<?xml version="1.0" encoding="us-ascii"?>
<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2021-02-23T20:44:43.9567381+00:00 -->
<!-- Version            : 5.0.1.571 -->
<!-- Package ID         : eec1b5ff80374e168dc3970275849a8b -->
<!-- Copyright (c) 2021 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="psn_IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities" name="IncreaseDecreaseInAccruedExpensesAndOtherCurrentLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_IncreaseDecreaseInBillingsInExcessOfCosts" name="IncreaseDecreaseInBillingsInExcessOfCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_IncreaseDecreaseInProvisionForContractLosses" name="IncreaseDecreaseInProvisionForContractLosses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_PaymentOfConvertibleNotesIssuanceTransactionCosts" name="PaymentOfConvertibleNotesIssuanceTransactionCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_PaymentsForPurchaseOfTreasuryStock" name="PaymentsForPurchaseOfTreasuryStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_PaymentsForTaxesPaidOnVestedStock" name="PaymentsForTaxesPaidOnVestedStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_DescriptionOfOperationsDisclosureAbstract" name="DescriptionOfOperationsDisclosureAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_TreasuryStockPolicyPolicyTextBlock" name="TreasuryStockPolicyPolicyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_RestrictedCashAndInvestmentsPolicyPolicyTextBlock" name="RestrictedCashAndInvestmentsPolicyPolicyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ConsolidationOfJointVentureAndVariableInterestEntityPolicyPolicyTextBlock" name="ConsolidationOfJointVentureAndVariableInterestEntityPolicyPolicyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_PolarisAlphaMember" name="PolarisAlphaMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_OGSystemsMember" name="OGSystemsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_QRCTechnologiesMember" name="QRCTechnologiesMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_BraxtonScienceTechnologyGroupMember" name="BraxtonScienceTechnologyGroupMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SummaryOfChangesInContractAssetsAndContractLiabilitiesTableTextBlock" name="SummaryOfChangesInContractAssetsAndContractLiabilitiesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_SummaryOfChangesInRevenuesTableTextBlock" name="SummaryOfChangesInRevenuesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfCashFlowInformationRelatedToLeasesTableTextBlock" name="ScheduleOfCashFlowInformationRelatedToLeasesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfBalanceSheetInformationRelatedToLeasesTableTextBlock" name="ScheduleOfBalanceSheetInformationRelatedToLeasesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfMaturitiesOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock" name="ScheduleOfMaturitiesOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LongTermGrowthUnitsMember" name="LongTermGrowthUnitsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ScheduleOfAmountPaidForCashSettledAwardsTableTextBlock" name="ScheduleOfAmountPaidForCashSettledAwardsTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfShareBasedCompensationRestrictedStockOutstandingActivityTableTextBlock" name="ScheduleOfShareBasedCompensationRestrictedStockOutstandingActivityTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfAggregateAmountDebtRepayableTableTextBlock" name="ScheduleOfAggregateAmountDebtRepayableTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfFinancialInformationOfConsolidatedJointVenturesTableTextBlock" name="ScheduleOfFinancialInformationOfConsolidatedJointVenturesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_SummaryOfFairValueAssetsAssociatedWithPensionPlanTableTextBlock" name="SummaryOfFairValueAssetsAssociatedWithPensionPlanTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ScheduleOfFairValueOfRedeemableCommonStockAssociatedEmployeeStockOwnershipPlanTableTextBlock" name="ScheduleOfFairValueOfRedeemableCommonStockAssociatedEmployeeStockOwnershipPlanTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_SummaryOfRevenuesAndPropertyAndEquipmentNetByGeographicAreaTableTextBlock" name="SummaryOfRevenuesAndPropertyAndEquipmentNetByGeographicAreaTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_PurchaseOfAdditionalSharesUponExerciseOfOptions" name="PurchaseOfAdditionalSharesUponExerciseOfOptions" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_UnderwritingDiscountPerShare" name="UnderwritingDiscountPerShare" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_FundsToDividendsThroughPublicOffering" name="FundsToDividendsThroughPublicOffering" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_RepaymentOnTermLoanThroughPublicOffering" name="RepaymentOnTermLoanThroughPublicOffering" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_DescriptionOfOperationsDisclosureLineItems" name="DescriptionOfOperationsDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_DescriptionOfOperationsDisclosureTable" name="DescriptionOfOperationsDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_CommonStockDividendRatio" name="CommonStockDividendRatio" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_DividendPayablePaymentDate" name="DividendPayablePaymentDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_SignificantAccountingPoliciesLineItems" name="SignificantAccountingPoliciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SignificantAccountingPoliciesTable" name="SignificantAccountingPoliciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_NetDeferredTaxAssetMember" name="NetDeferredTaxAssetMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_DeferredTaxAssetMember" name="DeferredTaxAssetMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_RevenuePerformanceObligationPaymentTerms" name="RevenuePerformanceObligationPaymentTerms" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_NumberOfCustomersRepresentingTenPercentOrMoreOfRevenues" name="NumberOfCustomersRepresentingTenPercentOrMoreOfRevenues" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_NumberOfCustomersRepresentingTenPercentOrMoreOfAccountsReceivable" name="NumberOfCustomersRepresentingTenPercentOrMoreOfAccountsReceivable" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_IndirectGeneralAndAdministrativeExpenseMember" name="IndirectGeneralAndAdministrativeExpenseMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_TermLoanMember" name="TermLoanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_BusinessAcquisitionProFormaNetIncomeLossIncludingPortionAttributableToNoncontrollingInterest" name="BusinessAcquisitionProFormaNetIncomeLossIncludingPortionAttributableToNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_CostPlusMember" name="CostPlusMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ContractWithCustomerAssetLiabilityNet" name="ContractWithCustomerAssetLiabilityNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_ChangeInContractWithCustomerAssetsAndLiabilitiesNet" name="ChangeInContractWithCustomerAssetsAndLiabilitiesNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_ChangeInContractWithCustomerAssets" name="ChangeInContractWithCustomerAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_ChangeInContractWithCustomerLiability" name="ChangeInContractWithCustomerLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_ContractWithCustomerAssetCumulativeCatchupAdjustmentToRevenueChangeInMeasureOfProgressPercent" name="ContractWithCustomerAssetCumulativeCatchupAdjustmentToRevenueChangeInMeasureOfProgressPercent" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ContractWithCustomerLiabilityCumulativeCatchupAdjustmentToRevenueChangeInMeasureOfProgressPercent" name="ContractWithCustomerLiabilityCumulativeCatchupAdjustmentToRevenueChangeInMeasureOfProgressPercent" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ContractWithCustomerAssetLiabilityCumulativeCatchupAdjustmentToRevenueChangeInMeasureOfProgressPercent" name="ContractWithCustomerAssetLiabilityCumulativeCatchupAdjustmentToRevenueChangeInMeasureOfProgressPercent" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ContractReceivableRetainageAssetsLiabilitiesNet" name="ContractReceivableRetainageAssetsLiabilitiesNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_ContractReceivableRetainageAssetLiabilitiesNetDueAfterOneYear" name="ContractReceivableRetainageAssetLiabilitiesNetDueAfterOneYear" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_ContractWithCustomerAdjustmentToRevenueImpactOfChangesInEstimatedClaimsOrIncentivesOverThreshold" name="ContractWithCustomerAdjustmentToRevenueImpactOfChangesInEstimatedClaimsOrIncentivesOverThreshold" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_BilledReceivablesCurrent" name="BilledReceivablesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_FederalSolutionSegmentMember" name="FederalSolutionSegmentMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_CriticalInfrastructureSegmentMember" name="CriticalInfrastructureSegmentMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_LesseeLeaseTermOfContract" name="LesseeLeaseTermOfContract" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LesseeLeaseOptionToExtend" name="LesseeLeaseOptionToExtend" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LesseeLeaseExistenceOfOptionToExtend" name="LesseeLeaseExistenceOfOptionToExtend" type="xbrli:booleanItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LesseeLeaseOptionToTerminate" name="LesseeLeaseOptionToTerminate" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LesseeLeaseExistenceOfOptionToTerminate" name="LesseeLeaseExistenceOfOptionToTerminate" type="xbrli:booleanItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_FinanceLeaseRightOfUseAssetsAccumulatedDepreciation" name="FinanceLeaseRightOfUseAssetsAccumulatedDepreciation" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_IndirectGeneralAndAdministrativeExpensesMember" name="IndirectGeneralAndAdministrativeExpensesMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_OperatingLeasesAbstract" name="OperatingLeasesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_LeaseLiabilitiesAbstract" name="LeaseLiabilitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_FinanceLeasesAbstract" name="FinanceLeasesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_FinanceLeasesOtherAssetsNoncurrent" name="FinanceLeasesOtherAssetsNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_WeightedAverageRemainingLeaseTermAbstract" name="WeightedAverageRemainingLeaseTermAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_WeightedAverageDiscountRateAbstract" name="WeightedAverageDiscountRateAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_OperatingLeaseNotYetCommencedExpense" name="OperatingLeaseNotYetCommencedExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromVestingOfAwards" name="EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromVestingOfAwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfYearsOverWhichSharePriceIncrease" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfYearsOverWhichSharePriceIncrease" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ServiceBasedRestrictedStockUnitsRSUMember" name="ServiceBasedRestrictedStockUnitsRSUMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ServiceAndPerformanceBasedRestrictedStockUnitsRSUMember" name="ServiceAndPerformanceBasedRestrictedStockUnitsRSUMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ShareBasedCompensationArrangementCommonStockRelatedToEmployeeStatutoryIncomeTaxWithholdingSharesRetired" name="ShareBasedCompensationArrangementCommonStockRelatedToEmployeeStatutoryIncomeTaxWithholdingSharesRetired" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_FiniteLivedIntangibleAssetsAmortizableAmount" name="FiniteLivedIntangibleAssetsAmortizableAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_ConstructionEquipmentMember" name="ConstructionEquipmentMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_NumberOfSaleLeasebackTransactionsConsummated" name="NumberOfSaleLeasebackTransactionsConsummated" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_NumberOfOfficeBuildingsSold" name="NumberOfOfficeBuildingsSold" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ProjectCostAccrualsCurrent" name="ProjectCostAccrualsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_LineOfCreditFacilityExtendedDate" name="LineOfCreditFacilityExtendedDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_AccruedExpensesAndOtherCurrentLiabilitiesMember" name="AccruedExpensesAndOtherCurrentLiabilitiesMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ConvertibleNoteHedgeAndWarrantTransactionMember" name="ConvertibleNoteHedgeAndWarrantTransactionMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SeriesASeniorNoteMember" name="SeriesASeniorNoteMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SeriesBSeniorNoteMember" name="SeriesBSeniorNoteMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SeriesCSeniorNoteMember" name="SeriesCSeniorNoteMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SeriesDSeniorNoteMember" name="SeriesDSeniorNoteMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_DebtInstrumentExerciseOfOptionByInitialPurchasersAggregatePrincipalAmount" name="DebtInstrumentExerciseOfOptionByInitialPurchasersAggregatePrincipalAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_ConvertibleNoteConvertedEachAmount" name="ConvertibleNoteConvertedEachAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_ConvertibleNotesConvertedEachIntoSharesOfCommonStock" name="ConvertibleNotesConvertedEachIntoSharesOfCommonStock" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_DebtInstrumentConvertibleBusinessPeriod" name="DebtInstrumentConvertibleBusinessPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_DebtInstrumentConvertibleConsecutiveBusinessDayPeriod" name="DebtInstrumentConvertibleConsecutiveBusinessDayPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_DebtInstrumentConvertiblePrincipalAmount" name="DebtInstrumentConvertiblePrincipalAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_DebtInstrumentConvertibleMeasurementPeriodPercentage" name="DebtInstrumentConvertibleMeasurementPeriodPercentage" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_PercentageOfPrincipalAmountToRedeemConvertibleSeniorNotes" name="PercentageOfPrincipalAmountToRedeemConvertibleSeniorNotes" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="psn_PercentageOfConvertibleSeniorNotesRepurchasedAtCash" name="PercentageOfConvertibleSeniorNotesRepurchasedAtCash" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="psn_DebtInstrumentConvertibleDebtLiability" name="DebtInstrumentConvertibleDebtLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_DebtInstrumentConvertibleNotesAdditionalPaidInCapital" name="DebtInstrumentConvertibleNotesAdditionalPaidInCapital" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_DebtInstrumentNumberOfSharesIssuableUponConversion" name="DebtInstrumentNumberOfSharesIssuableUponConversion" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_CostOfConvertibleNoteHedgeTransaction" name="CostOfConvertibleNoteHedgeTransaction" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_BondHedgeTerm" name="BondHedgeTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_NumberOfCommonStockAcquiredByOffsettingSaleWarrants" name="NumberOfCommonStockAcquiredByOffsettingSaleWarrants" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_PercentageOfBondHedgeAndWarrantTransactionsIncreasedConversionPrice" name="PercentageOfBondHedgeAndWarrantTransactionsIncreasedConversionPrice" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_NetCostOfPurchaseOfBondHedgesAndSaleOfWarrants" name="NetCostOfPurchaseOfBondHedgesAndSaleOfWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_OtherLiabilitiesNoncurrent1" name="OtherLiabilitiesNoncurrent1" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_PercentageOfNetOperatingLossCarryforwardsToOffsetOfTaxableIncomeDuringPeriod" name="PercentageOfNetOperatingLossCarryforwardsToOffsetOfTaxableIncomeDuringPeriod" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_AllowableBusinessInterestDeductionPercentageOfAdjustedTaxableIncome" name="AllowableBusinessInterestDeductionPercentageOfAdjustedTaxableIncome" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="psn_OperatingLossCarryforwardsTaxRefundClaimRelatedToAcquisition" name="OperatingLossCarryforwardsTaxRefundClaimRelatedToAcquisition" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_OperatingLossCarryforwardsDescription" name="OperatingLossCarryforwardsDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_IncomeTaxesLineItems" name="IncomeTaxesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_IncomeTaxesTable" name="IncomeTaxesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_CoronavirusAidReliefAndEconomicSecurityActMember" name="CoronavirusAidReliefAndEconomicSecurityActMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_StateAndLocalJurisdictionAndForeignMember" name="StateAndLocalJurisdictionAndForeignMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_EffectiveIncomeTaxRateReconciliationTransactionCosts" name="EffectiveIncomeTaxRateReconciliationTransactionCosts" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_AccountsReceivableBilledCurrent" name="AccountsReceivableBilledCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_DeferredTaxAssetsTaxDeferredExpenseProjectAndNonProjectReserves" name="DeferredTaxAssetsTaxDeferredExpenseProjectAndNonProjectReserves" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_DeferredTaxAssetsRevenueAndCostRecognition" name="DeferredTaxAssetsRevenueAndCostRecognition" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_DeferredTaxAssetsLeaseLiability" name="DeferredTaxAssetsLeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_DeferredTaxOperatingLossCarryforwardsExpirationDescription" name="DeferredTaxOperatingLossCarryforwardsExpirationDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_DeferredTaxOperatingLossCarryforwardsExpirationYear" name="DeferredTaxOperatingLossCarryforwardsExpirationYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_TaxCreditCarryForwardExpirationYear" name="TaxCreditCarryForwardExpirationYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LossContingencyNumberOfClaims" name="LossContingencyNumberOfClaims" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_LegalProceedingsLineItems" name="LegalProceedingsLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_LegalProceedingsTable" name="LegalProceedingsTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_CommonStockSharesOutstandingIncludingEmployeeStockOwnershipPlanShares" name="CommonStockSharesOutstandingIncludingEmployeeStockOwnershipPlanShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="psn_DirectCostsOfContractsAndIndirectGeneralAndAdministrativeExpenseMember" name="DirectCostsOfContractsAndIndirectGeneralAndAdministrativeExpenseMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_EmployeeStockOwnershipPlanESOPDividendsDeclaredPerShare" name="EmployeeStockOwnershipPlanESOPDividendsDeclaredPerShare" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_EmployeeStockOwnershipPlanESOPDividendsDeclaredToESOP" name="EmployeeStockOwnershipPlanESOPDividendsDeclaredToESOP" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_EmployeeStockOwnershipPlanESOPDividendsPaymentDate" name="EmployeeStockOwnershipPlanESOPDividendsPaymentDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_EmployeeStockOwnershipPlanESOPDividendDeclaredDate" name="EmployeeStockOwnershipPlanESOPDividendDeclaredDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_UnconsolidatedJointVenturesMember" name="UnconsolidatedJointVenturesMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_DistributionsFromContributionsToEquityMethodInvestment" name="DistributionsFromContributionsToEquityMethodInvestment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_DecreaseInOperatingIncomeAndNetIncomeNetOfTaxPercentage" name="DecreaseInOperatingIncomeAndNetIncomeNetOfTaxPercentage" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_DecreaseInOperatingIncome" name="DecreaseInOperatingIncome" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_DecreaseInNetIncomeNetOfTax" name="DecreaseInNetIncomeNetOfTax" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_DecreaseInEarningsPerShareDiluted" name="DecreaseInEarningsPerShareDiluted" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="psn_ReimbursableCostIncurred" name="ReimbursableCostIncurred" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="psn_RedeemableEquityCommonStockFairValue" name="RedeemableEquityCommonStockFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_RedeemableEquityCommonStockCarryingAmount" name="RedeemableEquityCommonStockCarryingAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesOfTreasuryStock" name="FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesOfTreasuryStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityContributionsOfTreasuryStockToESOP" name="FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityContributionsOfTreasuryStockToESOP" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySharePriceAdjustment" name="FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySharePriceAdjustment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_MobilitySolutionsMember" name="MobilitySolutionsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ReconciliationFromNetIncomeToAdjustedEBITDAAbstract" name="ReconciliationFromNetIncomeToAdjustedEBITDAAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_OtherNonoperatingIncomeMember" name="OtherNonoperatingIncomeMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_SpaceAndGeospatialSolutionsMember" name="SpaceAndGeospatialSolutionsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_CyberAndIntelligenceMember" name="CyberAndIntelligenceMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_MissileDefenseC5ISRMember" name="MissileDefenseC5ISRMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_EngineeredSystemsMember" name="EngineeredSystemsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_ConnectedCommunitiesMember" name="ConnectedCommunitiesMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_RevenueExcludingClaimSettlement" name="RevenueExcludingClaimSettlement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="psn_QuarterlyFinancialInformationLineItems" name="QuarterlyFinancialInformationLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="psn_QuarterlyFinancialInformationTable" name="QuarterlyFinancialInformationTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
</xsd:schema>
