Quantum Monte Carlo Jong Ho Choi University of Chicago 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

Quantum Monte Carlo (QMC) method is a numerical method to calculate energy of quantum system. Monte Carlo method is commonly used method to calculated an average of a variables in large dimensional space (e.g. a physical variable in a classical phase space). Metropolis-Hasting algorithm make sampling of a variable to follow specific probability distribution possible. In quantum mechanics, Monte Carlo process can be used, but the variable (energy) and the probability distribution depends on wavefunctions. Variational Monte Carlo (VMC) method is simpler method that a approximated trial wavefunctions are used for the Monte Carlo sampling. This method has a systematic error due to the wavefunctions. The more accurate method is Diffusion Monte Carlo (DMC) method where we sample energies from the exact ground state wave functions. QMC method can be used for complex system like transition metals. As an example, the transition energy of Cu atom and Cu+ ion result of Caffarel et. al. is presented and compared with other method: Hartree-Fock, Coupled-cluster, and Density functional theory. Application uses the Maple Quantum Chemistry Toolbox.

Monte Carlo method is a numeric method is effective way to calculate the variables in a space of large dimensions. The method is based on generating a large number of random samples, and then using statistical analysis to estimate the behavior or outcome of interest. The Monte Carlo method is particularly useful for systems that are too complex to model analytically or have too many variables to be solved directly. In statistical mechanics, the ensemble average of a variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYnLUYjNiUtSSNtaUdGJDYmUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGN0Y9LyUlb3BlbkdRKSZsYW5nbGU7RicvJSZjbG9zZUdRKSZyYW5nbGU7RictSSNtb0dGJDYuUSFGJ0Y3Rj0vJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZZRjdGPQ== is calculated from integrating the product of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTkYyRjw=and the probability density 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 in 6N-dimensional phase space. 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 This high-dimensional integral is impossible to do, so numerical methods are often used. Monte Carlo method is one way. If we can sample LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGNQ== to have probability distribution 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, we can estimate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiQtSSNtaUdGJDYmUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnRj0vJSVvcGVuR1EpJmxhbmdsZTtGJy8lJmNsb3NlR1EpJnJhbmdsZTtGJy1JI21vR0YkNi1RIn5GJ0Y9LyUmZmVuY2VHRjkvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWUY9. 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 So how can we sample the variable to follow a particular distribution? Metropolis\342\200\223Hastings algorithm makes this possible by focusing on the relative difference in probability, not the absolute probability density. Assume that i and f are the points in the 6N-dimensional phase space in NVT ensemble. Although the partition function (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) is needed to calculate the exact probability density, but the relative probability (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,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) is easy to know. In Metropolis\342\200\223Hastings algorithm, accept/deny process for a point moving randomly in the phase space makes sampling points with the relative probability possible. Let i is the present state, and the f is the possible following state. The acceptance probability 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 is defined as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEkYWNjRidGMkY1RjhGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRi82JlEiZkYnRjJGNUY4LUkjbW9HRiQ2LlEiLEYnRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82JlEiaUYnRjJGNUY4RjVGUkY1RlItRk82LlEifkYnRjVGUkZUL0ZXRjdGWEZaRmZuRmhuRmpuRlxvL0Zgb0Zeby1GTzYuUSI9RidGNUZSRlRGaG9GWEZaRmZuRmhuRmpuL0Zdb1EsMC4yNzc3Nzc4ZW1GJy9GYG9GXnBGZW8tRi82JlEkbWluRicvRjNGN0Y1RlItRkc2Jy1GIzYoLUkjbW5HRiQ2JVEiMUYnRjVGUkZOLUkmbWZyYWNHRiQ2KC1GIzYnLUZPNi5RIUYnRjVGUkZURmhvRlhGWkZmbkZobkZqbkZcb0Zpby1GIzYmLUYvNiZRJGV4cEYnRmNwRjVGUi1GRzYnLUYjNiYtRk82LlEqJnVtaW51czA7RidGNUZSRlRGaG9GWEZaRmZuRmhuRmpuL0Zdb1EsMC4yMjIyMjIyZW1GJy9GYG9GYXItRiw2Ji1GLzYmUSgmYmV0YTtFRidGMkY1RjhGS0ZARkNGNUZSRjVGUi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y1RlJGYXFGNUZSLUYjNidGZnEtRkc2Jy1GIzYmRl1yLUYsNiYtRi82JlEoJiM5NDY7RUYnRjJGNUY4LUYjNiZGYm9GMkY1RjhGQEZDRjVGUkY1RlJGaHJGW3NGMkY1RjgvJS5saW5ldGhpY2tuZXNzR0ZbcS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZfdC8lKWJldmVsbGVkR0Y3RmFxRjVGUkY1RlJGaHJGW3MtRk82LlEiLkYnRjVGUkZURmhvRlhGWkZmbkZobkZqbkZcb0Zpb0Y1RlI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg== If accepted, state f becomes the new state, and if denied, state i is sampled once again. If this process is repeated long enough, each point in space will be sampled by a relative probability. Same sampling process can be applied for quantum systems. The energy can be written as E = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUkmbWZyYWNHRiQ2KC1GIzYtLUkjbW9HRiQ2LlErJkludGVncmFsO0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSy1JJW1zdXBHRiQ2JS1JI21pR0YkNiZRJiZQaGk7RicvJSdpdGFsaWNHRjZGNEY3LUYjNiUtRjE2LlEpJmxvd2FzdDtGJ0Y0RjdGOkY8L0Y/RjZGQS9GREY2RkVGR0ZJRkxGNEY3LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GMTYuUSFGJ0Y0RjdGOkY8RmZuRkFGZ25GRUZHRklGTC1GUjYoUSJIRicvJSVib2xkR0ZAL0ZWRkBGNC9GOFEsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictRlI2JlEnJiM5MzQ7RidGY29GNC9GOFEnaXRhbGljRictRjE2LlEifkYnRjRGN0Y6RjxGZm5GQUZnbkZFRkdGSUZMLUYxNi5RMCZEaWZmZXJlbnRpYWxEO0YnRjRGNy9GO1EmdW5zZXRGJy9GPUZlcC9GP0ZlcC9GQkZlcC9GREZlcC9GRkZlcC9GSEZlcEZJRkwtRlI2KFEickYnRmFvRmNvRjRGZG9GZm9GY29GNEZccC1GIzYrRjAtRk82JS1GUjYmRltwRlVGNEY3LUYjNiZGWUZjb0Y0RlxwRmhuRmNxRl5wRmFwRlxxRmNvRjRGXHAvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxyLyUpYmV2ZWxsZWRHRjYtRjE2LlEiPUYnRjRGN0Y6RjxGZm5GQUZnbkZFRkcvRkpRLDAuMjc3Nzc3OGVtRicvRk1GZXItRiw2KC1GIzYrRjAtRk82JS1GIzYlLUkobWZlbmNlZEdGJDYoLUYjNiYtRlI2J0ZURlVGNC8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RidGNy1GYHM2Ji1GIzYlLUZSNidGXnFGY29GNEZmc0ZccEY0RjdGNEZmc0Y3RjRGN0Y0RmZzRjcvJSVvcGVuR1EifGdyRicvJSZjbG9zZUdGYXRGNEY3LUYjNiUtSSNtbkdGJDYmUSIyRidGNEZmc0Y3RjRGN0ZobkZecC1JJW1zdWJHRiQ2Ji1GUjYmUSJFRidGY29GNEZccC1GIzYmLUZSNiZRJGxvY0YnRmNvRjRGXHBGY29GNEZccC8lL3N1YnNjcmlwdHNoaWZ0R0Zqbi9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUZgczYlLUYjNiVGXHFGNEY3RjRGN0ZhcEZccUY0RjctRiM2KUYwLUZPNiUtRiM2JS1GYHM2Jy1GIzYmRmNxLUZgczYlLUYjNiUtRlI2JkZecUZjb0Y0RlxwRjRGN0Y0RjdGNEY3RjRGN0ZfdEZidEY0RjctRiM2Ji1GZ3Q2JUZpdEY0RjdGY29GNEZccEZobkZecEZhcEZccUY0RjdGZ3FGanFGXXJGX3JGXnAtRjE2LlEiO0YnRjRGN0Y6L0Y9RkBGZm5GQUZnbkZFRkdGSUZmckZecEZecEZecEZqdC1GYHM2JS1GIzYmRlxxRmNvRjRGXHBGNEY3Rl5wRmFyRl5wLUYsNigtRiM2Jy1GUjYmUShIJiM5MzQ7RidGY29GNEZccEZmd0Zjb0Y0RlxwLUYjNihGW28tRiM2JkZRRmp1RjRGN0Zbb0Zjb0Y0RlxwRmdxRmpxRl1yRl9yRl5wRmNvRjRGXHA= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY5LUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUSsmSW50ZWdyYWw7RidGMkY8Rj5GQC9GQ0YxRkQvRkdGMUZIRkovRk1RJjAuMGVtRicvRlBGVy1JJW1zdWJHRiQ2JkYrLUYjNiYtRiw2JlEkbG9jRidGL0YyRjVGL0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2KFEickYnLyUlYm9sZEdGMUYvRjIvRjZRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnRjJGPEYyRjwtRiw2JlEiUEYnRi9GMkY1RmFvLUY5Ni5RIn5GJ0YyRjxGPkZARkJGREZGRkhGSkZWRlgtRjk2LlEwJkRpZmZlcmVudGlhbEQ7RidGMkY8L0Y/USZ1bnNldEYnL0ZBRmpwL0ZDRmpwL0ZFRmpwL0ZHRmpwL0ZJRmpwL0ZLRmpwRlZGWEZmby1GOTYwRmVwRmlvRjIvRjZGX3BGXXBGPkZARkJGREZGRkhGSkZWRlgtRjk2LlEiO0YnRjJGPEY+L0ZBRjFGQkZERkZGSEZKRlZGT0ZjcEZjcEZjcEZgcEZhb0ZjcEY4RmNwLUkmbWZyYWNHRiQ2KC1GIzYmLUklbXN1cEdGJDYlLUYjNiUtRmJvNictRiM2Ji1GLDYmUSYmUGhpO0YnL0YwRjRGMkY8LUZibzYlLUYjNiUtRiw2JkZob0YvRjJGNUYyRjxGMkY8RjJGPEYyRjwvJSVvcGVuR1EifGdyRicvJSZjbG9zZUdGYnNGMkY8LUYjNiUtSSNtbkdGJDYlUSIyRidGMkY8RjJGPC8lMXN1cGVyc2NyaXB0c2hpZnRHRl1vLUY5Ni5RIUYnRjJGPEY+RkBGQkZERkZGSEZKRlZGWEYyRjwtRiM2KkZRRl1yRmNwRmZwRmZvRi9GMkY1LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZndC8lKWJldmVsbGVkR0Y0RjJGPA== As the energy is multi-dimensional integral of a variable 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multiplied by the probability distribution 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, the energy can be calculated by the Monte Carlo average by using the Metropolis algorithm. 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 To do this, one need to sample the local energy with probability distribution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUZJNidRInJGJy8lJWJvbGRHRk5GTC9GM1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGMkYyRitGMg==. We can simply use an approximated wave functions (variational quantum Monte Carlo), but also we can sample from the exact ground state wave function by Diffusion Quantum Monte Carlo method.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv There are two most important Quantum Monte Carlo methods: Variational quantum Monte Carlo (VMD) and Diffusion quantum Monte Carlo (DMC). The VMC is more efficient and simpler than the DMC, but also less accurate.

As told in previous section, the VMC energy can be written as 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 Here, the trial function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEnJiM5MzQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYlUSJURicvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRi82KFEickYnLyUlYm9sZEdGPEY7LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GNlEsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGNUZPRjVGNQ==is the approximated wavefunction. The most commonly used function is Jastrow-Slater form, a product of one or several Slater determinants 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 and a Jastrow correlation function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIlVGJ0YyRjVGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw==. 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 The Slater determinants are usually orbital calculated by Hartree-Fock or DFT, and the U of the Jastrow function depend on the electron-nucleus and electron-electron distance. The VMC method has two type of errors: a statistical uncertainty due to the finite number of sampling (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), and a systematic error due to approximated wavefunction.

The DMC method start with the time-dependent Schr\303\266dinger equation with imaginary time \317\204=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFLUkjbW5HRiQ2JVEiaUYnRi9GMkYvRjI=t. 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 Let the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmJnBzaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2JC1GLDYlUScmIzk2NDtGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRidGP0YvRjItSSNtb0dGJDYuUSFGJy8lK2V4ZWN1dGFibGVHRj5GPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRldGPw==is the solution of this equation and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiYtSSVtc3ViR0YkNiUtSSNtaUdGJDYnUSkmdmFycGhpO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUY0NidRImlGJ0Y3RjpGPUZAL0ZBUSdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEhRidGOkZILyUmZmVuY2VHRjwvJSpzZXBhcmF0b3JHRjwvJSlzdHJldGNoeUdGPC8lKnN5bW1ldHJpY0dGPC8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y8LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGW29GN0ZARkgvJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnRjdGQA== are eigenfunctions of the Hamiltonian. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg== For the long time limit, the higher energy of the state, the faster the contribution to the wavefunction decays so that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmJnBzaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2JC1GLDYlUSYmdGF1O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Ri9GMkY/ converges to the exact ground state 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. We introduced Green's function 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. Where 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 is the reference ground state energy. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmJnBzaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2JC1GLDYlUSJ0RidGL0YyL0YzUSdub3JtYWxGJ0YvRjJGPQ== can be expressed as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JlEmJnBzaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYnLUklbXN1YkdGJDYmLUYsNihRIlJGJy8lJWJvbGRHRjFGL0YyL0Y2USxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GIzYmLUYsNiZRImZGJ0YvRjJGNUYvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSSNtb0dGJDYuUSI7RidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy1GLDYmUSJ0RidGL0YyRjVGMkZZRi9GMkY1LUZWNi5RIj1GJ0YyRllGZW4vRmhuRjRGaW5GW29GXW9GX29GYW8vRmRvRmhvRmZvLUZWNi5RKyZJbnRlZ3JhbDtGJ0YyRllGZW5GX3AvRmpuRjFGW28vRl5vRjFGX29GYW9GY28vRmdvRmVvLUYsNiZRIkdGJ0YvRjJGNS1GOTYlLUYjNistRj42JkZARkxGT0ZSLUZWNi5RIn5GJ0YyRllGZW5GX3BGaW5GW29GXW9GX29GYW9GY29GZnAtRlY2LlEiLEYnRjJGWUZlbkZnbkZpbkZbb0Zdb0Zfb0Zhb0Zjby9GZ29RLDAuMzMzMzMzM2VtRictRj42JkZALUYsNihRImlGJ0ZDRi9GMkZFRkdGT0ZSRmBxRlVGaW9GMkZZRjJGWUZgcS1GIzYmLUY+NiYtRiw2JkYuL0YwRjRGMkZZRmdwRk9GUi1GOTYmLUYjNiUtRj42JkZALUYjNihGanFGQ0YvRjJGRUZHRk9GUkYyRllGL0YyRjVGMkZZLUZWNi5RMCZEaWZmZXJlbnRpYWxEO0YnRjJGWS9GZm5RJnVuc2V0RicvRmhuRmBzL0ZqbkZgcy9GXG9GYHMvRl5vRmBzL0Zgb0Zgcy9GYm9GYHNGY29GZnAtRj42JkZALUYjNiYtRiw2JkZcckYvRjJGNUYvRjJGNUZPRlJGYHFGMkZZ 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is guide wavefunction which approximates the ground state wavefunction. This function can be the same Jastrow-Slater function as VMC, but the role of the function is not the same. Let 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, and the equation can be reorganized as 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 As addressed before, in long enough time limits, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmJnBzaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2Ji1GLDYlUSJSRidGL0YyLUkjbW9HRiQ2LVEiO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy1GLDYlUSJ0RidGL0YyRkFGL0YyRkE= converges to the ground state wavefunction, so 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. For short enough timestep 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, 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 be expressed as 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 From the definition of 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with ignoring higher order term in LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEpJkRlbHRhO3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, the Green's function is proportional to following expression. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg== Generally, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiZRIkdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RInxpckYnRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0ZDLyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRkMvJShsYXJnZW9wR0ZDLyUubW92YWJsZWxpbWl0c0dGQy8lJ2FjY2VudEdGQy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlIvRk9GNy1GPDYuUSFGJ0Y1Rj8vRkJGNy9GRUY3RkYvRklGNy9GS0Y3L0ZNRjdGVUZQRlNGPw== is not a normalized probability density, so a stochastic process from this equation is not trivial. Nevertheless, we can write LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiZRIkdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RInxpckYnRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0ZDLyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRkMvJShsYXJnZW9wR0ZDLyUubW92YWJsZWxpbWl0c0dGQy8lJ2FjY2VudEdGQy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlIvRk9GNy1GPDYuUSFGJ0Y1Rj8vRkJGNy9GRUY3RkYvRklGNy9GS0Y3L0ZNRjdGVUZQRlNGPw== as a product of a stochastic part P and a weight part W. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiZRIkdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RInxpckYnRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0ZDLyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRkMvJShsYXJnZW9wR0ZDLyUubW92YWJsZWxpbWl0c0dGQy8lJ2FjY2VudEdGQy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlIvRk9GNy1JKG1mZW5jZWRHRiQ2JS1GIzYqLUklbXN1YkdGJDYlLUYvNiZRIlJGJ0YyRjVGOC1GLzYmUSJmRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GPDYuUSIsRidGNUY/RkEvRkVGNC9GR0ZDRkhGSkZMRk5GUC9GVFEsMC4zMzMzMzMzZW1GJy1GZm42JUZobi1GLzYmUSJpRidGMkY1RjhGXm8tRjw2LlEiO0YnRjVGP0ZBRmRvRmVvRkhGSkZMRk5GUC9GVFEsMC4yNzc3Nzc4ZW1GJy1GIzYmLUY8Ni5RIUYnRjVGPy9GQkY3L0ZFRjdGRi9GSUY3L0ZLRjcvRk1GN0ZVRlBGUy1GLzYmUSgmRGVsdGE7RicvRjNGN0Y1Rj9GNUY/LUYvNiZRInRGJ0YyRjVGOEY1Rj9GNUY/LUY8Ni5RIj1GJ0Y1Rj9GZ3BGaHBGRkZpcEZqcEZbcUZVL0ZRRmFwRmBwLUY8Ni5RIn5GJ0Y1Rj9GZ3BGaHBGRkZpcEZqcEZbcUZVRlBGUy1GLzYmUSJQRidGMkY1RjgtRlc2JS1GIzYnLUZmbjYmRmhuLUYjNiZGW29GMkY1RjhGXm8vSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GPDYuRmNvRjVGP0ZncEZkb0ZGRmlwRmpwRltxRlVGUEZmby1GZm42JkZobi1GIzYmRmpvRjJGNUY4Rl5vRmVyRjVGP0Y1Rj8tRi82JlEiV0YnRjJGNUY4LUZXNiUtRiM2Jy1GZm42JkZobkZbb0Zeb0ZlckZoci1GZm42JkZobkZqb0Zeb0ZlckY1Rj9GNUY/RjVGPw== 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Figure 1 A random walk process visualized for a Helium atom. The walker consists of the two electron positions. This image is from Ref [2] We can estimate the ground state energy from weighted random work with metropolis algorithm, w. First, we start from position LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjVGQQ== with weight 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. Sample the second position LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjVGQQ== with acceptance probability 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. The acceptance probability is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEkYWNjRidGMkY1RjhGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2Ji1GLzYmUSJSRidGMkY1RjgtRiM2Ji1GLzYmUSJmRidGMkY1RjhGMkY1RjhGQEZDLUkjbW9HRiQ2LlEiLEYnRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JkZNLUYjNiYtRi82JlEiaUYnRjJGNUY4RjJGNUY4RkBGQ0Y1RllGNUZZLUZWNi5RIn5GJ0Y1RllGZW4vRmhuRjdGaW5GW29GXW9GX29GYW9GY28vRmdvRmVvLUZWNi5RIj1GJ0Y1RllGZW5GY3BGaW5GW29GXW9GX29GYW8vRmRvUSwwLjI3Nzc3NzhlbUYnL0Znb0ZpcEZgcC1GLzYmUSRtaW5GJy9GM0Y3RjVGWS1GRzYnLUYjNigtSSNtbkdGJDYlUSIxRidGNUZZRlUtSSZtZnJhY0dGJDYoLUYjNihGLi1GRzYlLUYjNidGaW9GVUZLRjVGWUY1RlktRiw2Ji1GLzYmUScmIzk2ODtGJ0ZecUY1RlktRiM2Ji1GLzYmUSJHRidGMkY1RjhGMkY1RjhGQEZDLUklbXN1cEdGJDYlLUZHNiYtRiM2JkZLLUZWNi5RIUYnRjVGWUZlbkZjcEZpbkZbb0Zdb0Zfb0Zhb0Zjb0ZkcEY1RllGMkY1RjgtRiM2JS1GZHE2JVEiMkYnRjVGWUY1RlkvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZCRjVGWS1GIzYpRi5GRkZgci1GW3M2JS1GRzYmLUYjNiZGaW9GYXNGNUZZRjJGNUY4RmRzRmlzRjJGNUY4LyUubGluZXRoaWNrbmVzc0dGZnEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ3QvJSliZXZlbGxlZEdGN0Zhc0Y1RllGNUZZLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjVGWQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg== Give the second weight (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). Repeat this steps and it will reach to the stationary state. To improve sampling quality, we use LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEid0YnRjJGNUY4RjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y1L0Y5USdub3JtYWxGJw== independent walkers. From the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn steeps after the equilibration walk, the ground state energy LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIwRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdGQC9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjVGQQ== can be obtained by followings. 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 As independent walkers can be used for the process, DMC can be optimized easily with massively multi-processor computing. The Monte Carlo steps of each walker can be run independently and the trajectories are not needed to be shared. Note that the probability density which this process is sampling is 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv

As shown above the DMC sample the energy with probability that is proportional to 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. This function works only when the sign of 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EpJnZhcnBoaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21uR0YkNiZRIjBGJ0Y1RjgvRjxRJ25vcm1hbEYnRkQvJS9zdWJzY3JpcHRzaGlmdEdGQy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYvNidRIlJGJ0YyRjVGOEY7RkRGNUY4RkRGRA== are same. Since electron is fermion, the electronic wavefunction can be both positive and negative, and the sign of the function changed at the nodal surface. Therefore, if 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EpJnZhcnBoaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21uR0YkNiZRIjBGJ0Y1RjgvRjxRJ25vcm1hbEYnRkQvJS9zdWJzY3JpcHRzaGlmdEdGQy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYvNidRIlJGJ0YyRjVGOEY7RkRGNUY4RkRGRA==have different node position, distribution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSgmaW5maW47RicvRjNRJmZhbHNlRicvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1JKG1mZW5jZWRHRiQ2Jy1GIzYkLUYvNidRIlJGJ0YyLyUrZXhlY3V0YWJsZUdGPC8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RidGNUY9RjJGTUZPRjVGPQ== cannot be treated as probability. To solve this problem, Fixed-node DMC (FN-DMC) method is presented. This methods assume that the exact wavefunction (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EpJnZhcnBoaTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21uR0YkNiZRIjBGJ0Y1RjgvRjxRJ25vcm1hbEYnRkQvJS9zdWJzY3JpcHRzaGlmdEdGQy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYvNidRIlJGJ0YyRjVGOEY7RkRGNUY4RkRGRA==) have the same node with the guide function (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEmJnBzaTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYvNiVRIkdGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSShtZmVuY2VkR0YkNiYtRiM2JC1GLzYmUSJSRidGOy8lK2V4ZWN1dGFibGVHRjRGPUY1RjtGTUY9LUYsNiUtRi82J1EpJnZhcnBoaTtGJ0Y7Rk0vJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRj0tRiM2JC1JI21uR0YkNiZGQUZNRlRGNUY1Rj9GNQ==). The error of this assumption depends on how accurate the position of nodes in the guide function are. So, it is important to use a more accurate guide function to reduce this error.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv

The calculation of electronic structure is often difficult when transition metals are involved. [2] Caffarel et al. presented the effect of electron correlation in the cooper atom using all-electron fixed-node diffusion Monte Carlo method. [6] A "walker" is defined as the set of position of the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn electrons, 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. About 100 walkers were used for the FN-DMC. Each walker is propagated as a Langevin-type move. 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 Where the drift vector 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NTE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0 is a 3N-dimensional Gaussian random vector. To sample the space effectively, Metropolis algorithm is used and the acceptance of each move is defined as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYvRjI=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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEiLkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYvRjI= Where 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 The weight is given by 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 Where 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 In the long time limit, the probability distribution of walkers are proportional to 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. A Choice of guide wavefunction LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEmJnBzaTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYvNiVRIkdGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSShtZmVuY2VkR0YkNiUtRiM2JC1GLzYlUSJSRidGO0Y9RjVGO0Y9RjU=is important in FN-DMC. The standard form is 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 Where 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 SCF determinant from one-particle orbitals and 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 is Jastrow term taking into account n-body effect. The standard minimal form was chosen for the 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 Fixed-node DMC method entails four types of possible errors. The most fundamental error is "fixed-node" error which is due to the approximation that the solution of the Schr\303\266dinger equation and the guide wavefunction will have same node. From the previous researches this error is generally small. [6] The second error is short time error, which appears when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFLUYjNiQtSSNtaUdGJDYmUSgmRGVsdGE7RicvJSdpdGFsaWNHRjFGL0YyRjItRks2JlEidEYnL0ZPUSV0cnVlRidGLy9GM1EnaXRhbGljRidGMg== is not small enough. This error can be eliminated by conducting same calculation with different LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFLUYjNiQtSSNtaUdGJDYmUSgmRGVsdGE7RicvJSdpdGFsaWNHRjFGL0YyRjItRks2JlEidEYnL0ZPUSV0cnVlRidGLy9GM1EnaXRhbGljRidGMg== and extrapolate the result to the zero LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFLUYjNiQtSSNtaUdGJDYmUSgmRGVsdGE7RicvJSdpdGFsaWNHRjFGL0YyRjItRks2JlEidEYnL0ZPUSV0cnVlRidGLy9GM1EnaXRhbGljRidGMg== limit. The third error is population control error. Sometimes, the results of DMC depend on the number of walkers although the number of walkers supposed to affect only the efficiency of the sample, not the results. To consider this error, the calculation should be done with different number of walkers. The last error is the statistical uncertainty that necessarily accompanies the Monte Carlo method, which is inversely proportional to the number of Monte Carlo step. To reduce the error, large enough Monte Carlo steps should be done. First, the energies of three lowest electronic states (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 Cu atom and the ground state (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) of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEjQ3VGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiUtSSNtb0dGJDYtUSIrRidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk4vRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=ion from Hartree-Fock, CCSD(T), and FN-DMC are compared in the Table 1. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRI0hGRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSJ+RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlZGPUZA LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2Ji1GLDYmUSVDQ1NERidGL0YyRjUtRjk2JC1GIzYlLUYsNiVRIlRGJ0YvRjUvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRidGSkZHRkpGMkZKRkdGSg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRI0ZORidGL0YyLUkjbW9HRiQ2LVEoJm1pbnVzO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZULUYsNiVRJERNQ0YnRi9GMi8lK2V4ZWN1dGFibGVHRkVGQUZBRlpGQQ== 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSoxNjM4LjcyNzZGJ0YvLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSoxNjQwLjEyMDRGJ0YvLyUrZXhlY3V0YWJsZUdGNEYv 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 All-electron total energies and correlation energies of the low-lying states of copper and its cation using HF, CCSD(T), and FN-DMC. Energies in Hartree. Reprint Table II of Ref [6] The result shows that both CCSD(T) and FN-DMC energies are lower than the HF energies, so the correlation energy is restored for both methods. In addition, the FN-DMC energy is lower than the CCSD(T) energy. Therefore, the authors concluded that DMC is a better way to capture the correlation energy.[6]. Many people think that estimating the differences between energy levels is more important than estimating the energy itself. Table 2 shows the transition energies from HF, CCSD(T), and FN-DMC methods. The Hartree-Fock reproduced the tradition energy from 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 to 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 badly compared to the results from other methods. This is because the occupation of 3d shell changes during the transition, so the electronic correlation plays a major role in the process. [6] For other transition, where the occupancy of 3d shell does not change, HF results is much better, but still deviate from the other results. The FN-DMC results are overlapping the CCSD(T) results within the statistical errors (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). 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMjQ3NzlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMjk2NzNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEmMzAyODhGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEpJnBsdXNtbjtGJ0YvRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSi1GLDYlUSUxNTUyRidGL0YyLyUrZXhlY3V0YWJsZUdGO0Yy LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JlEjQ3VGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIihGJ0YyRjUvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZNLUkubW11bHRpc2NyaXB0c0dGJDYoLUYjNictRlE2KC1GIzYkLUYsNiZRIlNGJ0YvRjJGNUY1LUklbm9uZUdGJEYnRmZuLUksbXByZXNjcmlwdHNHRiRGJ0Zmbi1GIzYkLUkjbW5HRiQ2JVEiMkYnRjJGNUY1LUY5Ni5RIn5GJ0YyRjUvRj1GMUY/L0ZCRjFGQ0ZFRkdGSS9GTFEmMC4wZW1GJy9GT0Zmby1GOTYuUSIpRidGMkY1RjxGP0ZBRkNGRUZHRklGS0ZOLUY5Ni5RKiZJbXBsaWVzO0YnRjJGNUZjb0Y/RkFGQ0ZFRkdGSS9GTFEsMC4yNzc3Nzc4ZW1GJy9GT0ZfcEY1RmZuRmZuRmhuRmZuLUYjNiQtRjk2LlEhRicvJStleGVjdXRhYmxlR0YxRjVGY29GP0Zkb0ZDRkVGR0ZJRmVvRmdvRjVGY3AtRiM2JS1JJW1zdXBHRiQ2JUYrLUYjNiQtRjk2L1EiK0YnRmZwRjJGNUZjb0Y/RmRvRkNGRUZHRkkvRkxRLDAuMjIyMjIyMmVtRicvRk9GY3FGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiUtRiM2JkZjcC1GIzYlRmNwLUZRNihGV0ZmbkZmbkZobkZmbi1GIzYkLUZdbzYlUSIxRidGMkY1RjVGNUZjcEY1RjJGNUY1RmNwRmZwRjU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmNTE4MThGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmNjA3MjlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEmNjAxMzZGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEpJnBsdXNtbjtGJ0YvRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSi1GLDYlUSUxNzE0RidGL0YyLyUrZXhlY3V0YWJsZUdGO0Yy Transition energies calculated from HF, CCSD(T), and FN-DMC. Energies in 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 Reprint Table III of Ref [6] To describe the electron transition completely, the relativistic contributions needed to be evaluated. The relativistic contribution is calculated at the Dirac-Fock level. Table 3 shows the sum of the relativistic contribution (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) and non-relativistic transition energies (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEpJkRlbHRhO0VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlElQ0NTREYnRi9GMkY1LUY5NiQtRiM2JC1GLDYlUSJURidGL0Y1L0Y2USdub3JtYWxGJ0ZHRkdGMkZHRkc= and 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) and the experimental transition energies (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). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1GLzYkUSIyRidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkQvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZJRjI= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMTEyMDNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMTExMjNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1GLzYkUSIyRidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZIRjI= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMzA1MzVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMzA1MjlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEmMzExMjJGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlElJnBtO0YnRi9GMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZKLUYsNiVRJTE1NTJGJ0YvRjIvJStleGVjdXRhYmxlR0Y7RjI= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1GLzYkUSIyRidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkQvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZJRjI= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMzA3ODRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmMzA3MTFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEmMzEzMDRGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlElJnBtO0YnRi9GMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZKLUYsNiVRJTE1NTJGJ0YvRjIvJStleGVjdXRhYmxlR0Y7RjI= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRi8= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmNjIzMTdGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEmNjE4NzVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEmNjEzMDRGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlElJnBtO0YnRi9GMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZKLUYsNiVRJTE3MTRGJ0YvRjIvJStleGVjdXRhYmxlR0Y7RjI= The experimental transition energies from Ref [7] and the calculated transition energies with including the relativistic effects. Energies in 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 Reprint Table V of Ref [6] 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Figure 2 Pictograph represent the energy level of 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 (top) and 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 (bottom). FIG 1 and 2 of Ref [6] LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv The results shows that the relativistic contribution is not negligible in this system. The both experiment and CCSD results are in the error range of the FN-DMC results. Let's compare the ionization energy to a most common DFT calculation. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVErSUVfaGFydHJlZUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YrLUYsNi1RKiZjb2xvbmVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZTRistSShtZmVuY2VkR0YkNiQtRiM2KC1GRzYlUSZkYXRhMkYnRkpGTS1GVjYmLUYjNiQtRkc2JVEmZV90b3RGJ0ZKRk1GL0YvLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUYsNi1RKCZtaW51cztGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjIyMjIyMmVtRicvRkVGaG8tRkc2JVEmZGF0YTFGJ0ZKRk1GZ25GL0YvLUYsNi1RIjtGJ0YvRjIvRjZGTEY3RjlGO0Y9Rj9GQUZULyUrZXhlY3V0YWJsZUdGNEYv

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStJRV9oYXJ0cmVlR0YoJCIsOztYPiFIISM2NyNGLg==

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZJRV9jbUdGKCQiMF1DaVNMIXBqISM1NyNGLg==

The IE from B3LYP/cc-pVTZ is about 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 , compared to the CCSD(T) and FN-DMC results (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 ) the ionization energy is overestimated unlike the underestimating HF result (~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). This results shows that the for transition metal like Cu, higher level of calculation is required, and FN-DMC can be one option.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFRi9GMg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv

The quantum Monte Carlo method is a method of calculating the energy of a complex system numerically. This method is classified into an easy and simple but error-embedded VMC method, and a DMC method that requires more resources but enables sampling from exact grand state. In order for the DMC method to sample the ground state, it must always use a guide function with the same sign as the ground state wave function. It's not always possible, so a fixed node assumption is used. The VMC method can be used in systems that are complex to calculate with conventional quantum calculations, such as transition metals. The biggest advantage of this method is that it is easy to optimize for multi-processor computers by using multiple independent workers. Considering the recent development of multi-core CPU and GPGPU clusters, active use of QMC is expected.

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv