0.1,0.4,st3,'interpreter','latex','FontSize',18);
text(-0.1,0.15,st4,'interpreter','latex','FontSize',18);
axis off;

電子軌道の計算をします。 全然理解してませんが、球面調和関数を実数部分と虚数部分に分けたのち、 夫々に動径関数を掛けて、最大値・最小値の10%のところを表示することにしました。 計算はかなりかかります。 63x63x63の立体で計算を行うこととしました。 動径関数は中心から32分割までを計算することにしました。 予め緯度方向・経度方向に72分割した球面で球面調和関数を計算し、 立体の各格子点の角度を上記の角度にまるめることで計算量を減らしました。 各格子点で球面調和関数を計算 63^3=250047>> 予め分割した球面の球面調和関数の計算72^2=5164 格子点の数を増やし、球面の分割数を増やせば、きれいな画面が作成できますが、それなりに計算時間はかかります。

close all;clear;
N=5;border=0.1;
ang=5;% 3度刻み→多ければ計算時間を減らせる
Phi=0:ang:360;%経度
Theta=0:ang/2:180;%緯度
phi=Phi/180*pi;
theta=Theta/180*pi;
nph=length(phi);
nth=length(theta);
a0=0.529*1e-10;
seg2=31;% 少なければ計算時間を減らせる。seg2^3*8/2^20 MB必要
t=-seg2:seg2;
nt=length(t);
ts=4;
tt=(0:1/ts:seg2)/seg2;
[xx,yy,zz]=meshgrid(t,t,t);
[ph,th]=cart2sph(xx(:),yy(:),zz(:));
ph=ph+pi;
th=th+pi/2;
ph=ang*round(ph/pi*180/ang)';
th=ang*round(th/pi*180/ang*2)'/2;

vv=sqrt(xx.^2+yy.^2+zz.^2);
vv=round(vv*ts);
V=zeros(length(t),length(t),length(t));

for n=0:N
    switch n
        case 0;k=3e-10;% 実質ない
        case 1;k=3e-10;
        case 2;k=7e-10;
        case 3;k=1.5e-9;
        case 4;k=2.5e-9;
        case 5;k=4e-9;
    end;
    kxx=k/seg2*xx;
    kyy=k/seg2*yy;
    kzz=k/seg2*zz;
    r=tt*k;
    R2=exp(-r/n/a0);
    for l=0:n
        if n-l-1<0;continue;end;
        La=hns_laguerre(n+l,2*r/n/a0);
        R1=-(2/n/a0)^1.5*sqrt(factorial(n-l-1)/2/n/factorial(n+l));
        R3=r.^l;
        R4=La(2*l+2,:);
        R=R1*R2.*R3.*R4;% 動径関数
        % R=(R1*R2.*R3.*R4.*r).^2; % こちらは動径分布関数
        R=R/max(R(:));% 最大値を1とする
        V=V*0;
        V=V(:);
        for q=1:(seg2*ts)
            V(find(vv==q))=R(q);
        end;

        Le=legendre(l,cos(theta));
        for m=0:l;
            am=abs(m);
            LL=Le(abs(m)+1,:);
            c=(-1)^((m+am)/2)*sqrt((2*l+1)/(4*pi)*factorial(l-am)/factorial(l+am))*LL'*exp(1i*m*phi);
            W=V;
            for inth=1:nth
                fth=find(th==Theta(inth));
                for inph=1:nph
                    fph=find(ph==Phi(inph));
                    ff=intersect(fth,fph);
                    W(ff)=W(ff)*c(inth,inph);
                end;
            end;
            for mm=1:2
                if mm==1;
                    WW=real(W);

                else
                    WW=imag(W);
                    if max(WW)==0;continue;end;
                end;
                wmax=max(WW);
                wmin=min(WW);
                WW=reshape(WW,nt,nt,nt);
                figure('color',[1,1,1],'inverthardcopy','off','position',[50,50,800,800]);
                subplot(224);
                Vmax=isosurface(kxx,kyy,kzz,WW,border*wmax);
                hmax=patch(Vmax,'facecolor',[1,0,0],'edgecolor','none','facealpha',0.5);hold on;
                if wmin<0
                    Vmin=isosurface(kxx,kyy,kzz,WW,border*wmin);
                    hmin=patch(Vmin,'facecolor',[0,0,1],'edgecolor','none','facealpha',0.5);
                end;
                grid on;view([-40,30]);
                daspect([1,1,1]);
                axis tight;
                rotate3d on;
                st1=[sprintf('R_%d^%d',n,l),'\cdot'];
                if mm==1
                    st1=[st1,sprintf(' Re(Y_%d^{%d})',l,m)];
                else
                    st1=[st1,sprintf(' Im(Y_%d^{%d})',l,m)];
                end;

                switch l
                    case 0;st2='s';st3='';
                    case 1;
                        st2='p';
                        switch m;
                            case {-1,1};st3='_x';if mm==2;st3='_y';end;
                            case 0;st3='_z';     if mm==2;st3=''; end;
                        end;
                    case 2;
                        st2='d_{';
                        switch m;
                            case {-2,2};st3='x^2-y^2}';if mm==2;st3='xy}';end;
                            case {-1,1};st3='xz}';     if mm==2;st3='yz}';end;
                            case  0;st3='3z^2-r^2}';   if mm==2;st3='}';end;
                        end;
                    case 3;
                        st2='f_{';
                        switch m;
                            case {-3,3};st3='x^3-3xy^2}'; if mm==2;st3='y^3-3xy^2}';end;
                            case {-2,2};st3='x^2z-y^2z}'; if mm==2;st3='xyz}';end;
                            case {-1,1};st3='xr^2-5xz^2}';if mm==2;st3='yr^2-5yz^2}';end;
                            case  0;st3='5z^3-3zr^2}';    if mm==2;st3='}';end;
                        end;
                    case 4;st2='g';st3='';
                    case 5;st2='h';st3='';
                end;
                str=['$$',st1,'\ \ ',sprintf('%d',n),st2,st3,'$$'];
                title(str,'interpreter','latex','FontSize',15);
                wlim=max(abs(wmax),abs(wmin))*[-1,1];
                lim=[-1,1]*k;
                for mmm=1:3
                    subplot(2,2,mmm);
                    switch mmm
                        case 1;img=squeeze(WW(:,:,seg2+1));               st4='XY plane';
                        case 2;img=squeeze(WW(:,seg2+1,:));img=rot90(img);st4='XZ plane';
                        case 3;img=squeeze(WW(seg2+1,:,:));img=rot90(img);st4='YZ plane';
                    end;
                    imagesc(lim,lim,img);hold on;
                    lim2=linspace(-1,1,size(img,1))*lim(2);
                    hred=contour(lim2,lim2,img,wmax*border,'color',[1,0,0]);
                    hblue=contour(lim2,lim2,img,wmin*border,'color',[0,0,1]);
                    set(gca,'clim',wlim');
                    title(st4,'FontSize',15);
                end;
            end;
        end;
    end;
end;

電子軌道(動径関数×球面調和関数)を重ねてみる

電子軌道を重ねてみました。境界は最大値・最小値の20%にしてます。古い境界は薄くしました。

close all;clear;
N=5;border=0.2;
ang=5;% 3度刻み→多ければ計算時間を減らせる
Phi=0:ang:360;%経度
Theta=0:ang/2:180;%緯度
phi=Phi/180*pi;
theta=Theta/180*pi;
nph=length(phi);
nth=length(theta);
a0=0.529*1e-10;
seg2=31;% 少なければ計算時間を減らせる。seg2^3*8/2^20 MB必要
t=-seg2:seg2;
nt=length(t);
ts=4;
tt=(0:1/ts:seg2)/seg2;
[xx,yy,zz]=meshgrid(t,t,t);
[ph,th]=cart2sph(xx(:),yy(:),zz(:));
ph=ph+pi;
th=th+pi/2;
ph=ang*round(ph/pi*180/ang)';
th=ang*round(th/pi*180/ang*2)'/2;
vv=sqrt(xx.^2+yy.^2+zz.^2);
vv=round(vv*ts);
V=zeros(length(t),length(t),length(t));
horbit=1;
for n=0:N
    switch n
        case 0;k=3e-10;% 実質ない
        case 1;k=3e-10;
        case 2;k=7e-10;
        case 3;k=1.5e-9;
        case 4;k=2.5e-9;
        case 5;k=4e-9;
    end;
    kxx=k/seg2*xx;
    kyy=k/seg2*yy;
    kzz=k/seg2*zz;
    r=tt*k;
    R2=exp(-r/n/a0);
    for l=0:n
        if n-l-1<0;continue;end;
        La=hns_laguerre(n+l,2*r/n/a0);
        R1=-(2/n/a0)^1.5*sqrt(factorial(n-l-1)/2/n/factorial(n+l));
        R3=r.^l;
        R4=La(2*l+2,:);
        R=R1*R2.*R3.*R4;% 動径関数
        % R=(R1*R2.*R3.*R4.*r).^2; % こちらは動径分布関数
        R=R/max(R(:));% 最大値を1とする
        V=V*0;
        V=V(:);
        for q=1:(seg2*ts)
            V(find(vv==q))=R(q);
        end;
        if ~isempty(findobj('type','figure'));
            hchildren=get(gcf,'children');
        end;
        hf=figure('color',[1,1,1],'inverthardcopy','off','position',[50,50,400,400]);
        if exist('hchildren','var')
            copyobj(hchildren,hf);hold on;
            set(findobj(gcf,'type','patch'),'facealpha',0.1);
        end;
        st='';
        switch n
            case 1;st='K shell 1';
            case 2;st='L shell 2';
            case 3;st='M shell 3';
            case 4;st='N shell 4';
            case 5;st='O shell 5';
        end;
        switch l
            case 0;st=[st,'s'];
            case 1;st=[st,'p'];
            case 2;st=[st,'d'];
            case 3;st=[st,'f'];
            case 4;st=[st,'g'];
        end;
        Le=legendre(l,cos(theta));

        for m=0:l;
            am=abs(m);
            LL=Le(abs(m)+1,:);
            c=(-1)^((m+am)/2)*sqrt((2*l+1)/(4*pi)*factorial(l-am)/factorial(l+am))*LL'*exp(1i*m*phi);
            W=V;
            for inth=1:nth
                fth=find(th==Theta(inth));
                for inph=1:nph
                    fph=find(ph==Phi(inph));
                    ff=intersect(fth,fph);
                    W(ff)=W(ff)*c(inth,inph);
                end;
            end;
            for mm=1:2
                if mm==1;
                    WW=real(W);

                else
                    WW=imag(W);
                    if max(WW)==0;continue;end;
                end;
                wmax=max(WW);
                wmin=min(WW);
                WW=reshape(WW,nt,nt,nt);

                Vmax=isosurface(kxx,kyy,kzz,WW,border*wmax);
                hmax=patch(Vmax,'facecolor',[1,0,0],'edgecolor','none','facealpha',0.4);hold on;
                porbit{horbit}=hmax;
                if wmin<0
                    Vmin=isosurface(kxx,kyy,kzz,WW,border*wmin);
                    hmin=patch(Vmin,'facecolor',[0,0,1],'edgecolor','none','facealpha',0.4);
                    porbit{horbit}=[hmax;hmin];
                end;
                horbit=horbit+1;
                grid on;view([-40,30]);
                daspect([1,1,1]);
                axis tight;
                rotate3d on;
            end;
        end;
        title(st,'fontsize',15);
    end;
end;

電子軌道(動径分布×球面調和関数)を重ねてみる

電子軌道を重ねてみました。境界は最大値・最小値の20%にしてます。古い境界は薄くしました。 元素にはg軌道はなく、P殻はd軌道まで、Q核はp軌道までしかないので、その他は計算してません。

close all;clear;
N=7;border=0.2;
ang=5;% 3度刻み→多ければ計算時間を減らせる
Phi=0:ang:360;%経度
Theta=0:ang/2:180;%緯度
phi=Phi/180*pi;
theta=Theta/180*pi;
nph=length(phi);
nth=length(theta);
a0=0.529*1e-10;
seg2=31;% 少なければ計算時間を減らせる。seg2^3*8/2^20 MB必要
t=-seg2:seg2;
nt=length(t);
ts=4;
tt=(0:1/ts:seg2)/seg2;
[xx,yy,zz]=meshgrid(t,t,t);
[ph,th]=cart2sph(xx(:),yy(:),zz(:));
ph=ph+pi;
th=th+pi/2;
ph=ang*round(ph/pi*180/ang)';
th=ang*round(th/pi*180/ang*2)'/2;
vv=sqrt(xx.^2+yy.^2+zz.^2);
vv=round(vv*ts);
V=zeros(length(t),length(t),length(t));
horbit=1;
for n=0:7
    switch n
        case 0;k=3e-10;% 実質ない
        case 1;k=3e-10;
        case 2;k=7e-10;
        case 3;k=1.5e-9;
        case 4;k=2.5e-9;
        case 5;k=4e-9;
        case 6;k=6e-9;
        case 7;k=7e-9;
    end;
    kxx=k/seg2*xx;
    kyy=k/seg2*yy;
    kzz=k/seg2*zz;
    r=tt*k;
    R2=exp(-r/n/a0);
    for l=0:n
        if n-l-1<0;continue;end;
        if l>3 continue;end;
        if n==6 && l>2 continue;end;
        if n==7 && l>1 continue;end;
        La=hns_laguerre(n+l,2*r/n/a0);
        R1=-(2/n/a0)^1.5*sqrt(factorial(n-l-1)/2/n/factorial(n+l));
        R3=r.^l;
        R4=La(2*l+2,:);
        % R=R1*R2.*R3.*R4;% 動径関数
        R=(R1*R2.*R3.*R4.*r).^2; % こちらは動径分布関数
        R=R/max(R(:));% 最大値を1とする
        V=V*0;
        V=V(:);
        for q=1:(seg2*ts)
            V(find(vv==q))=R(q);
        end;
        if ~isempty(findobj('type','figure'));
            hchildren=get(gcf,'children');
        end;
        hf=figure('color',[1,1,1],'inverthardcopy','off','position',[50,50,400,400]);
        if exist('hchildren','var')
            copyobj(hchildren,hf);hold on;
            set(findobj(gcf,'type','patch'),'facealpha',0.1);
        end;
        st='';
        switch n
            case 1;st='K shell 1';
            case 2;st='L shell 2';
            case 3;st='M shell 3';
            case 4;st='N shell 4';
            case 5;st='O shell 5';
            case 6;st='P shell 6';
            case 7;st='Q shell 7';
        end;
        switch l
            case 0;st=[st,'s'];
            case 1;st=[st,'p'];
            case 2;st=[st,'d'];
            case 3;st=[st,'f'];
            case 4;st=[st,'g'];
        end;
        Le=legendre(l,cos(theta));

        for m=0:l;

            am=abs(m);
            LL=Le(abs(m)+1,:);
            c=(-1)^((m+am)/2)*sqrt((2*l+1)/(4*pi)*factorial(l-am)/factorial(l+am))*LL'*exp(1i*m*phi);
            W=V;
            for inth=1:nth
                fth=find(th==Theta(inth));
                for inph=1:nph
                    fph=find(ph==Phi(inph));
                    ff=intersect(fth,fph);
                    W(ff)=W(ff)*c(inth,inph);
                end;
            end;
            for mm=1:2
                if mm==1;
                    WW=real(W);

                else
                    WW=imag(W);
                    if max(WW)==0;continue;end;
                end;
                wmax=max(WW);
                wmin=min(WW);
                WW=reshape(WW,nt,nt,nt);

                Vmax=isosurface(kxx,kyy,kzz,WW,border*wmax);
                hmax=patch(Vmax,'facecolor',[1,0,0],'edgecolor','none','facealpha',0.4);hold on;
                porbit{horbit}=hmax;
                if wmin<0
                    Vmin=isosurface(kxx,kyy,kzz,WW,border*wmin);
                    hmin=patch(Vmin,'facecolor',[0,0,1],'edgecolor','none','facealpha',0.4);
                    porbit{horbit}=[hmax;hmin];
                end;
                horbit=horbit+1;
                grid on;view([-40,30]);
                daspect([1,1,1]);
                axis tight;
                rotate3d on;
            end;
        end;
        title(st,'fontsize',15);
    end;
end;

元素の周期表とその電子分布

原子核のクーロン力と電子同士の反発力を無視しました。 原子番号1の水素から原子番号88のラジウムまでです。

close(findobj('tag','aaa'));
e1s=porbit{1}(:);

e2s=porbit{2}(:);
e2p=[porbit{3}(:);porbit{4}(:);porbit{5}(:)];

e3s=porbit{6}(:);
e3p=[porbit{7}(:);porbit{8}(:);porbit{9}];
e3d=[porbit{10}(:);porbit{11}(:);porbit{12}(:);porbit{13}(:);porbit{14}(:)];

e4s=porbit{15}(:);
e4p=[porbit{16}(:);porbit{17}(:);porbit{18}];
e4d=[porbit{19}(:);porbit{20}(:);porbit{21}(:);porbit{22}(:);porbit{23}(:)];
e4f=[porbit{24}(:);porbit{25}(:);porbit{26}(:);porbit{27}(:);porbit{28}(:);porbit{29};porbit{30}];

e5s=porbit{31}(:);
e5p=[porbit{32}(:);porbit{33}(:);porbit{34}];
e5d=[porbit{35}(:);porbit{36}(:);porbit{37}(:);porbit{38}(:);porbit{39}(:)];
e5f=[porbit{40}(:);porbit{41}(:);porbit{42}(:);porbit{43}(:);porbit{44}(:);porbit{45};porbit{46}];

e6s=porbit{47}(:);
e6p=[porbit{48}(:);porbit{49}(:);porbit{50}];
e6d=[porbit{51}(:);porbit{52}(:);porbit{53}(:);porbit{54}(:);porbit{55}(:)];

e7s=porbit{56}(:);
e7p=[porbit{57}(:);porbit{58}(:);porbit{59}];

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj(e1s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;rotate3d on;daspect([1,1,1]);
title({'1s','','_1H _2He'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj(e1s,gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e2s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s','','_3Li _4Be'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e2p,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p','','_5B _6C _7N _8O _9F _{10}Ne'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e3s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s','', '_{11}Na _{12}Mg'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e3p,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p','', '_{13}Al _{14}Si _{15}P _{16}S _{17}Cl _{18}Ar'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e4s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s','','_{19}K _{20}Ca'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e3d,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d','','_{21}Sc _{22}Ti _{23}V _{24}Cr _{25}Mn _{26}Fe _{27}Co _{28}Ni _{29}Cu _{30}Zn'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e4p,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p','','_{31}Ga _{32}Ge _{33}As _{34}Se _{35}Br _{36}Kr'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e5s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s','','_{37}Rb _{38}Sr'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e5s],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e4d,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d','','_{39}Y _{40}Zr _{41}Nb _{42}Mo _{43}Tc _{44}Ru _{45}Rh _{46}Pd _{47}Ag _{48}Cd'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e5p,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p','','_{49}In _{50}Sn _{51}Sb _{52}Te _{53}I _{54}Xe'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d;e5p],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e6s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s','','_{55}Cs _{56}Ba'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d;e5p;e6s],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e5d,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 5d','','_{57}La'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d;e5p;e6s;e5d],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e4f,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s (5d) 4f','','_{58}Ce _{59}Pr _{60}Nd _{61}Pm _{62}Sm _{63}Eu _{64}Gd','','_{65}Tb _{66}Dy _{67}Ho _{68}Er _{69}Tm _{70}Yb'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d;e5p;e6s;e4f],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e5d,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d','','_{71}Lu _{72}Hf _{73}Ta _{74}W _{75}Re _{76}Os _{77}Ir _{78}Pt _{79}Au'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d;e5p;e6s;e4f;e5d],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e6p,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p','','_{81}Tl _{82}Pb _{83}Bi _{84}Po _{85}At _{86}Rn'},'FontSize',12);

figure('color',[1,1,1],'InvertHardCopy','off','position',[50,50,400,400],'tag','aaa');
h=copyobj([e1s;e2s;e2p;e3s;e3p;e4s;e3d;e4p;e4d;e5p;e6s;e4f;e5d;e6p],gca);set(h,'facealpha',0.1);hold on;rotate3d on;
h=copyobj(e7s,gca);set(h,'facealpha',0.4);view([-40,30]);grid on;axis tight;daspect([1,1,1]);
title({'1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s','','_{87}Fr _{88}Ra'},'FontSize',12);