Study of laser-driven multielectron dynamics of Ne atom using time-dependent optimised second-order many-body perturbation theory

Figures & data

Figure 1. The orbital sub-spacing for a spin-restricted case. The horizontal lines represent spatial orbitals, divided into frozen-core, dynamical core, and active. The active orbital space is further split into the hole and particle subspaces those occupied and virtual with respect to the Hartree-Fock determinant. The up and down arrows represent electrons.

Figure 2. HHG spectra of Ne exposed to a laser pulse with a wavelength of 800 nm and an intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$. Results of the TD-OMP2 method with different numbers of orbital configuration (m, n, o) and maximum angular momentum $L_{\max }=63$.

Figure 3. HHG spectra of Ne exposed to a laser pulse with a wavelength of 800 nm and an intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$. Results of the TD-OMP2 method obtained with different maximum angular momentum $L_{\max }$ with the orbital configuration $(1,0,13)$.

Figure 4. HHG spectra of Ne exposed to a laser pulse having a wavelength of 800 nm and varying intensities of $5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, $8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, and $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, obtained with the TD-OMP2 method with an orbital configuration $(1,0,13)$ and maximum angular momentum $L_{\max }=63$.

Figure 5. HHG spectra of Ne exposed to laser pulse with a wavelength of 800 nm and an intensity $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, Comparison of TD-OMP2 method with TD-CASSCF, and TDHF methods. Maximum angular momentum $L_{\max }=63$ and $(1,0,13)$ active space configuration for the correlation methods has been used.

Figure 6. HHG spectra of Ne exposed to a laser pulse with a wavelength of 1200 nm and an intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$. Results of the TDHF method obtained with different maximum angular momentum $L_{\max }$.

Figure 7. HHG spectra of Ne exposed to laser pulse with a wavelength of 1200 nm and varying intensities of $5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, $8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, and $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, obtained with TD-OMP2 method with the orbital configuration $(1,0,13)$ and the maximum angular momentum $L_{\max }=100$.

Figure 8. HHG spectra of Ne exposed to laser pulse with a wavelength of 1200 nm having intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, Comparison of TD-OMP2 method with TD-CASSCF, and TDHF method. Maximum angular momentum $L_{\max }=100$ and $(1,0,13)$ active space configuration for the correlation methods has been used.

Figure 9. Time evolution of the dipole moment of Ne irradiated by a laser pulse of a wavelength of (a) 800 nm, (b) 1200 nm at an intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, calculated with TDHF, TD-OMP2 and TD-CASSCF methods.

Figure 10. Time evolution of single ionisation probability of Ne irradiated by a laser pulse of a wavelength of (a) 800 nm, (b) 1200 nm at an intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, calculated with TDHF, TD-OMP2 and TD-CASSCF methods.

Figure 11. Time evolution of the dipole moment of Ne irradiated by a laser pulse of a wavelength of 800 nm at an intensity of $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, calculated with TDHF, TD-OMP2, TD-CC2 and TD-CASSCF methods.

Figure 12. HHG spectra of Ne irradiated by a laser pulse of a wavelength of 800 nm at an intensity of $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, calculated with TDHF, TD-OMP2, TD-CC2 and TD-CASSCF methods.

Figure 13. HHG spectra of Ne in the length gauge (LG) and velocity gauge (VG) irradiated by a laser pulse of a wavelength of 800 nm at an intensity of $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, calculated with (a) TD-OMP2, and (b) TD-CC2 method.

Table 1. Comparison of the CPU time (in second) spent for the evaluation of the $T_1$, ${\mathrm{\Lambda }}_1$, $T_2$, ${\mathrm{\Lambda }}_2$ equation, 1RDM, and 2RDM for TD-CC2 and TD-OMP2 methods.

TD-CC2						TD-OMP2
T${}_1$	${\mathrm{\Lambda }}_1$	T${}_2$	${\mathrm{\Lambda }}_2$	1RDM	2RDM	T${}_1$	${\mathrm{\Lambda }}_1$	T${}_2$	${\mathrm{\Lambda }}_2$	1RDM	2RDM
1.31	10.47	8.59	2.47	2.48	17.46	–	–	0.71	–	1.06	0.67

Note: CPU time spent for the simulation of Ne atom for 1000 time steps ($0\le t\le 0.1T$) of a real-time simulation ($I_0=5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and $\lambda =800\mathrm{nm}$), using an Intel(R) Xeon(R) Gold 6230 CPU with 40 processors having a clock speed of 2.10 GHz.

Table A1. Comparison of ground state energies of Be, and BH ($r_e=2.4\mathrm{bohr}$, within a $(6,6)$ active space configuration).

	Basis	Method	This work	Reference
Be	cc-pVDZ [73]	HF	−14.5723 376	−14.5723 376 [74]
		MP2	−14.5986 736	−14.5986 736 [74]
		OMP2	−14.5987 486	−14.5987 486 [74]
		CC2	−14.5988 233	−14.5988 233 [74]
		FCI	−14.6174 095	−14.6174 095 [74]
BH	DZP [75]	HF	−25.1247 420	−25.1247 42 [76]
		MP2	−25.1325 603
		OMP2	−25.1528 754
		CC2	−25.1325 787
		${}^{\mathrm{a}}$OCC2	−25.1528 704
		CASSCF	−25.1783 349	−25.1783 35 [76]

Note: The overlap, one-electron, and two-electron repulsion integrals over Gaussian basis functions are obtained from Gaussian09 program (Ref. [72]). Imaginary time relaxation is used to obtain the ground in the orthonormalised Gaussian basis. A convergence cutoff of ${10}^{-15}$ Hartree of energy difference is used in the subsequent time-step.${}^{\mathrm{a}}$It does not include hole-particle rotations.

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